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Search, Evaluate, and Read Evidence","\u002Fen\u002Facademic-writing\u002F02-reading-and-literature-matrix","en\u002Facademic-writing\u002F02-reading-and-literature-matrix",{"title":27,"path":28,"stem":29},"3. From Sources to Synthesis and Argument","\u002Fen\u002Facademic-writing\u002F03-arguments-outlines-and-paragraphs","en\u002Facademic-writing\u002F03-arguments-outlines-and-paragraphs",{"title":31,"path":32,"stem":33},"4. Literature Review and a Defensible Gap","\u002Fen\u002Facademic-writing\u002F04-writing-the-literature-review","en\u002Facademic-writing\u002F04-writing-the-literature-review",{"title":35,"path":36,"stem":37},"5. Research Design, Evidence, and Core Sections","\u002Fen\u002Facademic-writing\u002F05-core-sections-and-evidence","en\u002Facademic-writing\u002F05-core-sections-and-evidence",{"title":39,"path":40,"stem":41},"6. Citation, Paraphrasing, Integrity, and AI","\u002Fen\u002Facademic-writing\u002F06-citation-paraphrasing-and-integrity","en\u002Facademic-writing\u002F06-citation-paraphrasing-and-integrity",{"title":43,"path":44,"stem":45},"7. Revision, Review, and Submission","\u002Fen\u002Facademic-writing\u002F07-revision-style-and-submission","en\u002Facademic-writing\u002F07-revision-style-and-submission",{"title":47,"path":48,"stem":49},"8. Research Workbook","\u002Fen\u002Facademic-writing\u002F08-literature-review-checklist-and-template","en\u002Facademic-writing\u002F08-literature-review-checklist-and-template",{"title":51,"path":52,"stem":53},"9. Research Workflow and Tools","\u002Fen\u002Facademic-writing\u002F09-tools-for-academic-writing-and-literature-management","en\u002Facademic-writing\u002F09-tools-for-academic-writing-and-literature-management",{"title":55,"path":56,"stem":57},"10. Worked Project — From Question to Defensible Conclusion","\u002Fen\u002Facademic-writing\u002F10-worked-example-from-block-structure-to-question-chain","en\u002Facademic-writing\u002F10-worked-example-from-block-structure-to-question-chain",{"title":59,"path":60,"stem":61,"children":62,"page":249},"Accounting","\u002Fen\u002Faccounting","en\u002Faccounting",[63,69,87,93,193],{"title":64,"path":65,"stem":66,"children":67},"Accounting — From Evidence to Decisions","\u002Fen\u002Faccounting\u002F00-index","en\u002Faccounting\u002F00-index",[68],{"title":64,"path":65,"stem":66},{"title":70,"path":71,"stem":72,"children":73},"Accounting Appendix","\u002Fen\u002Faccounting\u002Fappendix","en\u002Faccounting\u002Fappendix\u002Findex",[74,75,79,83],{"title":70,"path":71,"stem":72},{"title":76,"path":77,"stem":78},"Worked Examples and Error Diagnosis","\u002Fen\u002Faccounting\u002Fappendix\u002F24-examples-pitfalls","en\u002Faccounting\u002Fappendix\u002F24-examples-pitfalls",{"title":80,"path":81,"stem":82},"Accounting Glossary","\u002Fen\u002Faccounting\u002Fappendix\u002F26-glossary","en\u002Faccounting\u002Fappendix\u002F26-glossary",{"title":84,"path":85,"stem":86},"Reading and Evidence Map","\u002Fen\u002Faccounting\u002Fappendix\u002F27-reading-map","en\u002Faccounting\u002Fappendix\u002F27-reading-map",{"title":88,"path":89,"stem":90,"children":91},"Northstar Record-to-Decision Capstone","\u002Fen\u002Faccounting\u002Fcapstone","en\u002Faccounting\u002Fcapstone\u002Findex",[92],{"title":88,"path":89,"stem":90},{"title":94,"path":95,"stem":96,"children":97},"Financial Accounting","\u002Fen\u002Faccounting\u002Ffinancial-accounting","en\u002Faccounting\u002Ffinancial-accounting\u002Findex",[98,99,117,131,165,179],{"title":94,"path":95,"stem":96},{"title":100,"path":101,"stem":102,"children":103},"1. Foundations","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations","en\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002Findex",[104,105,109,113],{"title":100,"path":101,"stem":102},{"title":106,"path":107,"stem":108},"Objectives and Qualitative Characteristics","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F01-objectives-qualitative-characteristics","en\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F01-objectives-qualitative-characteristics",{"title":110,"path":111,"stem":112},"Equation and Elements","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F02-equation-elements","en\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F02-equation-elements",{"title":114,"path":115,"stem":116},"Accrual Basis, Estimates and Periods","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F03-accounting-bases-principles","en\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F03-accounting-bases-principles",{"title":118,"path":119,"stem":120,"children":121},"2. Recording Transactions","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions","en\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions\u002Findex",[122,123,127],{"title":118,"path":119,"stem":120},{"title":124,"path":125,"stem":126},"Double-Entry and Debit\u002FCredit","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions\u002F04-double-entry-dr-cr","en\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions\u002F04-double-entry-dr-cr",{"title":128,"path":129,"stem":130},"Accounting Cycle","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions\u002F05-accounting-cycle","en\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions\u002F05-accounting-cycle",{"title":132,"path":133,"stem":134,"children":135},"3. Measurement and Adjustments","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002Findex",[136,137,141,145,149,153,157,161],{"title":132,"path":133,"stem":134},{"title":138,"path":139,"stem":140},"Revenue Recognition","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F07-revenue-recognition","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F07-revenue-recognition",{"title":142,"path":143,"stem":144},"Inventory","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F08-inventory","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F08-inventory",{"title":146,"path":147,"stem":148},"Receivables and Expected Credit Losses","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F09-receivables","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F09-receivables",{"title":150,"path":151,"stem":152},"Property, Plant and Equipment","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F10-ppe","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F10-ppe",{"title":154,"path":155,"stem":156},"Intangible Assets","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F11-intangibles","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F11-intangibles",{"title":158,"path":159,"stem":160},"Leases","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F12-leases","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F12-leases",{"title":162,"path":163,"stem":164},"Current and Deferred Income Tax","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F13-income-tax","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F13-income-tax",{"title":166,"path":167,"stem":168,"children":169},"4. Reporting and Cash","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash","en\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash\u002Findex",[170,171,175],{"title":166,"path":167,"stem":168},{"title":172,"path":173,"stem":174},"Linked Financial Statements","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash\u002F06-financial-statements","en\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash\u002F06-financial-statements",{"title":176,"path":177,"stem":178},"Cash, Reconciliation and Internal Control","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash\u002F14-cash-control","en\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash\u002F14-cash-control",{"title":180,"path":181,"stem":182,"children":183},"5. Analysis and Comparison","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison","en\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002Findex",[184,185,189],{"title":180,"path":181,"stem":182},{"title":186,"path":187,"stem":188},"Ratio Analysis","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002F15-ratio-analysis","en\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002F15-ratio-analysis",{"title":190,"path":191,"stem":192},"IFRS versus US GAAP","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002F25-ifrs-gaap","en\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002F25-ifrs-gaap",{"title":194,"path":195,"stem":196,"children":197},"Management Accounting","\u002Fen\u002Faccounting\u002Fmanagement-accounting","en\u002Faccounting\u002Fmanagement-accounting\u002Findex",[198,199,217,235],{"title":194,"path":195,"stem":196},{"title":200,"path":201,"stem":202,"children":203},"1. Cost Foundations","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations","en\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002Findex",[204,205,209,213],{"title":200,"path":201,"stem":202},{"title":206,"path":207,"stem":208},"Cost Concepts and Behaviour","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F16-cost-concepts","en\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F16-cost-concepts",{"title":210,"path":211,"stem":212},"Costing Systems","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F17-costing-systems","en\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F17-costing-systems",{"title":214,"path":215,"stem":216},"Variable and Absorption Costing","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F19-variable-vs-absorption","en\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F19-variable-vs-absorption",{"title":218,"path":219,"stem":220,"children":221},"2. Planning and Control","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control","en\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002Findex",[222,223,227,231],{"title":218,"path":219,"stem":220},{"title":224,"path":225,"stem":226},"Cost–Volume–Profit Analysis","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F18-cvp-analysis","en\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F18-cvp-analysis",{"title":228,"path":229,"stem":230},"Budgeting and Variance Analysis","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F20-budgeting-variances","en\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F20-budgeting-variances",{"title":232,"path":233,"stem":234},"Performance Measurement","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F21-performance-measurement","en\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F21-performance-measurement",{"title":236,"path":237,"stem":238,"children":239},"3. Decisions and Investment","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment","en\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment\u002Findex",[240,241,245],{"title":236,"path":237,"stem":238},{"title":242,"path":243,"stem":244},"Short-Term Decisions","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment\u002F22-short-term-decisions","en\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment\u002F22-short-term-decisions",{"title":246,"path":247,"stem":248},"Capital Budgeting","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment\u002F23-capital-budgeting","en\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment\u002F23-capital-budgeting",false,{"title":251,"path":252,"stem":253,"children":254,"page":249},"Business Analytics","\u002Fen\u002Fbusiness-analytics","en\u002Fbusiness-analytics",[255,261,279,305,335,365,383,400],{"title":256,"path":257,"stem":258,"children":259},"Business Analytics — From Data to Defensible Action","\u002Fen\u002Fbusiness-analytics\u002F00-index","en\u002Fbusiness-analytics\u002F00-index",[260],{"title":256,"path":257,"stem":258},{"title":262,"path":263,"stem":264,"children":265},"0. Decision and Data Foundations","\u002Fen\u002Fbusiness-analytics\u002F00-intro","en\u002Fbusiness-analytics\u002F00-intro\u002Findex",[266,267,271,275],{"title":262,"path":263,"stem":264},{"title":268,"path":269,"stem":270},"Decision Framing","\u002Fen\u002Fbusiness-analytics\u002F00-intro\u002F01-decision-framing","en\u002Fbusiness-analytics\u002F00-intro\u002F01-decision-framing",{"title":272,"path":273,"stem":274},"Data Contracts","\u002Fen\u002Fbusiness-analytics\u002F00-intro\u002F02-data-contracts","en\u002Fbusiness-analytics\u002F00-intro\u002F02-data-contracts",{"title":276,"path":277,"stem":278},"Reproducible Analytics Workflow","\u002Fen\u002Fbusiness-analytics\u002F00-intro\u002F03-reproducible-workflow","en\u002Fbusiness-analytics\u002F00-intro\u002F03-reproducible-workflow",{"title":280,"path":281,"stem":282,"children":283},"1. Descriptive Analytics","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive","en\u002Fbusiness-analytics\u002F01-descriptive\u002Findex",[284,285,289,293,297,301],{"title":280,"path":281,"stem":282},{"title":286,"path":287,"stem":288},"Distributions and Exploratory Data Analysis","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive\u002F04-distributions-eda","en\u002Fbusiness-analytics\u002F01-descriptive\u002F04-distributions-eda",{"title":290,"path":291,"stem":292},"KPIs and Denominators","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive\u002F05-kpis-denominators","en\u002Fbusiness-analytics\u002F01-descriptive\u002F05-kpis-denominators",{"title":294,"path":295,"stem":296},"Segments, Cohorts and Funnels","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive\u002F06-segmentation-cohorts-funnels","en\u002Fbusiness-analytics\u002F01-descriptive\u002F06-segmentation-cohorts-funnels",{"title":298,"path":299,"stem":300},"Visual Evidence and Data Stories","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive\u002F07-visualisation-story","en\u002Fbusiness-analytics\u002F01-descriptive\u002F07-visualisation-story",{"title":302,"path":303,"stem":304},"Experiments and Causal Boundaries","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive\u002F08-experiments-causal-boundary","en\u002Fbusiness-analytics\u002F01-descriptive\u002F08-experiments-causal-boundary",{"title":306,"path":307,"stem":308,"children":309},"2. Predictive Analytics","\u002Fen\u002Fbusiness-analytics\u002F02-predictive","en\u002Fbusiness-analytics\u002F02-predictive\u002Findex",[310,311,315,319,323,327,331],{"title":306,"path":307,"stem":308},{"title":312,"path":313,"stem":314},"Validation, Baselines and Leakage","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F09-validation-leakage","en\u002Fbusiness-analytics\u002F02-predictive\u002F09-validation-leakage",{"title":316,"path":317,"stem":318},"Regression and Forecasting","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F10-regression-forecasting","en\u002Fbusiness-analytics\u002F02-predictive\u002F10-regression-forecasting",{"title":320,"path":321,"stem":322},"Classification and Calibration","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F11-classification-calibration","en\u002Fbusiness-analytics\u002F02-predictive\u002F11-classification-calibration",{"title":324,"path":325,"stem":326},"Trees and Ensembles","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F12-trees-ensembles","en\u002Fbusiness-analytics\u002F02-predictive\u002F12-trees-ensembles",{"title":328,"path":329,"stem":330},"Decision Metrics and Thresholds","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F13-decision-metrics-thresholds","en\u002Fbusiness-analytics\u002F02-predictive\u002F13-decision-metrics-thresholds",{"title":332,"path":333,"stem":334},"Explainability, Monitoring and Drift","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F14-explainability-drift","en\u002Fbusiness-analytics\u002F02-predictive\u002F14-explainability-drift",{"title":336,"path":337,"stem":338,"children":339},"3. Prescriptive Analytics","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive","en\u002Fbusiness-analytics\u002F03-prescriptive\u002Findex",[340,341,345,349,353,357,361],{"title":336,"path":337,"stem":338},{"title":342,"path":343,"stem":344},"Decision-Making under Uncertainty","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F15-decision-uncertainty","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F15-decision-uncertainty",{"title":346,"path":347,"stem":348},"Linear Optimisation","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F16-linear-optimization","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F16-linear-optimization",{"title":350,"path":351,"stem":352},"Inventory and Allocation","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F17-inventory-allocation","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F17-inventory-allocation",{"title":354,"path":355,"stem":356},"Queueing and Simulation","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F18-queueing-simulation","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F18-queueing-simulation",{"title":358,"path":359,"stem":360},"Pricing and Revenue Management","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F19-pricing-experimentation","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F19-pricing-experimentation",{"title":362,"path":363,"stem":364},"Causal Targeting and Policy Learning","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F20-causal-targeting","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F20-causal-targeting",{"title":366,"path":367,"stem":368,"children":369},"4. Deployment and Governance","\u002Fen\u002Fbusiness-analytics\u002F04-deployment","en\u002Fbusiness-analytics\u002F04-deployment\u002Findex",[370,371,375,379],{"title":366,"path":367,"stem":368},{"title":372,"path":373,"stem":374},"Data Products and Monitoring","\u002Fen\u002Fbusiness-analytics\u002F04-deployment\u002F21-data-products-monitoring","en\u002Fbusiness-analytics\u002F04-deployment\u002F21-data-products-monitoring",{"title":376,"path":377,"stem":378},"Governance, Fairness and Privacy","\u002Fen\u002Fbusiness-analytics\u002F04-deployment\u002F22-governance-fairness-privacy","en\u002Fbusiness-analytics\u002F04-deployment\u002F22-governance-fairness-privacy",{"title":380,"path":381,"stem":382},"Adoption and Business Value","\u002Fen\u002Fbusiness-analytics\u002F04-deployment\u002F23-adoption-value","en\u002Fbusiness-analytics\u002F04-deployment\u002F23-adoption-value",{"title":384,"path":385,"stem":386,"children":387},"Appendix and Revision Tools","\u002Fen\u002Fbusiness-analytics\u002Fappendix","en\u002Fbusiness-analytics\u002Fappendix\u002Findex",[388,389,393,397],{"title":384,"path":385,"stem":386},{"title":390,"path":391,"stem":392},"Formula and Decision Map","\u002Fen\u002Fbusiness-analytics\u002Fappendix\u002F24-formula-map","en\u002Fbusiness-analytics\u002Fappendix\u002F24-formula-map",{"title":394,"path":395,"stem":396},"Worked Examples and Pitfalls","\u002Fen\u002Fbusiness-analytics\u002Fappendix\u002F25-worked-examples-pitfalls","en\u002Fbusiness-analytics\u002Fappendix\u002F25-worked-examples-pitfalls",{"title":84,"path":398,"stem":399},"\u002Fen\u002Fbusiness-analytics\u002Fappendix\u002F26-reading-map","en\u002Fbusiness-analytics\u002Fappendix\u002F26-reading-map",{"title":401,"path":402,"stem":403,"children":404},"Capstone — The Evening Delivery Promise","\u002Fen\u002Fbusiness-analytics\u002Fcapstone","en\u002Fbusiness-analytics\u002Fcapstone\u002Findex",[405],{"title":401,"path":402,"stem":403},{"title":407,"path":408,"stem":409,"children":410,"page":249},"Financial Economic Time Series","\u002Fen\u002Ffinancial-economic-time-series","en\u002Ffinancial-economic-time-series",[411,417,423,429,435,441,447,453,459,465,471],{"title":412,"path":413,"stem":414,"children":415},"Financial and Economic Time Series — Course Guide","\u002Fen\u002Ffinancial-economic-time-series\u002F00-intro","en\u002Ffinancial-economic-time-series\u002F00-intro\u002Findex",[416],{"title":412,"path":413,"stem":414},{"title":418,"path":419,"stem":420,"children":421},"Three Versions of Time Series","\u002Fen\u002Ffinancial-economic-time-series\u002F01-bridge","en\u002Ffinancial-economic-time-series\u002F01-bridge\u002Findex",[422],{"title":418,"path":419,"stem":420},{"title":424,"path":425,"stem":426,"children":427},"Data, Clocks, and Transformations","\u002Fen\u002Ffinancial-economic-time-series\u002F02-data-transformations","en\u002Ffinancial-economic-time-series\u002F02-data-transformations\u002Findex",[428],{"title":424,"path":425,"stem":426},{"title":430,"path":431,"stem":432,"children":433},"Predictive Regressions and Persistent Predictors","\u002Fen\u002Ffinancial-economic-time-series\u002F03-predictive-regressions","en\u002Ffinancial-economic-time-series\u002F03-predictive-regressions\u002Findex",[434],{"title":430,"path":431,"stem":432},{"title":436,"path":437,"stem":438,"children":439},"Volatility, Tails, and Financial Risk","\u002Fen\u002Ffinancial-economic-time-series\u002F04-volatility-risk","en\u002Ffinancial-economic-time-series\u002F04-volatility-risk\u002Findex",[440],{"title":436,"path":437,"stem":438},{"title":442,"path":443,"stem":444,"children":445},"Unit Roots, Cointegration, and Error Correction","\u002Fen\u002Ffinancial-economic-time-series\u002F05-unit-roots-cointegration","en\u002Ffinancial-economic-time-series\u002F05-unit-roots-cointegration\u002Findex",[446],{"title":442,"path":443,"stem":444},{"title":448,"path":449,"stem":450,"children":451},"VAR, Structural Identification, and Local Projections","\u002Fen\u002Ffinancial-economic-time-series\u002F06-var-identification","en\u002Ffinancial-economic-time-series\u002F06-var-identification\u002Findex",[452],{"title":448,"path":449,"stem":450},{"title":454,"path":455,"stem":456,"children":457},"State Space, Mixed Frequency, and Nowcasting","\u002Fen\u002Ffinancial-economic-time-series\u002F07-state-space-nowcasting","en\u002Ffinancial-economic-time-series\u002F07-state-space-nowcasting\u002Findex",[458],{"title":454,"path":455,"stem":456},{"title":460,"path":461,"stem":462,"children":463},"Forecast Evaluation for Decisions","\u002Fen\u002Ffinancial-economic-time-series\u002F08-forecast-evaluation","en\u002Ffinancial-economic-time-series\u002F08-forecast-evaluation\u002Findex",[464],{"title":460,"path":461,"stem":462},{"title":466,"path":467,"stem":468,"children":469},"Integrated R Laboratory","\u002Fen\u002Ffinancial-economic-time-series\u002F09-r-laboratory","en\u002Ffinancial-economic-time-series\u002F09-r-laboratory\u002Findex",[470],{"title":466,"path":467,"stem":468},{"title":472,"path":473,"stem":474,"children":475},"Capstones, Data, and Reading Ladder","\u002Fen\u002Ffinancial-economic-time-series\u002F10-capstone-readings","en\u002Ffinancial-economic-time-series\u002F10-capstone-readings\u002Findex",[476],{"title":472,"path":473,"stem":474},{"title":478,"path":479,"stem":480,"children":481,"page":249},"Intro To Economics","\u002Fen\u002Fintro-to-economics","en\u002Fintro-to-economics",[482,486,490,494,498,502,506,510,514,518,522,526,530],{"title":483,"path":484,"stem":485},"Introduction to Economics — Decisions, Markets, and the Macroeconomy","\u002Fen\u002Fintro-to-economics\u002F00-intro","en\u002Fintro-to-economics\u002F00-intro",{"title":487,"path":488,"stem":489},"Chapter 1 — Choice, Opportunity Cost, and Trade","\u002Fen\u002Fintro-to-economics\u002F01-foundations","en\u002Fintro-to-economics\u002F01-foundations",{"title":491,"path":492,"stem":493},"Chapter 2 — Demand, Supply, Equilibrium, and Welfare","\u002Fen\u002Fintro-to-economics\u002F02-demand-and-supply","en\u002Fintro-to-economics\u002F02-demand-and-supply",{"title":495,"path":496,"stem":497},"Chapter 3 — Elasticity, Revenue, and Tax Incidence","\u002Fen\u002Fintro-to-economics\u002F03-elasticity","en\u002Fintro-to-economics\u002F03-elasticity",{"title":499,"path":500,"stem":501},"Chapter 4 — Firms, Market Power, and Market Failure","\u002Fen\u002Fintro-to-economics\u002F04-market-structures","en\u002Fintro-to-economics\u002F04-market-structures",{"title":503,"path":504,"stem":505},"Chapter 5 — GDP, Income, Wealth, and Welfare","\u002Fen\u002Fintro-to-economics\u002F05-gdp-and-wealth","en\u002Fintro-to-economics\u002F05-gdp-and-wealth",{"title":507,"path":508,"stem":509},"Chapter 6 — Inflation, Purchasing Power, and Labour Markets","\u002Fen\u002Fintro-to-economics\u002F06-inflation-and-unemployment","en\u002Fintro-to-economics\u002F06-inflation-and-unemployment",{"title":511,"path":512,"stem":513},"Chapter 7 — Productivity, Technology, and Economic Growth","\u002Fen\u002Fintro-to-economics\u002F07-economic-growth","en\u002Fintro-to-economics\u002F07-economic-growth",{"title":515,"path":516,"stem":517},"Chapter 8 — Money, Credit, and Banking","\u002Fen\u002Fintro-to-economics\u002F08-money-and-banking","en\u002Fintro-to-economics\u002F08-money-and-banking",{"title":519,"path":520,"stem":521},"Chapter 9 — Business Cycles, AD–AS, and Monetary Policy","\u002Fen\u002Fintro-to-economics\u002F09-monetary-policy-and-ad-as","en\u002Fintro-to-economics\u002F09-monetary-policy-and-ad-as",{"title":523,"path":524,"stem":525},"Chapter 10 — Fiscal Policy, Distribution, and Public Debt","\u002Fen\u002Fintro-to-economics\u002F10-fiscal-policy","en\u002Fintro-to-economics\u002F10-fiscal-policy",{"title":527,"path":528,"stem":529},"Chapter 11 — Trade, Capital Flows, and Exchange Rates","\u002Fen\u002Fintro-to-economics\u002F11-open-economy-and-exchange-rates","en\u002Fintro-to-economics\u002F11-open-economy-and-exchange-rates",{"title":531,"path":532,"stem":533},"Chapter 12 — Integrated Economic Analysis Studio","\u002Fen\u002Fintro-to-economics\u002F12-review-and-case-studies","en\u002Fintro-to-economics\u002F12-review-and-case-studies",{"title":535,"path":536,"stem":537,"children":538,"page":249},"Microeconometrics","\u002Fen\u002Fmicroeconometrics","en\u002Fmicroeconometrics",[539,557,563,581,603,629,651,673,691,709],{"title":540,"path":541,"stem":542,"children":543},"0. Causal Questions and Designs","\u002Fen\u002Fmicroeconometrics\u002F00-foundations","en\u002Fmicroeconometrics\u002F00-foundations\u002Findex",[544,545,549,553],{"title":540,"path":541,"stem":542},{"title":546,"path":547,"stem":548},"Causal Questions and Estimands","\u002Fen\u002Fmicroeconometrics\u002F00-foundations\u002F01-causal-question-estimands","en\u002Fmicroeconometrics\u002F00-foundations\u002F01-causal-question-estimands",{"title":550,"path":551,"stem":552},"Potential Outcomes and Experiments","\u002Fen\u002Fmicroeconometrics\u002F00-foundations\u002F02-potential-outcomes-experiments","en\u002Fmicroeconometrics\u002F00-foundations\u002F02-potential-outcomes-experiments",{"title":554,"path":555,"stem":556},"Causal Diagrams and Controls","\u002Fen\u002Fmicroeconometrics\u002F00-foundations\u002F03-dags-controls","en\u002Fmicroeconometrics\u002F00-foundations\u002F03-dags-controls",{"title":558,"path":559,"stem":560,"children":561},"Microeconometrics — Designing Credible Counterfactuals","\u002Fen\u002Fmicroeconometrics\u002F00-index","en\u002Fmicroeconometrics\u002F00-index",[562],{"title":558,"path":559,"stem":560},{"title":564,"path":565,"stem":566,"children":567},"1. Regression and Inference","\u002Fen\u002Fmicroeconometrics\u002F01-regression","en\u002Fmicroeconometrics\u002F01-regression\u002Findex",[568,569,573,577],{"title":564,"path":565,"stem":566},{"title":570,"path":571,"stem":572},"OLS as a Projection","\u002Fen\u002Fmicroeconometrics\u002F01-regression\u002F04-ols-projection","en\u002Fmicroeconometrics\u002F01-regression\u002F04-ols-projection",{"title":574,"path":575,"stem":576},"FWL, Selection and Controls","\u002Fen\u002Fmicroeconometrics\u002F01-regression\u002F05-fwl-selection-controls","en\u002Fmicroeconometrics\u002F01-regression\u002F05-fwl-selection-controls",{"title":578,"path":579,"stem":580},"Inference and Clustering","\u002Fen\u002Fmicroeconometrics\u002F01-regression\u002F06-inference-clustering","en\u002Fmicroeconometrics\u002F01-regression\u002F06-inference-clustering",{"title":582,"path":583,"stem":584,"children":585},"2. Instruments and Panel Data","\u002Fen\u002Fmicroeconometrics\u002F02-iv-panel","en\u002Fmicroeconometrics\u002F02-iv-panel\u002Findex",[586,587,591,595,599],{"title":582,"path":583,"stem":584},{"title":588,"path":589,"stem":590},"Instrumental Variables","\u002Fen\u002Fmicroeconometrics\u002F02-iv-panel\u002F07-iv-identification","en\u002Fmicroeconometrics\u002F02-iv-panel\u002F07-iv-identification",{"title":592,"path":593,"stem":594},"Weak Instruments and LATE","\u002Fen\u002Fmicroeconometrics\u002F02-iv-panel\u002F08-weak-iv-late","en\u002Fmicroeconometrics\u002F02-iv-panel\u002F08-weak-iv-late",{"title":596,"path":597,"stem":598},"Panel Fixed Effects","\u002Fen\u002Fmicroeconometrics\u002F02-iv-panel\u002F09-panel-fixed-effects","en\u002Fmicroeconometrics\u002F02-iv-panel\u002F09-panel-fixed-effects",{"title":600,"path":601,"stem":602},"Dynamic Panels and Limits","\u002Fen\u002Fmicroeconometrics\u002F02-iv-panel\u002F10-dynamic-panel","en\u002Fmicroeconometrics\u002F02-iv-panel\u002F10-dynamic-panel",{"title":604,"path":605,"stem":606,"children":607},"3. Policy Evaluation Designs","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs","en\u002Fmicroeconometrics\u002F03-policy-designs\u002Findex",[608,609,613,617,621,625],{"title":604,"path":605,"stem":606},{"title":610,"path":611,"stem":612},"Difference-in-Differences","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs\u002F11-did-core","en\u002Fmicroeconometrics\u002F03-policy-designs\u002F11-did-core",{"title":614,"path":615,"stem":616},"Staggered DID and Event Studies","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs\u002F12-staggered-event-studies","en\u002Fmicroeconometrics\u002F03-policy-designs\u002F12-staggered-event-studies",{"title":618,"path":619,"stem":620},"Regression Discontinuity","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs\u002F13-rdd","en\u002Fmicroeconometrics\u002F03-policy-designs\u002F13-rdd",{"title":622,"path":623,"stem":624},"Matching, Weighting and Overlap","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs\u002F14-matching-weighting","en\u002Fmicroeconometrics\u002F03-policy-designs\u002F14-matching-weighting",{"title":626,"path":627,"stem":628},"Synthetic Control","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs\u002F15-synthetic-control","en\u002Fmicroeconometrics\u002F03-policy-designs\u002F15-synthetic-control",{"title":630,"path":631,"stem":632,"children":633},"Module 4 — Choice and Limited Outcomes","\u002Fen\u002Fmicroeconometrics\u002F04-outcomes-choice","en\u002Fmicroeconometrics\u002F04-outcomes-choice\u002Findex",[634,635,639,643,647],{"title":630,"path":631,"stem":632},{"title":636,"path":637,"stem":638},"Binary Choice","\u002Fen\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F16-binary-choice","en\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F16-binary-choice",{"title":640,"path":641,"stem":642},"Multinomial and Ordered Choice","\u002Fen\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F17-multinomial-choice","en\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F17-multinomial-choice",{"title":644,"path":645,"stem":646},"Count Outcomes","\u002Fen\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F18-count-outcomes","en\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F18-count-outcomes",{"title":648,"path":649,"stem":650},"Censoring, Truncation and Selection","\u002Fen\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F19-censoring-selection","en\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F19-censoring-selection",{"title":652,"path":653,"stem":654,"children":655},"Module 5 — Modern Causal Analysis","\u002Fen\u002Fmicroeconometrics\u002F05-modern-causal","en\u002Fmicroeconometrics\u002F05-modern-causal\u002Findex",[656,657,661,665,669],{"title":652,"path":653,"stem":654},{"title":658,"path":659,"stem":660},"Double Machine Learning","\u002Fen\u002Fmicroeconometrics\u002F05-modern-causal\u002F20-dml","en\u002Fmicroeconometrics\u002F05-modern-causal\u002F20-dml",{"title":662,"path":663,"stem":664},"Heterogeneity and Policy Learning","\u002Fen\u002Fmicroeconometrics\u002F05-modern-causal\u002F21-heterogeneity-policy","en\u002Fmicroeconometrics\u002F05-modern-causal\u002F21-heterogeneity-policy",{"title":666,"path":667,"stem":668},"Sensitivity and Partial Identification","\u002Fen\u002Fmicroeconometrics\u002F05-modern-causal\u002F22-sensitivity-partial-id","en\u002Fmicroeconometrics\u002F05-modern-causal\u002F22-sensitivity-partial-id",{"title":670,"path":671,"stem":672},"External Validity and Transport","\u002Fen\u002Fmicroeconometrics\u002F05-modern-causal\u002F23-external-validity","en\u002Fmicroeconometrics\u002F05-modern-causal\u002F23-external-validity",{"title":674,"path":675,"stem":676,"children":677},"Module 6 — From Data to Auditable Evidence","\u002Fen\u002Fmicroeconometrics\u002F06-workflow","en\u002Fmicroeconometrics\u002F06-workflow\u002Findex",[678,679,683,687],{"title":674,"path":675,"stem":676},{"title":680,"path":681,"stem":682},"Data Provenance","\u002Fen\u002Fmicroeconometrics\u002F06-workflow\u002F24-data-provenance","en\u002Fmicroeconometrics\u002F06-workflow\u002F24-data-provenance",{"title":684,"path":685,"stem":686},"Reproducibility and Reporting","\u002Fen\u002Fmicroeconometrics\u002F06-workflow\u002F25-reproducibility-reporting","en\u002Fmicroeconometrics\u002F06-workflow\u002F25-reproducibility-reporting",{"title":688,"path":689,"stem":690},"Paper and Evidence Audit","\u002Fen\u002Fmicroeconometrics\u002F06-workflow\u002F26-paper-audit","en\u002Fmicroeconometrics\u002F06-workflow\u002F26-paper-audit",{"title":692,"path":693,"stem":694,"children":695},"Appendix — Revision and Evidence Map","\u002Fen\u002Fmicroeconometrics\u002Fappendix","en\u002Fmicroeconometrics\u002Fappendix\u002Findex",[696,697,701,705],{"title":692,"path":693,"stem":694},{"title":698,"path":699,"stem":700},"Formula and Design Map","\u002Fen\u002Fmicroeconometrics\u002Fappendix\u002F27-formula-design-map","en\u002Fmicroeconometrics\u002Fappendix\u002F27-formula-design-map",{"title":702,"path":703,"stem":704},"Ten Worked Microeconometric Pitfalls","\u002Fen\u002Fmicroeconometrics\u002Fappendix\u002F28-worked-pitfalls","en\u002Fmicroeconometrics\u002Fappendix\u002F28-worked-pitfalls",{"title":706,"path":707,"stem":708},"Reading and Software Map","\u002Fen\u002Fmicroeconometrics\u002Fappendix\u002F29-reading-software-map","en\u002Fmicroeconometrics\u002Fappendix\u002F29-reading-software-map",{"title":710,"path":711,"stem":712,"children":713},"Capstone — Should Northbridge Expand Pathways?","\u002Fen\u002Fmicroeconometrics\u002Fcapstone","en\u002Fmicroeconometrics\u002Fcapstone\u002Findex",[714],{"title":710,"path":711,"stem":712},{"title":716,"path":717,"stem":718,"children":719,"page":249},"Microeconomics","\u002Fen\u002Fmicroeconomics","en\u002Fmicroeconomics",[720,726,732,738,744,750,756,762,768,774,780,786,792],{"title":721,"path":722,"stem":723,"children":724},"Advanced Microeconomics — Course Guide","\u002Fen\u002Fmicroeconomics\u002F00-intro","en\u002Fmicroeconomics\u002F00-intro\u002Findex",[725],{"title":721,"path":722,"stem":723},{"title":727,"path":728,"stem":729,"children":730},"Module 1 — Choice, Duality, and Revealed Preference","\u002Fen\u002Fmicroeconomics\u002F01-fundations","en\u002Fmicroeconomics\u002F01-fundations\u002Findex",[731],{"title":727,"path":728,"stem":729},{"title":733,"path":734,"stem":735,"children":736},"Module 2 — Comparative Statics and Welfare Measurement","\u002Fen\u002Fmicroeconomics\u002F02-comparative-statics","en\u002Fmicroeconomics\u002F02-comparative-statics\u002Findex",[737],{"title":733,"path":734,"stem":735},{"title":739,"path":740,"stem":741,"children":742},"Module 3 — Choice under Risk and Insurance","\u002Fen\u002Fmicroeconomics\u002F03-uncertainty","en\u002Fmicroeconomics\u002F03-uncertainty\u002Findex",[743],{"title":739,"path":740,"stem":741},{"title":745,"path":746,"stem":747,"children":748},"Module 4 — General Equilibrium and Welfare","\u002Fen\u002Fmicroeconomics\u002F04-general-equilibrium","en\u002Fmicroeconomics\u002F04-general-equilibrium\u002Findex",[749],{"title":745,"path":746,"stem":747},{"title":751,"path":752,"stem":753,"children":754},"Module 5 — Static, Dynamic, and Repeated Games","\u002Fen\u002Fmicroeconomics\u002F05-game-theory","en\u002Fmicroeconomics\u002F05-game-theory\u002Findex",[755],{"title":751,"path":752,"stem":753},{"title":757,"path":758,"stem":759,"children":760},"Module 6 — Oligopoly, Entry, and Algorithmic Pricing","\u002Fen\u002Fmicroeconomics\u002F06-oligopoly","en\u002Fmicroeconomics\u002F06-oligopoly\u002Findex",[761],{"title":757,"path":758,"stem":759},{"title":763,"path":764,"stem":765,"children":766},"Module 7 — Information Economics and Contracts","\u002Fen\u002Fmicroeconomics\u002F07-information-economics","en\u002Fmicroeconomics\u002F07-information-economics\u002Findex",[767],{"title":763,"path":764,"stem":765},{"title":769,"path":770,"stem":771,"children":772},"Module 8 — Mechanism Design and Auctions","\u002Fen\u002Fmicroeconomics\u002F08-mechanism-design","en\u002Fmicroeconomics\u002F08-mechanism-design\u002Findex",[773],{"title":769,"path":770,"stem":771},{"title":775,"path":776,"stem":777,"children":778},"Module 9 — Behavioural and Experimental Microeconomics","\u002Fen\u002Fmicroeconomics\u002F09-behavioural-economics","en\u002Fmicroeconomics\u002F09-behavioural-economics\u002Findex",[779],{"title":775,"path":776,"stem":777},{"title":781,"path":782,"stem":783,"children":784},"Module 10 — Externalities, Public Goods, and Collective Action","\u002Fen\u002Fmicroeconomics\u002F10-externalities-public-goods","en\u002Fmicroeconomics\u002F10-externalities-public-goods\u002Findex",[785],{"title":781,"path":782,"stem":783},{"title":787,"path":788,"stem":789,"children":790},"Module 11 — Matching and Market Design","\u002Fen\u002Fmicroeconomics\u002F11-market-design","en\u002Fmicroeconomics\u002F11-market-design\u002Findex",[791],{"title":787,"path":788,"stem":789},{"title":793,"path":794,"stem":795,"children":796},"Module 12 — Integrated Microeconomic Design Studio","\u002Fen\u002Fmicroeconomics\u002F12-review","en\u002Fmicroeconomics\u002F12-review\u002Findex",[797],{"title":793,"path":794,"stem":795},{"title":799,"path":800,"stem":801,"children":802},"Playground","\u002Fen\u002Fplayground","en\u002Fplayground\u002Findex",[803,804,808,812,816,820],{"title":799,"path":800,"stem":801},{"title":805,"path":806,"stem":807},"Typst Plugin Playground","\u002Fen\u002Fplayground\u002F01-typstex","en\u002Fplayground\u002F01-typstex",{"title":809,"path":810,"stem":811},"Citation Plugin Test","\u002Fen\u002Fplayground\u002F02-citation","en\u002Fplayground\u002F02-citation",{"title":813,"path":814,"stem":815},"Pyodide Playground","\u002Fen\u002Fplayground\u002F03-pyodide","en\u002Fplayground\u002F03-pyodide",{"title":817,"path":818,"stem":819},"WebR Playground","\u002Fen\u002Fplayground\u002F04-webr","en\u002Fplayground\u002F04-webr",{"title":821,"path":822,"stem":823},"Chart.js 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文献综述的构建与写作","\u002Fzh\u002Facademic-writing\u002F04-writing-the-literature-review","zh\u002Facademic-writing\u002F04-writing-the-literature-review",{"title":1056,"path":1057,"stem":1058},"8. 文献综述清单与模板","\u002Fzh\u002Facademic-writing\u002F08-literature-review-checklist-and-template","zh\u002Facademic-writing\u002F08-literature-review-checklist-and-template",{"title":1060,"path":1061,"stem":1062},"10. 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Alpha 策略全流程","\u002Fzh\u002Fquant\u002F09-case-study","zh\u002Fquant\u002F09-case-study",{"title":1779,"path":1780,"stem":1781},"量化投资文献与软件图谱","\u002Fzh\u002Fquant\u002F10-reading-software-map","zh\u002Fquant\u002F10-reading-software-map",{"path":752},{"id":1784,"title":1578,"body":1785,"description":18024,"extension":18025,"features":18026,"hero":18026,"layout":18026,"locale":18026,"meta":18027,"navigation":18026,"path":1579,"published":18028,"seo":18029,"stem":1580,"__hash__":18030},"docs\u002Fzh\u002Fmicroeconomics\u002F05-game-theory\u002Findex.md",{"type":1786,"value":1787,"toc":17970},"minimark",[1788,1793,1797,1801,1804,1820,1823,1847,1851,1854,1861,1869,1874,1889,1892,1896,1901,1954,2537,2542,3411,3415,3420,3468,3473,3487,3491,3511,3513,3517,3521,3909,4323,4390,4632,5025,5030,5052,5058,5062,5394,5942,5948,5953,5967,5971,5976,5979,5984,6016,6534,6799,6804,6845,6850,6861,6867,6873,6877,6882,6893,6898,6912,6917,6958,6962,6981,6987,6991,7067,7073,7483,7486,7488,7492,7496,7502,7508,7664,7823,8053,8057,8262,8700,8704,8797,9355,9419,9425,9429,9434,9472,9475,9480,9542,9548,9735,9989,10080,10141,10146,10325,10575,10658,10717,10723,10728,11096,11452,11455,11459,11516,11522,11561,11567,11569,11573,11577,11583,11588,11614,11624,11628,11634,11639,11656,11661,11670,11675,11683,11689,11695,11699,11705,11710,11716,11720,11734,11738,11744,11749,11766,11772,11778,11783,11797,11800,11802,11806,11810,11905,12058,12064,12360,12366,12370,12480,12485,12728,12821,12827,12831,12836,12847,12852,12863,12867,12873,12879,12916,12924,12928,12965,12970,12974,12979,13019,13024,13027,13284,13289,13531,13645,13726,13844,13905,13910,13979,13981,13985,13989,13995,14035,14040,14045,14048,14062,14068,14073,14133,14136,14302,14551,14641,14758,14761,14927,15177,15285,15344,15461,15621,15624,16273,16985,16989,16994,17002,17005,17009,17012,17018,17021,17038,17042,17055,17061,17067,17069,17073,17077,17080,17083,17149,17269,17276,17280,17394,17397,17429,17621,17734,17738,17741,17744,17746,17750,17755,17773,17778,17801,17803,17807,17884,17902,17905,17911,17917,17920,17934,17937,17954,17957,17960],[1789,1790,1792],"h1",{"id":1791},"第-5-讲博弈论静态与动态博弈","第 5 讲：博弈论：静态与动态博弈",[1794,1795,1796],"h2",{"id":1796},"本章导学",[1798,1799,1800],"p",{},"从这一章开始，经济主体不再只是“面对价格做选择”，而是必须预判他人的行动。博弈论给我们一套分析策略互动的语言：什么是策略，什么是最优反应，什么样的结果没有人愿意单方面偏离。",[1798,1802,1803],{},"学完本章后，你应当能够：",[1805,1806,1807,1811,1814,1817],"ul",{},[1808,1809,1810],"li",{},"把经济情境写成标准式或扩展式博弈。",[1808,1812,1813],{},"找出占优策略、纯策略纳什均衡和混合策略纳什均衡。",[1808,1815,1816],{},"用逆向归纳法求动态博弈的子博弈精炼均衡。",[1808,1818,1819],{},"解释重复博弈中合作为什么可能出现，以及折现因子如何影响合作稳定性。",[1798,1821,1822],{},"常见考查会从支付矩阵、进入博弈或重复囚徒困境开始，要求你逐步排除劣策略、求最优反应或验证均衡。答题时最重要的是检查“偏离”：一个策略组合只有在每个参与者都没有单方面获利偏离时才是均衡。",[1798,1824,1825,1826,1831,1832,1836,1837,1841,1842,1846],{},"本章向前区别于",[1827,1828,1830],"a",{"href":1829},"..\u002F04-general-equilibrium\u002F","第 4 章","的价格接受者模型，向后直接支撑",[1827,1833,1835],{"href":1834},"..\u002F06-oligopoly\u002F","第 6 章","的寡头竞争、",[1827,1838,1840],{"href":1839},"..\u002F08-mechanism-design\u002F","第 8 章","的机制设计和",[1827,1843,1845],{"href":1844},"..\u002F11-market-design\u002F","第 11 章","的匹配机制。",[1794,1848,1850],{"id":1849},"经济动机-economic-motivation","经济动机 (Economic Motivation)",[1798,1852,1853],{},"在许多经济和社会情境中，一个决策者的最优选择取决于其他决策者的选择。例如，寡头市场中的公司定价、拍卖中的出价策略、甚至国家间的贸易谈判。博弈论提供了一个强大的数学框架，用于分析这种\"策略互动\"情境。",[1798,1855,1856,1860],{},[1857,1858,1859],"strong",{},"与之前章节的区别",":",[1805,1862,1863,1866],{},[1808,1864,1865],{},"第1-4章：单个决策者或价格接受者（非策略性）",[1808,1867,1868],{},"第5章开始：策略互动（我的最优选择取决于你的选择）",[1798,1870,1871,1860],{},[1857,1872,1873],{},"博弈论的核心问题",[1875,1876,1877,1880,1883,1886],"ol",{},[1808,1878,1879],{},"理性的参与者会如何行动？",[1808,1881,1882],{},"存在稳定的结果（均衡）吗？",[1808,1884,1885],{},"如何预测博弈的结果？",[1808,1887,1888],{},"如何设计规则以实现期望的结果？",[1890,1891],"hr",{},[1794,1893,1895],{"id":1894},"_1-博弈的基本要素","1. 博弈的基本要素",[1897,1898,1900],"h3",{"id":1899},"_11-标准式博弈-normal-form-game","1.1 标准式博弈 (Normal Form Game)",[1798,1902,1903,1906,1907,1953],{},[1857,1904,1905],{},"定义",": 一个",[1908,1909,1912,1934],"span",{"className":1910},[1911],"katex",[1908,1913,1916],{"className":1914},[1915],"katex-mathml",[1917,1918,1920],"math",{"xmlns":1919},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[1921,1922,1923,1930],"semantics",{},[1924,1925,1926],"mrow",{},[1927,1928,1929],"mi",{},"n",[1931,1932,1929],"annotation",{"encoding":1933},"application\u002Fx-tex",[1908,1935,1939],{"className":1936,"ariaHidden":1938},[1937],"katex-html","true",[1908,1940,1943,1948],{"className":1941},[1942],"base",[1908,1944],{"className":1945,"style":1947},[1946],"strut","height:0.4306em;",[1908,1949,1929],{"className":1950},[1951,1952],"mord","mathnormal","人标准式博弈由以下三要素组成：",[1875,1955,1956,2087,2214],{},[1808,1957,1958,1961,1962],{},[1857,1959,1960],{},"参与者集合",": ",[1908,1963,1965,2010],{"className":1964},[1911],[1908,1966,1968],{"className":1967},[1915],[1917,1969,1970],{"xmlns":1919},[1921,1971,1972,2007],{},[1924,1973,1974,1977,1981,1985,1989,1992,1995,1997,2000,2002,2004],{},[1927,1975,1976],{},"N",[1978,1979,1980],"mo",{},"=",[1978,1982,1984],{"stretchy":1983},"false","{",[1986,1987,1988],"mn",{},"1",[1978,1990,1991],{"separator":1938},",",[1986,1993,1994],{},"2",[1978,1996,1991],{"separator":1938},[1978,1998,1999],{},"…",[1978,2001,1991],{"separator":1938},[1927,2003,1929],{},[1978,2005,2006],{"stretchy":1983},"}",[1931,2008,2009],{"encoding":1933},"N = \\{1, 2, \\ldots, n\\}",[1908,2011,2013,2036],{"className":2012,"ariaHidden":1938},[1937],[1908,2014,2016,2020,2024,2029,2033],{"className":2015},[1942],[1908,2017],{"className":2018,"style":2019},[1946],"height:0.6833em;",[1908,2021,1976],{"className":2022,"style":2023},[1951,1952],"margin-right:0.109em;",[1908,2025],{"className":2026,"style":2028},[2027],"mspace","margin-right:0.2778em;",[1908,2030,1980],{"className":2031},[2032],"mrel",[1908,2034],{"className":2035,"style":2028},[2027],[1908,2037,2039,2043,2047,2050,2054,2058,2061,2064,2067,2071,2074,2077,2080,2083],{"className":2038},[1942],[1908,2040],{"className":2041,"style":2042},[1946],"height:1em;vertical-align:-0.25em;",[1908,2044,1984],{"className":2045},[2046],"mopen",[1908,2048,1988],{"className":2049},[1951],[1908,2051,1991],{"className":2052},[2053],"mpunct",[1908,2055],{"className":2056,"style":2057},[2027],"margin-right:0.1667em;",[1908,2059,1994],{"className":2060},[1951],[1908,2062,1991],{"className":2063},[2053],[1908,2065],{"className":2066,"style":2057},[2027],[1908,2068,1999],{"className":2069},[2070],"minner",[1908,2072],{"className":2073,"style":2057},[2027],[1908,2075,1991],{"className":2076},[2053],[1908,2078],{"className":2079,"style":2057},[2027],[1908,2081,1929],{"className":2082},[1951,1952],[1908,2084,2006],{"className":2085},[2086],"mclose",[1808,2088,2089,2092,2093,2123,2124],{},[1857,2090,2091],{},"策略空间",": 每个参与者",[1908,2094,2096,2110],{"className":2095},[1911],[1908,2097,2099],{"className":2098},[1915],[1917,2100,2101],{"xmlns":1919},[1921,2102,2103,2108],{},[1924,2104,2105],{},[1927,2106,2107],{},"i",[1931,2109,2107],{"encoding":1933},[1908,2111,2113],{"className":2112,"ariaHidden":1938},[1937],[1908,2114,2116,2120],{"className":2115},[1942],[1908,2117],{"className":2118,"style":2119},[1946],"height:0.6595em;",[1908,2121,2107],{"className":2122},[1951,1952],"有策略集",[1908,2125,2127,2147],{"className":2126},[1911],[1908,2128,2130],{"className":2129},[1915],[1917,2131,2132],{"xmlns":1919},[1921,2133,2134,2144],{},[1924,2135,2136],{},[2137,2138,2139,2142],"msub",{},[1927,2140,2141],{},"S",[1927,2143,2107],{},[1931,2145,2146],{"encoding":1933},"S_i",[1908,2148,2150],{"className":2149,"ariaHidden":1938},[1937],[1908,2151,2153,2157],{"className":2152},[1942],[1908,2154],{"className":2155,"style":2156},[1946],"height:0.8333em;vertical-align:-0.15em;",[1908,2158,2160,2164],{"className":2159},[1951],[1908,2161,2141],{"className":2162,"style":2163},[1951,1952],"margin-right:0.0576em;",[1908,2165,2168],{"className":2166},[2167],"msupsub",[1908,2169,2173,2205],{"className":2170},[2171,2172],"vlist-t","vlist-t2",[1908,2174,2177,2200],{"className":2175},[2176],"vlist-r",[1908,2178,2182],{"className":2179,"style":2181},[2180],"vlist","height:0.3117em;",[1908,2183,2185,2190],{"style":2184},"top:-2.55em;margin-left:-0.0576em;margin-right:0.05em;",[1908,2186],{"className":2187,"style":2189},[2188],"pstrut","height:2.7em;",[1908,2191,2197],{"className":2192},[2193,2194,2195,2196],"sizing","reset-size6","size3","mtight",[1908,2198,2107],{"className":2199},[1951,1952,2196],[1908,2201,2204],{"className":2202},[2203],"vlist-s","​",[1908,2206,2208],{"className":2207},[2176],[1908,2209,2212],{"className":2210,"style":2211},[2180],"height:0.15em;",[1908,2213],{},[1808,2215,2216,1961,2219],{},[1857,2217,2218],{},"支付函数",[1908,2220,2222,2278],{"className":2221},[1911],[1908,2223,2225],{"className":2224},[1915],[1917,2226,2227],{"xmlns":1919},[1921,2228,2229,2275],{},[1924,2230,2231,2238,2240,2246,2249,2255,2257,2260,2262,2268,2271],{},[2137,2232,2233,2236],{},[1927,2234,2235],{},"u",[1927,2237,2107],{},[1978,2239,1860],{},[2137,2241,2242,2244],{},[1927,2243,2141],{},[1986,2245,1988],{},[1978,2247,2248],{},"×",[2137,2250,2251,2253],{},[1927,2252,2141],{},[1986,2254,1994],{},[1978,2256,2248],{},[1978,2258,2259],{},"⋯",[1978,2261,2248],{},[2137,2263,2264,2266],{},[1927,2265,2141],{},[1927,2267,1929],{},[1978,2269,2270],{},"→",[1927,2272,2274],{"mathvariant":2273},"double-struck","R",[1931,2276,2277],{"encoding":1933},"u_i: S_1 \\times S_2 \\times \\cdots \\times S_n \\to \\mathbb{R}",[1908,2279,2281,2338,2396,2451,2470,2526],{"className":2280,"ariaHidden":1938},[1937],[1908,2282,2284,2288,2329,2332,2335],{"className":2283},[1942],[1908,2285],{"className":2286,"style":2287},[1946],"height:0.5806em;vertical-align:-0.15em;",[1908,2289,2291,2294],{"className":2290},[1951],[1908,2292,2235],{"className":2293},[1951,1952],[1908,2295,2297],{"className":2296},[2167],[1908,2298,2300,2321],{"className":2299},[2171,2172],[1908,2301,2303,2318],{"className":2302},[2176],[1908,2304,2306],{"className":2305,"style":2181},[2180],[1908,2307,2309,2312],{"style":2308},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[1908,2310],{"className":2311,"style":2189},[2188],[1908,2313,2315],{"className":2314},[2193,2194,2195,2196],[1908,2316,2107],{"className":2317},[1951,1952,2196],[1908,2319,2204],{"className":2320},[2203],[1908,2322,2324],{"className":2323},[2176],[1908,2325,2327],{"className":2326,"style":2211},[2180],[1908,2328],{},[1908,2330],{"className":2331,"style":2028},[2027],[1908,2333,1860],{"className":2334},[2032],[1908,2336],{"className":2337,"style":2028},[2027],[1908,2339,2341,2344,2385,2389,2393],{"className":2340},[1942],[1908,2342],{"className":2343,"style":2156},[1946],[1908,2345,2347,2350],{"className":2346},[1951],[1908,2348,2141],{"className":2349,"style":2163},[1951,1952],[1908,2351,2353],{"className":2352},[2167],[1908,2354,2356,2377],{"className":2355},[2171,2172],[1908,2357,2359,2374],{"className":2358},[2176],[1908,2360,2363],{"className":2361,"style":2362},[2180],"height:0.3011em;",[1908,2364,2365,2368],{"style":2184},[1908,2366],{"className":2367,"style":2189},[2188],[1908,2369,2371],{"className":2370},[2193,2194,2195,2196],[1908,2372,1988],{"className":2373},[1951,2196],[1908,2375,2204],{"className":2376},[2203],[1908,2378,2380],{"className":2379},[2176],[1908,2381,2383],{"className":2382,"style":2211},[2180],[1908,2384],{},[1908,2386],{"className":2387,"style":2388},[2027],"margin-right:0.2222em;",[1908,2390,2248],{"className":2391},[2392],"mbin",[1908,2394],{"className":2395,"style":2388},[2027],[1908,2397,2399,2402,2442,2445,2448],{"className":2398},[1942],[1908,2400],{"className":2401,"style":2156},[1946],[1908,2403,2405,2408],{"className":2404},[1951],[1908,2406,2141],{"className":2407,"style":2163},[1951,1952],[1908,2409,2411],{"className":2410},[2167],[1908,2412,2414,2434],{"className":2413},[2171,2172],[1908,2415,2417,2431],{"className":2416},[2176],[1908,2418,2420],{"className":2419,"style":2362},[2180],[1908,2421,2422,2425],{"style":2184},[1908,2423],{"className":2424,"style":2189},[2188],[1908,2426,2428],{"className":2427},[2193,2194,2195,2196],[1908,2429,1994],{"className":2430},[1951,2196],[1908,2432,2204],{"className":2433},[2203],[1908,2435,2437],{"className":2436},[2176],[1908,2438,2440],{"className":2439,"style":2211},[2180],[1908,2441],{},[1908,2443],{"className":2444,"style":2388},[2027],[1908,2446,2248],{"className":2447},[2392],[1908,2449],{"className":2450,"style":2388},[2027],[1908,2452,2454,2458,2461,2464,2467],{"className":2453},[1942],[1908,2455],{"className":2456,"style":2457},[1946],"height:0.6667em;vertical-align:-0.0833em;",[1908,2459,2259],{"className":2460},[2070],[1908,2462],{"className":2463,"style":2388},[2027],[1908,2465,2248],{"className":2466},[2392],[1908,2468],{"className":2469,"style":2388},[2027],[1908,2471,2473,2476,2517,2520,2523],{"className":2472},[1942],[1908,2474],{"className":2475,"style":2156},[1946],[1908,2477,2479,2482],{"className":2478},[1951],[1908,2480,2141],{"className":2481,"style":2163},[1951,1952],[1908,2483,2485],{"className":2484},[2167],[1908,2486,2488,2509],{"className":2487},[2171,2172],[1908,2489,2491,2506],{"className":2490},[2176],[1908,2492,2495],{"className":2493,"style":2494},[2180],"height:0.1514em;",[1908,2496,2497,2500],{"style":2184},[1908,2498],{"className":2499,"style":2189},[2188],[1908,2501,2503],{"className":2502},[2193,2194,2195,2196],[1908,2504,1929],{"className":2505},[1951,1952,2196],[1908,2507,2204],{"className":2508},[2203],[1908,2510,2512],{"className":2511},[2176],[1908,2513,2515],{"className":2514,"style":2211},[2180],[1908,2516],{},[1908,2518],{"className":2519,"style":2028},[2027],[1908,2521,2270],{"className":2522},[2032],[1908,2524],{"className":2525,"style":2028},[2027],[1908,2527,2529,2533],{"className":2528},[1942],[1908,2530],{"className":2531,"style":2532},[1946],"height:0.6889em;",[1908,2534,2274],{"className":2535},[1951,2536],"mathbb",[1798,2538,2539,1860],{},[1857,2540,2541],{},"记号",[1805,2543,2544,2776,3189],{},[1808,2545,2546,2547],{},"策略组合: ",[1908,2548,2550,2599],{"className":2549},[1911],[1908,2551,2553],{"className":2552},[1915],[1917,2554,2555],{"xmlns":1919},[1921,2556,2557,2596],{},[1924,2558,2559,2562,2564,2567,2573,2575,2581,2583,2585,2587,2593],{},[1927,2560,2561],{},"s",[1978,2563,1980],{},[1978,2565,2566],{"stretchy":1983},"(",[2137,2568,2569,2571],{},[1927,2570,2561],{},[1986,2572,1988],{},[1978,2574,1991],{"separator":1938},[2137,2576,2577,2579],{},[1927,2578,2561],{},[1986,2580,1994],{},[1978,2582,1991],{"separator":1938},[1978,2584,1999],{},[1978,2586,1991],{"separator":1938},[2137,2588,2589,2591],{},[1927,2590,2561],{},[1927,2592,1929],{},[1978,2594,2595],{"stretchy":1983},")",[1931,2597,2598],{"encoding":1933},"s = (s_1, s_2, \\ldots, 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8,3190,3191,3192,3220,3221],{},"参与者",[1908,3193,3195,3208],{"className":3194},[1911],[1908,3196,3198],{"className":3197},[1915],[1917,3199,3200],{"xmlns":1919},[1921,3201,3202,3206],{},[1924,3203,3204],{},[1927,3205,2107],{},[1931,3207,2107],{"encoding":1933},[1908,3209,3211],{"className":3210,"ariaHidden":1938},[1937],[1908,3212,3214,3217],{"className":3213},[1942],[1908,3215],{"className":3216,"style":2119},[1946],[1908,3218,2107],{"className":3219},[1951,1952],"的支付: ",[1908,3222,3224,3264],{"className":3223},[1911],[1908,3225,3227],{"className":3226},[1915],[1917,3228,3229],{"xmlns":1919},[1921,3230,3231,3261],{},[1924,3232,3233,3239,3241,3247,3249,3259],{},[2137,3234,3235,3237],{},[1927,3236,2235],{},[1927,3238,2107],{},[1978,3240,2566],{"stretchy":1983},[2137,3242,3243,3245],{},[1927,3244,2561],{},[1927,3246,2107],{},[1978,3248,1991],{"separator":1938},[2137,3250,3251,3253],{},[1927,3252,2561],{},[1924,3254,3255,3257],{},[1978,3256,2828],{},[1927,3258,2107],{},[1978,3260,2595],{"stretchy":1983},[1931,3262,3263],{"encoding":1933},"u_i(s_i, s_{-i})",[1908,3265,3267],{"className":3266,"ariaHidden":1938},[1937],[1908,3268,3270,3273,3313,3316,3356,3359,3362,3408],{"className":3269},[1942],[1908,3271],{"className":3272,"style":2042},[1946],[1908,3274,3276,3279],{"className":3275},[1951],[1908,3277,2235],{"className":3278},[1951,1952],[1908,3280,3282],{"className":3281},[2167],[1908,3283,3285,3305],{"className":3284},[2171,2172],[1908,3286,3288,3302],{"className":3287},[2176],[1908,3289,3291],{"className":3290,"style":2181},[2180],[1908,3292,3293,3296],{"style":2308},[1908,3294],{"className":3295,"style":2189},[2188],[1908,3297,3299],{"className":3298},[2193,2194,2195,2196],[1908,3300,2107],{"className":3301},[1951,1952,2196],[1908,3303,2204],{"className":3304},[2203],[1908,3306,3308],{"className":3307},[2176],[1908,3309,3311],{"className":3310,"style":2211},[2180],[1908,3312],{},[1908,3314,2566],{"className":3315},[2046],[1908,3317,3319,3322],{"className":3318},[1951],[1908,3320,2561],{"className":3321},[1951,1952],[1908,3323,3325],{"className":3324},[2167],[1908,3326,3328,3348],{"className":3327},[2171,2172],[1908,3329,3331,3345],{"className":3330},[2176],[1908,3332,3334],{"className":3333,"style":2181},[2180],[1908,3335,3336,3339],{"style":2308},[1908,3337],{"className":3338,"style":2189},[2188],[1908,3340,3342],{"className":3341},[2193,2194,2195,2196],[1908,3343,2107],{"className":3344},[1951,1952,2196],[1908,3346,2204],{"className":3347},[2203],[1908,3349,3351],{"className":3350},[2176],[1908,3352,3354],{"className":3353,"style":2211},[2180],[1908,3355],{},[1908,3357,1991],{"className":3358},[2053],[1908,3360],{"className":3361,"style":2057},[2027],[1908,3363,3365,3368],{"className":3364},[1951],[1908,3366,2561],{"className":3367},[1951,1952],[1908,3369,3371],{"className":3370},[2167],[1908,3372,3374,3400],{"className":3373},[2171,2172],[1908,3375,3377,3397],{"className":3376},[2176],[1908,3378,3380],{"className":3379,"style":2181},[2180],[1908,3381,3382,3385],{"style":2308},[1908,3383],{"className":3384,"style":2189},[2188],[1908,3386,3388],{"className":3387},[2193,2194,2195,2196],[1908,3389,3391,3394],{"className":3390},[1951,2196],[1908,3392,2828],{"className":3393},[1951,2196],[1908,3395,2107],{"className":3396},[1951,1952,2196],[1908,3398,2204],{"className":3399},[2203],[1908,3401,3403],{"className":3402},[2176],[1908,3404,3406],{"className":3405,"style":2945},[2180],[1908,3407],{},[1908,3409,2595],{"className":3410},[2086],[1897,3412,3414],{"id":3413},"_12-支付矩阵表示法","1.2 支付矩阵表示法",[1798,3416,3417,1860],{},[1857,3418,3419],{},"两人博弈示例 - 囚徒困境",[3421,3422,3423,3438],"table",{},[3424,3425,3426],"thead",{},[3427,3428,3429,3432,3435],"tr",{},[3430,3431],"th",{},[3430,3433,3434],{},"参与者2：合作(C)",[3430,3436,3437],{},"参与者2：背叛(D)",[3439,3440,3441,3455],"tbody",{},[3427,3442,3443,3449,3452],{},[3444,3445,3446],"td",{},[1857,3447,3448],{},"参与者1：合作(C)",[3444,3450,3451],{},"(-1, -1)",[3444,3453,3454],{},"(-3, 0)",[3427,3456,3457,3462,3465],{},[3444,3458,3459],{},[1857,3460,3461],{},"参与者1：背叛(D)",[3444,3463,3464],{},"(0, -3)",[3444,3466,3467],{},"(-2, -2)",[1798,3469,3470,1860],{},[1857,3471,3472],{},"解读",[1805,3474,3475,3478,3481,3484],{},[1808,3476,3477],{},"第一个数字是参与者1的支付",[1808,3479,3480],{},"如果都合作：各判1年",[1808,3482,3483],{},"如果一方背叛：背叛者释放，合作者判3年",[1808,3485,3486],{},"如果都背叛：各判2年",[1897,3488,3490],{"id":3489},"_13-关键假设","1.3 关键假设",[1875,3492,3493,3499,3505],{},[1808,3494,3495,3498],{},[1857,3496,3497],{},"共同知识 (Common Knowledge)",": 所有参与者知道博弈的规则，且知道其他人知道，且知道其他人知道其他人知道……（无限递归）",[1808,3500,3501,3504],{},[1857,3502,3503],{},"理性 (Rationality)",": 参与者追求自身支付最大化",[1808,3506,3507,3510],{},[1857,3508,3509],{},"互相理性 (Mutual Rationality)",": 每个人都是理性的，且每个人都知道其他人是理性的",[1890,3512],{},[1794,3514,3516],{"id":3515},"_2-纳什均衡","2. 纳什均衡",[1897,3518,3520],{"id":3519},"_21-占优策略-dominant-strategy","2.1 占优策略 (Dominant Strategy)",[1798,3522,3523,3526,3527,3617,3618,3827,3828,3908],{},[1857,3524,3525],{},"严格占优",": 策略",[1908,3528,3530,3552],{"className":3529},[1911],[1908,3531,3533],{"className":3532},[1915],[1917,3534,3535],{"xmlns":1919},[1921,3536,3537,3549],{},[1924,3538,3539],{},[3540,3541,3542,3544,3546],"msubsup",{},[1927,3543,2561],{},[1927,3545,2107],{},[1978,3547,3548],{},"∗",[1931,3550,3551],{"encoding":1933},"s_i^*",[1908,3553,3555],{"className":3554,"ariaHidden":1938},[1937],[1908,3556,3558,3562],{"className":3557},[1942],[1908,3559],{"className":3560,"style":3561},[1946],"height:0.9474em;vertical-align:-0.2587em;",[1908,3563,3565,3568],{"className":3564},[1951],[1908,3566,2561],{"className":3567},[1951,1952],[1908,3569,3571],{"className":3570},[2167],[1908,3572,3574,3608],{"className":3573},[2171,2172],[1908,3575,3577,3605],{"className":3576},[2176],[1908,3578,3581,3593],{"className":3579,"style":3580},[2180],"height:0.6887em;",[1908,3582,3584,3587],{"style":3583},"top:-2.4413em;margin-left:0em;margin-right:0.05em;",[1908,3585],{"className":3586,"style":2189},[2188],[1908,3588,3590],{"className":3589},[2193,2194,2195,2196],[1908,3591,2107],{"className":3592},[1951,1952,2196],[1908,3594,3596,3599],{"style":3595},"top:-3.063em;margin-right:0.05em;",[1908,3597],{"className":3598,"style":2189},[2188],[1908,3600,3602],{"className":3601},[2193,2194,2195,2196],[1908,3603,3548],{"className":3604},[2392,2196],[1908,3606,2204],{"className":3607},[2203],[1908,3609,3611],{"className":3610},[2176],[1908,3612,3615],{"className":3613,"style":3614},[2180],"height:0.2587em;",[1908,3616],{},"严格占优，如果对所有",[1908,3619,3621,3655],{"className":3620},[1911],[1908,3622,3624],{"className":3623},[1915],[1917,3625,3626],{"xmlns":1919},[1921,3627,3628,3652],{},[1924,3629,3630,3641,3644],{},[3540,3631,3632,3634,3636],{},[1927,3633,2561],{},[1927,3635,2107],{},[1978,3637,3640],{"mathvariant":3638,"lspace":3639,"rspace":3639},"normal","0em","′",[1978,3642,3643],{"mathvariant":3638},"≠",[3540,3645,3646,3648,3650],{},[1927,3647,2561],{},[1927,3649,2107],{},[1978,3651,3548],{},[1931,3653,3654],{"encoding":1933},"s_i' \\neq s_i^*",[1908,3656,3658,3770],{"className":3657,"ariaHidden":1938},[1937],[1908,3659,3661,3665,3720,3723,3767],{"className":3660},[1942],[1908,3662],{"className":3663,"style":3664},[1946],"height:1.0106em;vertical-align:-0.2587em;",[1908,3666,3668,3671],{"className":3667},[1951],[1908,3669,2561],{"className":3670},[1951,1952],[1908,3672,3674],{"className":3673},[2167],[1908,3675,3677,3712],{"className":3676},[2171,2172],[1908,3678,3680,3709],{"className":3679},[2176],[1908,3681,3684,3695],{"className":3682,"style":3683},[2180],"height:0.7519em;",[1908,3685,3686,3689],{"style":3583},[1908,3687],{"className":3688,"style":2189},[2188],[1908,3690,3692],{"className":3691},[2193,2194,2195,2196],[1908,3693,2107],{"className":3694},[1951,1952,2196],[1908,3696,3697,3700],{"style":3595},[1908,3698],{"className":3699,"style":2189},[2188],[1908,3701,3703],{"className":3702},[2193,2194,2195,2196],[1908,3704,3706],{"className":3705},[1951,2196],[1908,3707,3640],{"className":3708},[1951,2196],[1908,3710,2204],{"className":3711},[2203],[1908,3713,3715],{"className":3714},[2176],[1908,3716,3718],{"className":3717,"style":3614},[2180],[1908,3719],{},[1908,3721],{"className":3722,"style":2028},[2027],[1908,3724,3726,3760,3764],{"className":3725},[2032],[1908,3727,3729],{"className":3728},[2032],[1908,3730,3733],{"className":3731},[1951,3732],"vbox",[1908,3734,3737],{"className":3735},[3736],"thinbox",[1908,3738,3741,3745,3756],{"className":3739},[3740],"rlap",[1908,3742],{"className":3743,"style":3744},[1946],"height:0.8889em;vertical-align:-0.1944em;",[1908,3746,3749],{"className":3747},[3748],"inner",[1908,3750,3752],{"className":3751},[1951],[1908,3753,3755],{"className":3754},[2032],"",[1908,3757],{"className":3758},[3759],"fix",[1908,3761],{"className":3762},[2027,3763],"nobreak",[1908,3765,1980],{"className":3766},[2032],[1908,3768],{"className":3769,"style":2028},[2027],[1908,3771,3773,3776],{"className":3772},[1942],[1908,3774],{"className":3775,"style":3561},[1946],[1908,3777,3779,3782],{"className":3778},[1951],[1908,3780,2561],{"className":3781},[1951,1952],[1908,3783,3785],{"className":3784},[2167],[1908,3786,3788,3819],{"className":3787},[2171,2172],[1908,3789,3791,3816],{"className":3790},[2176],[1908,3792,3794,3805],{"className":3793,"style":3580},[2180],[1908,3795,3796,3799],{"style":3583},[1908,3797],{"className":3798,"style":2189},[2188],[1908,3800,3802],{"className":3801},[2193,2194,2195,2196],[1908,3803,2107],{"className":3804},[1951,1952,2196],[1908,3806,3807,3810],{"style":3595},[1908,3808],{"className":3809,"style":2189},[2188],[1908,3811,3813],{"className":3812},[2193,2194,2195,2196],[1908,3814,3548],{"className":3815},[2392,2196],[1908,3817,2204],{"className":3818},[2203],[1908,3820,3822],{"className":3821},[2176],[1908,3823,3825],{"className":3824,"style":3614},[2180],[1908,3826],{},"和所有",[1908,3829,3831,3853],{"className":3830},[1911],[1908,3832,3834],{"className":3833},[1915],[1917,3835,3836],{"xmlns":1919},[1921,3837,3838,3850],{},[1924,3839,3840],{},[2137,3841,3842,3844],{},[1927,3843,2561],{},[1924,3845,3846,3848],{},[1978,3847,2828],{},[1927,3849,2107],{},[1931,3851,3852],{"encoding":1933},"s_{-i}",[1908,3854,3856],{"className":3855,"ariaHidden":1938},[1937],[1908,3857,3859,3862],{"className":3858},[1942],[1908,3860],{"className":3861,"style":2900},[1946],[1908,3863,3865,3868],{"className":3864},[1951],[1908,3866,2561],{"className":3867},[1951,1952],[1908,3869,3871],{"className":3870},[2167],[1908,3872,3874,3900],{"className":3873},[2171,2172],[1908,3875,3877,3897],{"className":3876},[2176],[1908,3878,3880],{"className":3879,"style":2181},[2180],[1908,3881,3882,3885],{"style":2308},[1908,3883],{"className":3884,"style":2189},[2188],[1908,3886,3888],{"className":3887},[2193,2194,2195,2196],[1908,3889,3891,3894],{"className":3890},[1951,2196],[1908,3892,2828],{"className":3893},[1951,2196],[1908,3895,2107],{"className":3896},[1951,1952,2196],[1908,3898,2204],{"className":3899},[2203],[1908,3901,3903],{"className":3902},[2176],[1908,3904,3906],{"className":3905,"style":2945},[2180],[1908,3907],{},"：",[1908,3910,3913],{"className":3911},[3912],"katex-display",[1908,3914,3916,3992],{"className":3915},[1911],[1908,3917,3919],{"className":3918},[1915],[1917,3920,3922],{"xmlns":1919,"display":3921},"block",[1921,3923,3924,3989],{},[1924,3925,3926,3932,3934,3942,3944,3954,3956,3959,3965,3967,3975,3977,3987],{},[2137,3927,3928,3930],{},[1927,3929,2235],{},[1927,3931,2107],{},[1978,3933,2566],{"stretchy":1983},[3540,3935,3936,3938,3940],{},[1927,3937,2561],{},[1927,3939,2107],{},[1978,3941,3548],{},[1978,3943,1991],{"separator":1938},[2137,3945,3946,3948],{},[1927,3947,2561],{},[1924,3949,3950,3952],{},[1978,3951,2828],{},[1927,3953,2107],{},[1978,3955,2595],{"stretchy":1983},[1978,3957,3958],{},">",[2137,3960,3961,3963],{},[1927,3962,2235],{},[1927,3964,2107],{},[1978,3966,2566],{"stretchy":1983},[3540,3968,3969,3971,3973],{},[1927,3970,2561],{},[1927,3972,2107],{},[1978,3974,3640],{"mathvariant":3638,"lspace":3639,"rspace":3639},[1978,3976,1991],{"separator":1938},[2137,3978,3979,3981],{},[1927,3980,2561],{},[1924,3982,3983,3985],{},[1978,3984,2828],{},[1927,3986,2107],{},[1978,3988,2595],{"stretchy":1983},[1931,3990,3991],{"encoding":1933},"u_i(s_i^*, s_{-i}) > u_i(s_i', s_{-i})",[1908,3993,3995,4163],{"className":3994,"ariaHidden":1938},[1937],[1908,3996,3998,4001,4041,4044,4099,4102,4105,4151,4154,4157,4160],{"className":3997},[1942],[1908,3999],{"className":4000,"style":2042},[1946],[1908,4002,4004,4007],{"className":4003},[1951],[1908,4005,2235],{"className":4006},[1951,1952],[1908,4008,4010],{"className":4009},[2167],[1908,4011,4013,4033],{"className":4012},[2171,2172],[1908,4014,4016,4030],{"className":4015},[2176],[1908,4017,4019],{"className":4018,"style":2181},[2180],[1908,4020,4021,4024],{"style":2308},[1908,4022],{"className":4023,"style":2189},[2188],[1908,4025,4027],{"className":4026},[2193,2194,2195,2196],[1908,4028,2107],{"className":4029},[1951,1952,2196],[1908,4031,2204],{"className":4032},[2203],[1908,4034,4036],{"className":4035},[2176],[1908,4037,4039],{"className":4038,"style":2211},[2180],[1908,4040],{},[1908,4042,2566],{"className":4043},[2046],[1908,4045,4047,4050],{"className":4046},[1951],[1908,4048,2561],{"className":4049},[1951,1952],[1908,4051,4053],{"className":4052},[2167],[1908,4054,4056,4090],{"className":4055},[2171,2172],[1908,4057,4059,4087],{"className":4058},[2176],[1908,4060,4063,4075],{"className":4061,"style":4062},[2180],"height:0.7387em;",[1908,4064,4066,4069],{"style":4065},"top:-2.453em;margin-left:0em;margin-right:0.05em;",[1908,4067],{"className":4068,"style":2189},[2188],[1908,4070,4072],{"className":4071},[2193,2194,2195,2196],[1908,4073,2107],{"className":4074},[1951,1952,2196],[1908,4076,4078,4081],{"style":4077},"top:-3.113em;margin-right:0.05em;",[1908,4079],{"className":4080,"style":2189},[2188],[1908,4082,4084],{"className":4083},[2193,2194,2195,2196],[1908,4085,3548],{"className":4086},[2392,2196],[1908,4088,2204],{"className":4089},[2203],[1908,4091,4093],{"className":4092},[2176],[1908,4094,4097],{"className":4095,"style":4096},[2180],"height:0.247em;",[1908,4098],{},[1908,4100,1991],{"className":4101},[2053],[1908,4103],{"className":4104,"style":2057},[2027],[1908,4106,4108,4111],{"className":4107},[1951],[1908,4109,2561],{"className":4110},[1951,1952],[1908,4112,4114],{"className":4113},[2167],[1908,4115,4117,4143],{"className":4116},[2171,2172],[1908,4118,4120,4140],{"className":4119},[2176],[1908,4121,4123],{"className":4122,"style":2181},[2180],[1908,4124,4125,4128],{"style":2308},[1908,4126],{"className":4127,"style":2189},[2188],[1908,4129,4131],{"className":4130},[2193,2194,2195,2196],[1908,4132,4134,4137],{"className":4133},[1951,2196],[1908,4135,2828],{"className":4136},[1951,2196],[1908,4138,2107],{"className":4139},[1951,1952,2196],[1908,4141,2204],{"className":4142},[2203],[1908,4144,4146],{"className":4145},[2176],[1908,4147,4149],{"className":4148,"style":2945},[2180],[1908,4150],{},[1908,4152,2595],{"className":4153},[2086],[1908,4155],{"className":4156,"style":2028},[2027],[1908,4158,3958],{"className":4159},[2032],[1908,4161],{"className":4162,"style":2028},[2027],[1908,4164,4166,4170,4210,4213,4268,4271,4274,4320],{"className":4165},[1942],[1908,4167],{"className":4168,"style":4169},[1946],"height:1.0519em;vertical-align:-0.25em;",[1908,4171,4173,4176],{"className":4172},[1951],[1908,4174,2235],{"className":4175},[1951,1952],[1908,4177,4179],{"className":4178},[2167],[1908,4180,4182,4202],{"className":4181},[2171,2172],[1908,4183,4185,4199],{"className":4184},[2176],[1908,4186,4188],{"className":4187,"style":2181},[2180],[1908,4189,4190,4193],{"style":2308},[1908,4191],{"className":4192,"style":2189},[2188],[1908,4194,4196],{"className":4195},[2193,2194,2195,2196],[1908,4197,2107],{"className":4198},[1951,1952,2196],[1908,4200,2204],{"className":4201},[2203],[1908,4203,4205],{"className":4204},[2176],[1908,4206,4208],{"className":4207,"style":2211},[2180],[1908,4209],{},[1908,4211,2566],{"className":4212},[2046],[1908,4214,4216,4219],{"className":4215},[1951],[1908,4217,2561],{"className":4218},[1951,1952],[1908,4220,4222],{"className":4221},[2167],[1908,4223,4225,4260],{"className":4224},[2171,2172],[1908,4226,4228,4257],{"className":4227},[2176],[1908,4229,4232,4243],{"className":4230,"style":4231},[2180],"height:0.8019em;",[1908,4233,4234,4237],{"style":4065},[1908,4235],{"className":4236,"style":2189},[2188],[1908,4238,4240],{"className":4239},[2193,2194,2195,2196],[1908,4241,2107],{"className":4242},[1951,1952,2196],[1908,4244,4245,4248],{"style":4077},[1908,4246],{"className":4247,"style":2189},[2188],[1908,4249,4251],{"className":4250},[2193,2194,2195,2196],[1908,4252,4254],{"className":4253},[1951,2196],[1908,4255,3640],{"className":4256},[1951,2196],[1908,4258,2204],{"className":4259},[2203],[1908,4261,4263],{"className":4262},[2176],[1908,4264,4266],{"className":4265,"style":4096},[2180],[1908,4267],{},[1908,4269,1991],{"className":4270},[2053],[1908,4272],{"className":4273,"style":2057},[2027],[1908,4275,4277,4280],{"className":4276},[1951],[1908,4278,2561],{"className":4279},[1951,1952],[1908,4281,4283],{"className":4282},[2167],[1908,4284,4286,4312],{"className":4285},[2171,2172],[1908,4287,4289,4309],{"className":4288},[2176],[1908,4290,4292],{"className":4291,"style":2181},[2180],[1908,4293,4294,4297],{"style":2308},[1908,4295],{"className":4296,"style":2189},[2188],[1908,4298,4300],{"className":4299},[2193,2194,2195,2196],[1908,4301,4303,4306],{"className":4302},[1951,2196],[1908,4304,2828],{"className":4305},[1951,2196],[1908,4307,2107],{"className":4308},[1951,1952,2196],[1908,4310,2204],{"className":4311},[2203],[1908,4313,4315],{"className":4314},[2176],[1908,4316,4318],{"className":4317,"style":2945},[2180],[1908,4319],{},[1908,4321,2595],{"className":4322},[2086],[1798,4324,4325,4328,4329,4358,4359],{},[1857,4326,4327],{},"弱占优",": 将",[1908,4330,4332,4345],{"className":4331},[1911],[1908,4333,4335],{"className":4334},[1915],[1917,4336,4337],{"xmlns":1919},[1921,4338,4339,4343],{},[1924,4340,4341],{},[1978,4342,3958],{},[1931,4344,3958],{"encoding":1933},[1908,4346,4348],{"className":4347,"ariaHidden":1938},[1937],[1908,4349,4351,4355],{"className":4350},[1942],[1908,4352],{"className":4353,"style":4354},[1946],"height:0.5782em;vertical-align:-0.0391em;",[1908,4356,3958],{"className":4357},[2032],"替换为",[1908,4360,4362,4377],{"className":4361},[1911],[1908,4363,4365],{"className":4364},[1915],[1917,4366,4367],{"xmlns":1919},[1921,4368,4369,4374],{},[1924,4370,4371],{},[1978,4372,4373],{},"≥",[1931,4375,4376],{"encoding":1933},"\\ge",[1908,4378,4380],{"className":4379,"ariaHidden":1938},[1937],[1908,4381,4383,4387],{"className":4382},[1942],[1908,4384],{"className":4385,"style":4386},[1946],"height:0.7719em;vertical-align:-0.136em;",[1908,4388,4373],{"className":4389},[2032],[1798,4391,4392,3526,4395,4465,4466,4552,4553,3908],{},[1857,4393,4394],{},"严格劣势",[1908,4396,4398,4416],{"className":4397},[1911],[1908,4399,4401],{"className":4400},[1915],[1917,4402,4403],{"xmlns":1919},[1921,4404,4405,4413],{},[1924,4406,4407],{},[2137,4408,4409,4411],{},[1927,4410,2561],{},[1927,4412,2107],{},[1931,4414,4415],{"encoding":1933},"s_i",[1908,4417,4419],{"className":4418,"ariaHidden":1938},[1937],[1908,4420,4422,4425],{"className":4421},[1942],[1908,4423],{"className":4424,"style":2287},[1946],[1908,4426,4428,4431],{"className":4427},[1951],[1908,4429,2561],{"className":4430},[1951,1952],[1908,4432,4434],{"className":4433},[2167],[1908,4435,4437,4457],{"className":4436},[2171,2172],[1908,4438,4440,4454],{"className":4439},[2176],[1908,4441,4443],{"className":4442,"style":2181},[2180],[1908,4444,4445,4448],{"style":2308},[1908,4446],{"className":4447,"style":2189},[2188],[1908,4449,4451],{"className":4450},[2193,2194,2195,2196],[1908,4452,2107],{"className":4453},[1951,1952,2196],[1908,4455,2204],{"className":4456},[2203],[1908,4458,4460],{"className":4459},[2176],[1908,4461,4463],{"className":4462,"style":2211},[2180],[1908,4464],{},"严格劣于",[1908,4467,4469,4489],{"className":4468},[1911],[1908,4470,4472],{"className":4471},[1915],[1917,4473,4474],{"xmlns":1919},[1921,4475,4476,4486],{},[1924,4477,4478],{},[3540,4479,4480,4482,4484],{},[1927,4481,2561],{},[1927,4483,2107],{},[1978,4485,3640],{"mathvariant":3638,"lspace":3639,"rspace":3639},[1931,4487,4488],{"encoding":1933},"s_i'",[1908,4490,4492],{"className":4491,"ariaHidden":1938},[1937],[1908,4493,4495,4498],{"className":4494},[1942],[1908,4496],{"className":4497,"style":3664},[1946],[1908,4499,4501,4504],{"className":4500},[1951],[1908,4502,2561],{"className":4503},[1951,1952],[1908,4505,4507],{"className":4506},[2167],[1908,4508,4510,4544],{"className":4509},[2171,2172],[1908,4511,4513,4541],{"className":4512},[2176],[1908,4514,4516,4527],{"className":4515,"style":3683},[2180],[1908,4517,4518,4521],{"style":3583},[1908,4519],{"className":4520,"style":2189},[2188],[1908,4522,4524],{"className":4523},[2193,2194,2195,2196],[1908,4525,2107],{"className":4526},[1951,1952,2196],[1908,4528,4529,4532],{"style":3595},[1908,4530],{"className":4531,"style":2189},[2188],[1908,4533,4535],{"className":4534},[2193,2194,2195,2196],[1908,4536,4538],{"className":4537},[1951,2196],[1908,4539,3640],{"className":4540},[1951,2196],[1908,4542,2204],{"className":4543},[2203],[1908,4545,4547],{"className":4546},[2176],[1908,4548,4550],{"className":4549,"style":3614},[2180],[1908,4551],{},"，如果对所有",[1908,4554,4556,4577],{"className":4555},[1911],[1908,4557,4559],{"className":4558},[1915],[1917,4560,4561],{"xmlns":1919},[1921,4562,4563,4575],{},[1924,4564,4565],{},[2137,4566,4567,4569],{},[1927,4568,2561],{},[1924,4570,4571,4573],{},[1978,4572,2828],{},[1927,4574,2107],{},[1931,4576,3852],{"encoding":1933},[1908,4578,4580],{"className":4579,"ariaHidden":1938},[1937],[1908,4581,4583,4586],{"className":4582},[1942],[1908,4584],{"className":4585,"style":2900},[1946],[1908,4587,4589,4592],{"className":4588},[1951],[1908,4590,2561],{"className":4591},[1951,1952],[1908,4593,4595],{"className":4594},[2167],[1908,4596,4598,4624],{"className":4597},[2171,2172],[1908,4599,4601,4621],{"className":4600},[2176],[1908,4602,4604],{"className":4603,"style":2181},[2180],[1908,4605,4606,4609],{"style":2308},[1908,4607],{"className":4608,"style":2189},[2188],[1908,4610,4612],{"className":4611},[2193,2194,2195,2196],[1908,4613,4615,4618],{"className":4614},[1951,2196],[1908,4616,2828],{"className":4617},[1951,2196],[1908,4619,2107],{"className":4620},[1951,1952,2196],[1908,4622,2204],{"className":4623},[2203],[1908,4625,4627],{"className":4626},[2176],[1908,4628,4630],{"className":4629,"style":2945},[2180],[1908,4631],{},[1908,4633,4635],{"className":4634},[3912],[1908,4636,4638,4711],{"className":4637},[1911],[1908,4639,4641],{"className":4640},[1915],[1917,4642,4643],{"xmlns":1919,"display":3921},[1921,4644,4645,4708],{},[1924,4646,4647,4653,4655,4661,4663,4673,4675,4678,4684,4686,4694,4696,4706],{},[2137,4648,4649,4651],{},[1927,4650,2235],{},[1927,4652,2107],{},[1978,4654,2566],{"stretchy":1983},[2137,4656,4657,4659],{},[1927,4658,2561],{},[1927,4660,2107],{},[1978,4662,1991],{"separator":1938},[2137,4664,4665,4667],{},[1927,4666,2561],{},[1924,4668,4669,4671],{},[1978,4670,2828],{},[1927,4672,2107],{},[1978,4674,2595],{"stretchy":1983},[1978,4676,4677],{},"\u003C",[2137,4679,4680,4682],{},[1927,4681,2235],{},[1927,4683,2107],{},[1978,4685,2566],{"stretchy":1983},[3540,4687,4688,4690,4692],{},[1927,4689,2561],{},[1927,4691,2107],{},[1978,4693,3640],{"mathvariant":3638,"lspace":3639,"rspace":3639},[1978,4695,1991],{"separator":1938},[2137,4697,4698,4700],{},[1927,4699,2561],{},[1924,4701,4702,4704],{},[1978,4703,2828],{},[1927,4705,2107],{},[1978,4707,2595],{"stretchy":1983},[1931,4709,4710],{"encoding":1933},"u_i(s_i, s_{-i}) \u003C u_i(s_i', s_{-i})",[1908,4712,4714,4867],{"className":4713,"ariaHidden":1938},[1937],[1908,4715,4717,4720,4760,4763,4803,4806,4809,4855,4858,4861,4864],{"className":4716},[1942],[1908,4718],{"className":4719,"style":2042},[1946],[1908,4721,4723,4726],{"className":4722},[1951],[1908,4724,2235],{"className":4725},[1951,1952],[1908,4727,4729],{"className":4728},[2167],[1908,4730,4732,4752],{"className":4731},[2171,2172],[1908,4733,4735,4749],{"className":4734},[2176],[1908,4736,4738],{"className":4737,"style":2181},[2180],[1908,4739,4740,4743],{"style":2308},[1908,4741],{"className":4742,"style":2189},[2188],[1908,4744,4746],{"className":4745},[2193,2194,2195,2196],[1908,4747,2107],{"className":4748},[1951,1952,2196],[1908,4750,2204],{"className":4751},[2203],[1908,4753,4755],{"className":4754},[2176],[1908,4756,4758],{"className":4757,"style":2211},[2180],[1908,4759],{},[1908,4761,2566],{"className":4762},[2046],[1908,4764,4766,4769],{"className":4765},[1951],[1908,4767,2561],{"className":4768},[1951,1952],[1908,4770,4772],{"className":4771},[2167],[1908,4773,4775,4795],{"className":4774},[2171,2172],[1908,4776,4778,4792],{"className":4777},[2176],[1908,4779,4781],{"className":4780,"style":2181},[2180],[1908,4782,4783,4786],{"style":2308},[1908,4784],{"className":4785,"style":2189},[2188],[1908,4787,4789],{"className":4788},[2193,2194,2195,2196],[1908,4790,2107],{"className":4791},[1951,1952,2196],[1908,4793,2204],{"className":4794},[2203],[1908,4796,4798],{"className":4797},[2176],[1908,4799,4801],{"className":4800,"style":2211},[2180],[1908,4802],{},[1908,4804,1991],{"className":4805},[2053],[1908,4807],{"className":4808,"style":2057},[2027],[1908,4810,4812,4815],{"className":4811},[1951],[1908,4813,2561],{"className":4814},[1951,1952],[1908,4816,4818],{"className":4817},[2167],[1908,4819,4821,4847],{"className":4820},[2171,2172],[1908,4822,4824,4844],{"className":4823},[2176],[1908,4825,4827],{"className":4826,"style":2181},[2180],[1908,4828,4829,4832],{"style":2308},[1908,4830],{"className":4831,"style":2189},[2188],[1908,4833,4835],{"className":4834},[2193,2194,2195,2196],[1908,4836,4838,4841],{"className":4837},[1951,2196],[1908,4839,2828],{"className":4840},[1951,2196],[1908,4842,2107],{"className":4843},[1951,1952,2196],[1908,4845,2204],{"className":4846},[2203],[1908,4848,4850],{"className":4849},[2176],[1908,4851,4853],{"className":4852,"style":2945},[2180],[1908,4854],{},[1908,4856,2595],{"className":4857},[2086],[1908,4859],{"className":4860,"style":2028},[2027],[1908,4862,4677],{"className":4863},[2032],[1908,4865],{"className":4866,"style":2028},[2027],[1908,4868,4870,4873,4913,4916,4970,4973,4976,5022],{"className":4869},[1942],[1908,4871],{"className":4872,"style":4169},[1946],[1908,4874,4876,4879],{"className":4875},[1951],[1908,4877,2235],{"className":4878},[1951,1952],[1908,4880,4882],{"className":4881},[2167],[1908,4883,4885,4905],{"className":4884},[2171,2172],[1908,4886,4888,4902],{"className":4887},[2176],[1908,4889,4891],{"className":4890,"style":2181},[2180],[1908,4892,4893,4896],{"style":2308},[1908,4894],{"className":4895,"style":2189},[2188],[1908,4897,4899],{"className":4898},[2193,2194,2195,2196],[1908,4900,2107],{"className":4901},[1951,1952,2196],[1908,4903,2204],{"className":4904},[2203],[1908,4906,4908],{"className":4907},[2176],[1908,4909,4911],{"className":4910,"style":2211},[2180],[1908,4912],{},[1908,4914,2566],{"className":4915},[2046],[1908,4917,4919,4922],{"className":4918},[1951],[1908,4920,2561],{"className":4921},[1951,1952],[1908,4923,4925],{"className":4924},[2167],[1908,4926,4928,4962],{"className":4927},[2171,2172],[1908,4929,4931,4959],{"className":4930},[2176],[1908,4932,4934,4945],{"className":4933,"style":4231},[2180],[1908,4935,4936,4939],{"style":4065},[1908,4937],{"className":4938,"style":2189},[2188],[1908,4940,4942],{"className":4941},[2193,2194,2195,2196],[1908,4943,2107],{"className":4944},[1951,1952,2196],[1908,4946,4947,4950],{"style":4077},[1908,4948],{"className":4949,"style":2189},[2188],[1908,4951,4953],{"className":4952},[2193,2194,2195,2196],[1908,4954,4956],{"className":4955},[1951,2196],[1908,4957,3640],{"className":4958},[1951,2196],[1908,4960,2204],{"className":4961},[2203],[1908,4963,4965],{"className":4964},[2176],[1908,4966,4968],{"className":4967,"style":4096},[2180],[1908,4969],{},[1908,4971,1991],{"className":4972},[2053],[1908,4974],{"className":4975,"style":2057},[2027],[1908,4977,4979,4982],{"className":4978},[1951],[1908,4980,2561],{"className":4981},[1951,1952],[1908,4983,4985],{"className":4984},[2167],[1908,4986,4988,5014],{"className":4987},[2171,2172],[1908,4989,4991,5011],{"className":4990},[2176],[1908,4992,4994],{"className":4993,"style":2181},[2180],[1908,4995,4996,4999],{"style":2308},[1908,4997],{"className":4998,"style":2189},[2188],[1908,5000,5002],{"className":5001},[2193,2194,2195,2196],[1908,5003,5005,5008],{"className":5004},[1951,2196],[1908,5006,2828],{"className":5007},[1951,2196],[1908,5009,2107],{"className":5010},[1951,1952,2196],[1908,5012,2204],{"className":5013},[2203],[1908,5015,5017],{"className":5016},[2176],[1908,5018,5020],{"className":5019,"style":2945},[2180],[1908,5021],{},[1908,5023,2595],{"className":5024},[2086],[1798,5026,5027,1860],{},[1857,5028,5029],{},"囚徒困境分析",[1805,5031,5032,5043,5046],{},[1808,5033,5034,5035],{},"对参与者1：无论参与者2选择什么，背叛(D)总是优于合作(C)\n",[1805,5036,5037,5040],{},[1808,5038,5039],{},"如果2选C：D得到0 > C得到-1",[1808,5041,5042],{},"如果2选D：D得到-2 > C得到-3",[1808,5044,5045],{},"同理，对参与者2，D也是占优策略",[1808,5047,5048,5051],{},[1857,5049,5050],{},"占优策略均衡",": (D, D)",[1798,5053,5054,5057],{},[1857,5055,5056],{},"理性悖论",": 双方都理性地选择背叛，结果(-2, -2)却劣于双方合作(-1, -1)！这展示了个体理性与集体理性的冲突。",[1897,5059,5061],{"id":5060},"_22-纳什均衡的定义","2.2 纳什均衡的定义",[1798,5063,5064,5066,5067,5365,5366,3908],{},[1857,5065,1905],{},": 策略组合",[1908,5068,5070,5127],{"className":5069},[1911],[1908,5071,5073],{"className":5072},[1915],[1917,5074,5075],{"xmlns":1919},[1921,5076,5077,5124],{},[1924,5078,5079,5086,5088,5090,5098,5100,5108,5110,5112,5114,5122],{},[5080,5081,5082,5084],"msup",{},[1927,5083,2561],{},[1978,5085,3548],{},[1978,5087,1980],{},[1978,5089,2566],{"stretchy":1983},[3540,5091,5092,5094,5096],{},[1927,5093,2561],{},[1986,5095,1988],{},[1978,5097,3548],{},[1978,5099,1991],{"separator":1938},[3540,5101,5102,5104,5106],{},[1927,5103,2561],{},[1986,5105,1994],{},[1978,5107,3548],{},[1978,5109,1991],{"separator":1938},[1978,5111,1999],{},[1978,5113,1991],{"separator":1938},[3540,5115,5116,5118,5120],{},[1927,5117,2561],{},[1927,5119,1929],{},[1978,5121,3548],{},[1978,5123,2595],{"stretchy":1983},[1931,5125,5126],{"encoding":1933},"s^* = (s_1^*, s_2^*, \\ldots, s_n^*)",[1908,5128,5130,5174],{"className":5129,"ariaHidden":1938},[1937],[1908,5131,5133,5136,5165,5168,5171],{"className":5132},[1942],[1908,5134],{"className":5135,"style":3580},[1946],[1908,5137,5139,5142],{"className":5138},[1951],[1908,5140,2561],{"className":5141},[1951,1952],[1908,5143,5145],{"className":5144},[2167],[1908,5146,5148],{"className":5147},[2171],[1908,5149,5151],{"className":5150},[2176],[1908,5152,5154],{"className":5153,"style":3580},[2180],[1908,5155,5156,5159],{"style":3595},[1908,5157],{"className":5158,"style":2189},[2188],[1908,5160,5162],{"className":5161},[2193,2194,2195,2196],[1908,5163,3548],{"className":5164},[2392,2196],[1908,5166],{"className":5167,"style":2028},[2027],[1908,5169,1980],{"className":5170},[2032],[1908,5172],{"className":5173,"style":2028},[2027],[1908,5175,5177,5180,5183,5236,5239,5242,5293,5296,5299,5302,5305,5308,5311,5362],{"className":5176},[1942],[1908,5178],{"className":5179,"style":2042},[1946],[1908,5181,2566],{"className":5182},[2046],[1908,5184,5186,5189],{"className":5185},[1951],[1908,5187,2561],{"className":5188},[1951,1952],[1908,5190,5192],{"className":5191},[2167],[1908,5193,5195,5227],{"className":5194},[2171,2172],[1908,5196,5198,5224],{"className":5197},[2176],[1908,5199,5201,5213],{"className":5200,"style":3580},[2180],[1908,5202,5204,5207],{"style":5203},"top:-2.4519em;margin-left:0em;margin-right:0.05em;",[1908,5205],{"className":5206,"style":2189},[2188],[1908,5208,5210],{"className":5209},[2193,2194,2195,2196],[1908,5211,1988],{"className":5212},[1951,2196],[1908,5214,5215,5218],{"style":3595},[1908,5216],{"className":5217,"style":2189},[2188],[1908,5219,5221],{"className":5220},[2193,2194,2195,2196],[1908,5222,3548],{"className":5223},[2392,2196],[1908,5225,2204],{"className":5226},[2203],[1908,5228,5230],{"className":5229},[2176],[1908,5231,5234],{"className":5232,"style":5233},[2180],"height:0.2481em;",[1908,5235],{},[1908,5237,1991],{"className":5238},[2053],[1908,5240],{"className":5241,"style":2057},[2027],[1908,5243,5245,5248],{"className":5244},[1951],[1908,5246,2561],{"className":5247},[1951,1952],[1908,5249,5251],{"className":5250},[2167],[1908,5252,5254,5285],{"className":5253},[2171,2172],[1908,5255,5257,5282],{"className":5256},[2176],[1908,5258,5260,5271],{"className":5259,"style":3580},[2180],[1908,5261,5262,5265],{"style":5203},[1908,5263],{"className":5264,"style":2189},[2188],[1908,5266,5268],{"className":5267},[2193,2194,2195,2196],[1908,5269,1994],{"className":5270},[1951,2196],[1908,5272,5273,5276],{"style":3595},[1908,5274],{"className":5275,"style":2189},[2188],[1908,5277,5279],{"className":5278},[2193,2194,2195,2196],[1908,5280,3548],{"className":5281},[2392,2196],[1908,5283,2204],{"className":5284},[2203],[1908,5286,5288],{"className":5287},[2176],[1908,5289,5291],{"className":5290,"style":5233},[2180],[1908,5292],{},[1908,5294,1991],{"className":5295},[2053],[1908,5297],{"className":5298,"style":2057},[2027],[1908,5300,1999],{"className":5301},[2070],[1908,5303],{"className":5304,"style":2057},[2027],[1908,5306,1991],{"className":5307},[2053],[1908,5309],{"className":5310,"style":2057},[2027],[1908,5312,5314,5317],{"className":5313},[1951],[1908,5315,2561],{"className":5316},[1951,1952],[1908,5318,5320],{"className":5319},[2167],[1908,5321,5323,5354],{"className":5322},[2171,2172],[1908,5324,5326,5351],{"className":5325},[2176],[1908,5327,5329,5340],{"className":5328,"style":3580},[2180],[1908,5330,5331,5334],{"style":4065},[1908,5332],{"className":5333,"style":2189},[2188],[1908,5335,5337],{"className":5336},[2193,2194,2195,2196],[1908,5338,1929],{"className":5339},[1951,1952,2196],[1908,5341,5342,5345],{"style":3595},[1908,5343],{"className":5344,"style":2189},[2188],[1908,5346,5348],{"className":5347},[2193,2194,2195,2196],[1908,5349,3548],{"className":5350},[2392,2196],[1908,5352,2204],{"className":5353},[2203],[1908,5355,5357],{"className":5356},[2176],[1908,5358,5360],{"className":5359,"style":4096},[2180],[1908,5361],{},[1908,5363,2595],{"className":5364},[2086],"是纳什均衡，如果对每个参与者",[1908,5367,5369,5382],{"className":5368},[1911],[1908,5370,5372],{"className":5371},[1915],[1917,5373,5374],{"xmlns":1919},[1921,5375,5376,5380],{},[1924,5377,5378],{},[1927,5379,2107],{},[1931,5381,2107],{"encoding":1933},[1908,5383,5385],{"className":5384,"ariaHidden":1938},[1937],[1908,5386,5388,5391],{"className":5387},[1942],[1908,5389],{"className":5390,"style":2119},[1946],[1908,5392,2107],{"className":5393},[1951,1952],[1908,5395,5397],{"className":5396},[3912],[1908,5398,5400,5499],{"className":5399},[1911],[1908,5401,5403],{"className":5402},[1915],[1917,5404,5405],{"xmlns":1919,"display":3921},[1921,5406,5407,5496],{},[1924,5408,5409,5415,5417,5425,5427,5439,5441,5443,5449,5451,5457,5459,5471,5473,5475,5478,5481,5487,5490],{},[2137,5410,5411,5413],{},[1927,5412,2235],{},[1927,5414,2107],{},[1978,5416,2566],{"stretchy":1983},[3540,5418,5419,5421,5423],{},[1927,5420,2561],{},[1927,5422,2107],{},[1978,5424,3548],{},[1978,5426,1991],{"separator":1938},[3540,5428,5429,5431,5437],{},[1927,5430,2561],{},[1924,5432,5433,5435],{},[1978,5434,2828],{},[1927,5436,2107],{},[1978,5438,3548],{},[1978,5440,2595],{"stretchy":1983},[1978,5442,4373],{},[2137,5444,5445,5447],{},[1927,5446,2235],{},[1927,5448,2107],{},[1978,5450,2566],{"stretchy":1983},[2137,5452,5453,5455],{},[1927,5454,2561],{},[1927,5456,2107],{},[1978,5458,1991],{"separator":1938},[3540,5460,5461,5463,5469],{},[1927,5462,2561],{},[1924,5464,5465,5467],{},[1978,5466,2828],{},[1927,5468,2107],{},[1978,5470,3548],{},[1978,5472,2595],{"stretchy":1983},[1978,5474,1991],{"separator":1938},[2027,5476],{"width":5477},"1em",[1927,5479,5480],{"mathvariant":3638},"∀",[2137,5482,5483,5485],{},[1927,5484,2561],{},[1927,5486,2107],{},[1978,5488,5489],{},"∈",[2137,5491,5492,5494],{},[1927,5493,2141],{},[1927,5495,2107],{},[1931,5497,5498],{"encoding":1933},"u_i(s_i^*, s_{-i}^*) \\ge u_i(s_i, s_{-i}^*), \\quad \\forall s_i \\in S_i",[1908,5500,5502,5679,5896],{"className":5501,"ariaHidden":1938},[1937],[1908,5503,5505,5509,5549,5552,5603,5606,5609,5667,5670,5673,5676],{"className":5504},[1942],[1908,5506],{"className":5507,"style":5508},[1946],"height:1.0553em;vertical-align:-0.3053em;",[1908,5510,5512,5515],{"className":5511},[1951],[1908,5513,2235],{"className":5514},[1951,1952],[1908,5516,5518],{"className":5517},[2167],[1908,5519,5521,5541],{"className":5520},[2171,2172],[1908,5522,5524,5538],{"className":5523},[2176],[1908,5525,5527],{"className":5526,"style":2181},[2180],[1908,5528,5529,5532],{"style":2308},[1908,5530],{"className":5531,"style":2189},[2188],[1908,5533,5535],{"className":5534},[2193,2194,2195,2196],[1908,5536,2107],{"className":5537},[1951,1952,2196],[1908,5539,2204],{"className":5540},[2203],[1908,5542,5544],{"className":5543},[2176],[1908,5545,5547],{"className":5546,"style":2211},[2180],[1908,5548],{},[1908,5550,2566],{"className":5551},[2046],[1908,5553,5555,5558],{"className":5554},[1951],[1908,5556,2561],{"className":5557},[1951,1952],[1908,5559,5561],{"className":5560},[2167],[1908,5562,5564,5595],{"className":5563},[2171,2172],[1908,5565,5567,5592],{"className":5566},[2176],[1908,5568,5570,5581],{"className":5569,"style":4062},[2180],[1908,5571,5572,5575],{"style":4065},[1908,5573],{"className":5574,"style":2189},[2188],[1908,5576,5578],{"className":5577},[2193,2194,2195,2196],[1908,5579,2107],{"className":5580},[1951,1952,2196],[1908,5582,5583,5586],{"style":4077},[1908,5584],{"className":5585,"style":2189},[2188],[1908,5587,5589],{"className":5588},[2193,2194,2195,2196],[1908,5590,3548],{"className":5591},[2392,2196],[1908,5593,2204],{"className":5594},[2203],[1908,5596,5598],{"className":5597},[2176],[1908,5599,5601],{"className":5600,"style":4096},[2180],[1908,5602],{},[1908,5604,1991],{"className":5605},[2053],[1908,5607],{"className":5608,"style":2057},[2027],[1908,5610,5612,5615],{"className":5611},[1951],[1908,5613,2561],{"className":5614},[1951,1952],[1908,5616,5618],{"className":5617},[2167],[1908,5619,5621,5658],{"className":5620},[2171,2172],[1908,5622,5624,5655],{"className":5623},[2176],[1908,5625,5627,5644],{"className":5626,"style":4062},[2180],[1908,5628,5629,5632],{"style":4065},[1908,5630],{"className":5631,"style":2189},[2188],[1908,5633,5635],{"className":5634},[2193,2194,2195,2196],[1908,5636,5638,5641],{"className":5637},[1951,2196],[1908,5639,2828],{"className":5640},[1951,2196],[1908,5642,2107],{"className":5643},[1951,1952,2196],[1908,5645,5646,5649],{"style":4077},[1908,5647],{"className":5648,"style":2189},[2188],[1908,5650,5652],{"className":5651},[2193,2194,2195,2196],[1908,5653,3548],{"className":5654},[2392,2196],[1908,5656,2204],{"className":5657},[2203],[1908,5659,5661],{"className":5660},[2176],[1908,5662,5665],{"className":5663,"style":5664},[2180],"height:0.3053em;",[1908,5666],{},[1908,5668,2595],{"className":5669},[2086],[1908,5671],{"className":5672,"style":2028},[2027],[1908,5674,4373],{"className":5675},[2032],[1908,5677],{"className":5678,"style":2028},[2027],[1908,5680,5682,5685,5725,5728,5768,5771,5774,5831,5834,5837,5841,5844,5847,5887,5890,5893],{"className":5681},[1942],[1908,5683],{"className":5684,"style":5508},[1946],[1908,5686,5688,5691],{"className":5687},[1951],[1908,5689,2235],{"className":5690},[1951,1952],[1908,5692,5694],{"className":5693},[2167],[1908,5695,5697,5717],{"className":5696},[2171,2172],[1908,5698,5700,5714],{"className":5699},[2176],[1908,5701,5703],{"className":5702,"style":2181},[2180],[1908,5704,5705,5708],{"style":2308},[1908,5706],{"className":5707,"style":2189},[2188],[1908,5709,5711],{"className":5710},[2193,2194,2195,2196],[1908,5712,2107],{"className":5713},[1951,1952,2196],[1908,5715,2204],{"className":5716},[2203],[1908,5718,5720],{"className":5719},[2176],[1908,5721,5723],{"className":5722,"style":2211},[2180],[1908,5724],{},[1908,5726,2566],{"className":5727},[2046],[1908,5729,5731,5734],{"className":5730},[1951],[1908,5732,2561],{"className":5733},[1951,1952],[1908,5735,5737],{"className":5736},[2167],[1908,5738,5740,5760],{"className":5739},[2171,2172],[1908,5741,5743,5757],{"className":5742},[2176],[1908,5744,5746],{"className":5745,"style":2181},[2180],[1908,5747,5748,5751],{"style":2308},[1908,5749],{"className":5750,"style":2189},[2188],[1908,5752,5754],{"className":5753},[2193,2194,2195,2196],[1908,5755,2107],{"className":5756},[1951,1952,2196],[1908,5758,2204],{"className":5759},[2203],[1908,5761,5763],{"className":5762},[2176],[1908,5764,5766],{"className":5765,"style":2211},[2180],[1908,5767],{},[1908,5769,1991],{"className":5770},[2053],[1908,5772],{"className":5773,"style":2057},[2027],[1908,5775,5777,5780],{"className":5776},[1951],[1908,5778,2561],{"className":5779},[1951,1952],[1908,5781,5783],{"className":5782},[2167],[1908,5784,5786,5823],{"className":5785},[2171,2172],[1908,5787,5789,5820],{"className":5788},[2176],[1908,5790,5792,5809],{"className":5791,"style":4062},[2180],[1908,5793,5794,5797],{"style":4065},[1908,5795],{"className":5796,"style":2189},[2188],[1908,5798,5800],{"className":5799},[2193,2194,2195,2196],[1908,5801,5803,5806],{"className":5802},[1951,2196],[1908,5804,2828],{"className":5805},[1951,2196],[1908,5807,2107],{"className":5808},[1951,1952,2196],[1908,5810,5811,5814],{"style":4077},[1908,5812],{"className":5813,"style":2189},[2188],[1908,5815,5817],{"className":5816},[2193,2194,2195,2196],[1908,5818,3548],{"className":5819},[2392,2196],[1908,5821,2204],{"className":5822},[2203],[1908,5824,5826],{"className":5825},[2176],[1908,5827,5829],{"className":5828,"style":5664},[2180],[1908,5830],{},[1908,5832,2595],{"className":5833},[2086],[1908,5835,1991],{"className":5836},[2053],[1908,5838],{"className":5839,"style":5840},[2027],"margin-right:1em;",[1908,5842],{"className":5843,"style":2057},[2027],[1908,5845,5480],{"className":5846},[1951],[1908,5848,5850,5853],{"className":5849},[1951],[1908,5851,2561],{"className":5852},[1951,1952],[1908,5854,5856],{"className":5855},[2167],[1908,5857,5859,5879],{"className":5858},[2171,2172],[1908,5860,5862,5876],{"className":5861},[2176],[1908,5863,5865],{"className":5864,"style":2181},[2180],[1908,5866,5867,5870],{"style":2308},[1908,5868],{"className":5869,"style":2189},[2188],[1908,5871,5873],{"className":5872},[2193,2194,2195,2196],[1908,5874,2107],{"className":5875},[1951,1952,2196],[1908,5877,2204],{"className":5878},[2203],[1908,5880,5882],{"className":5881},[2176],[1908,5883,5885],{"className":5884,"style":2211},[2180],[1908,5886],{},[1908,5888],{"className":5889,"style":2028},[2027],[1908,5891,5489],{"className":5892},[2032],[1908,5894],{"className":5895,"style":2028},[2027],[1908,5897,5899,5902],{"className":5898},[1942],[1908,5900],{"className":5901,"style":2156},[1946],[1908,5903,5905,5908],{"className":5904},[1951],[1908,5906,2141],{"className":5907,"style":2163},[1951,1952],[1908,5909,5911],{"className":5910},[2167],[1908,5912,5914,5934],{"className":5913},[2171,2172],[1908,5915,5917,5931],{"className":5916},[2176],[1908,5918,5920],{"className":5919,"style":2181},[2180],[1908,5921,5922,5925],{"style":2184},[1908,5923],{"className":5924,"style":2189},[2188],[1908,5926,5928],{"className":5927},[2193,2194,2195,2196],[1908,5929,2107],{"className":5930},[1951,1952,2196],[1908,5932,2204],{"className":5933},[2203],[1908,5935,5937],{"className":5936},[2176],[1908,5938,5940],{"className":5939,"style":2211},[2180],[1908,5941],{},[1798,5943,5944,5947],{},[1857,5945,5946],{},"直觉",": 纳什均衡是一种\"稳定\"状态——给定其他人的策略，没有人有动机单方面偏离。",[1798,5949,5950,1860],{},[1857,5951,5952],{},"重要性质",[1875,5954,5955,5958,5961,5964],{},[1808,5956,5957],{},"占优策略均衡必然是纳什均衡",[1808,5959,5960],{},"纳什均衡未必是占优策略均衡",[1808,5962,5963],{},"纳什均衡未必帕累托有效（囚徒困境）",[1808,5965,5966],{},"纳什均衡可能不唯一",[1897,5968,5970],{"id":5969},"_23-寻找纯策略纳什均衡","2.3 寻找纯策略纳什均衡",[1798,5972,5973],{},[1857,5974,5975],{},"方法1: 下划线法",[1798,5977,5978],{},"在每个参与者的每个策略下，对其他参与者的每种策略组合，找到该参与者的最优反应并划线。两条线都划的格子就是纳什均衡。",[1798,5980,5981],{},[1857,5982,5983],{},"方法2: 最优反应函数",[1798,5985,5986,5987,6015],{},"定义参与者",[1908,5988,5990,6003],{"className":5989},[1911],[1908,5991,5993],{"className":5992},[1915],[1917,5994,5995],{"xmlns":1919},[1921,5996,5997,6001],{},[1924,5998,5999],{},[1927,6000,2107],{},[1931,6002,2107],{"encoding":1933},[1908,6004,6006],{"className":6005,"ariaHidden":1938},[1937],[1908,6007,6009,6012],{"className":6008},[1942],[1908,6010],{"className":6011,"style":2119},[1946],[1908,6013,2107],{"className":6014},[1951,1952],"的最优反应函数：",[1908,6017,6019],{"className":6018},[3912],[1908,6020,6022,6119],{"className":6021},[1911],[1908,6023,6025],{"className":6024},[1915],[1917,6026,6027],{"xmlns":1919,"display":3921},[1921,6028,6029,6116],{},[1924,6030,6031,6034,6040,6042,6052,6054,6056,6059,6062,6088,6094,6096,6102,6104,6114],{},[1927,6032,6033],{},"B",[2137,6035,6036,6038],{},[1927,6037,2274],{},[1927,6039,2107],{},[1978,6041,2566],{"stretchy":1983},[2137,6043,6044,6046],{},[1927,6045,2561],{},[1924,6047,6048,6050],{},[1978,6049,2828],{},[1927,6051,2107],{},[1978,6053,2595],{"stretchy":1983},[1978,6055,1980],{},[1927,6057,6058],{},"arg",[1978,6060,6061],{},"⁡",[6063,6064,6065,6072],"munder",{},[1924,6066,6067,6070],{},[1927,6068,6069],{},"max",[1978,6071,6061],{},[1924,6073,6074,6080,6082],{},[2137,6075,6076,6078],{},[1927,6077,2561],{},[1927,6079,2107],{},[1978,6081,5489],{},[2137,6083,6084,6086],{},[1927,6085,2141],{},[1927,6087,2107],{},[2137,6089,6090,6092],{},[1927,6091,2235],{},[1927,6093,2107],{},[1978,6095,2566],{"stretchy":1983},[2137,6097,6098,6100],{},[1927,6099,2561],{},[1927,6101,2107],{},[1978,6103,1991],{"separator":1938},[2137,6105,6106,6108],{},[1927,6107,2561],{},[1924,6109,6110,6112],{},[1978,6111,2828],{},[1927,6113,2107],{},[1978,6115,2595],{"stretchy":1983},[1931,6117,6118],{"encoding":1933},"BR_i(s_{-i}) = \\arg\\max_{s_i \\in S_i} u_i(s_i, s_{-i})",[1908,6120,6122,6235],{"className":6121,"ariaHidden":1938},[1937],[1908,6123,6125,6128,6132,6174,6177,6223,6226,6229,6232],{"className":6124},[1942],[1908,6126],{"className":6127,"style":2042},[1946],[1908,6129,6033],{"className":6130,"style":6131},[1951,1952],"margin-right:0.0502em;",[1908,6133,6135,6139],{"className":6134},[1951],[1908,6136,2274],{"className":6137,"style":6138},[1951,1952],"margin-right:0.0077em;",[1908,6140,6142],{"className":6141},[2167],[1908,6143,6145,6166],{"className":6144},[2171,2172],[1908,6146,6148,6163],{"className":6147},[2176],[1908,6149,6151],{"className":6150,"style":2181},[2180],[1908,6152,6154,6157],{"style":6153},"top:-2.55em;margin-left:-0.0077em;margin-right:0.05em;",[1908,6155],{"className":6156,"style":2189},[2188],[1908,6158,6160],{"className":6159},[2193,2194,2195,2196],[1908,6161,2107],{"className":6162},[1951,1952,2196],[1908,6164,2204],{"className":6165},[2203],[1908,6167,6169],{"className":6168},[2176],[1908,6170,6172],{"className":6171,"style":2211},[2180],[1908,6173],{},[1908,6175,2566],{"className":6176},[2046],[1908,6178,6180,6183],{"className":6179},[1951],[1908,6181,2561],{"className":6182},[1951,1952],[1908,6184,6186],{"className":6185},[2167],[1908,6187,6189,6215],{"className":6188},[2171,2172],[1908,6190,6192,6212],{"className":6191},[2176],[1908,6193,6195],{"className":6194,"style":2181},[2180],[1908,6196,6197,6200],{"style":2308},[1908,6198],{"className":6199,"style":2189},[2188],[1908,6201,6203],{"className":6202},[2193,2194,2195,2196],[1908,6204,6206,6209],{"className":6205},[1951,2196],[1908,6207,2828],{"className":6208},[1951,2196],[1908,6210,2107],{"className":6211},[1951,1952,2196],[1908,6213,2204],{"className":6214},[2203],[1908,6216,6218],{"className":6217},[2176],[1908,6219,6221],{"className":6220,"style":2945},[2180],[1908,6222],{},[1908,6224,2595],{"className":6225},[2086],[1908,6227],{"className":6228,"style":2028},[2027],[1908,6230,1980],{"className":6231},[2032],[1908,6233],{"className":6234,"style":2028},[2027],[1908,6236,6238,6242,6251,6254,6393,6396,6436,6439,6479,6482,6485,6531],{"className":6237},[1942],[1908,6239],{"className":6240,"style":6241},[1946],"height:1.5944em;vertical-align:-0.8444em;",[1908,6243,6246,6247],{"className":6244},[6245],"mop","ar",[1908,6248,6250],{"style":6249},"margin-right:0.0139em;","g",[1908,6252],{"className":6253,"style":2057},[2027],[1908,6255,6258],{"className":6256},[6245,6257],"op-limits",[1908,6259,6261,6384],{"className":6260},[2171,2172],[1908,6262,6264,6381],{"className":6263},[2176],[1908,6265,6267,6370],{"className":6266,"style":1947},[2180],[1908,6268,6270,6274],{"style":6269},"top:-2.3557em;margin-left:0em;",[1908,6271],{"className":6272,"style":6273},[2188],"height:3em;",[1908,6275,6277],{"className":6276},[2193,2194,2195,2196],[1908,6278,6280,6326,6329],{"className":6279},[1951,2196],[1908,6281,6283,6286],{"className":6282},[1951,2196],[1908,6284,2561],{"className":6285},[1951,1952,2196],[1908,6287,6289],{"className":6288},[2167],[1908,6290,6292,6317],{"className":6291},[2171,2172],[1908,6293,6295,6314],{"className":6294},[2176],[1908,6296,6299],{"className":6297,"style":6298},[2180],"height:0.3281em;",[1908,6300,6302,6306],{"style":6301},"top:-2.357em;margin-left:0em;margin-right:0.0714em;",[1908,6303],{"className":6304,"style":6305},[2188],"height:2.5em;",[1908,6307,6311],{"className":6308},[2193,6309,6310,2196],"reset-size3","size1",[1908,6312,2107],{"className":6313},[1951,1952,2196],[1908,6315,2204],{"className":6316},[2203],[1908,6318,6320],{"className":6319},[2176],[1908,6321,6324],{"className":6322,"style":6323},[2180],"height:0.143em;",[1908,6325],{},[1908,6327,5489],{"className":6328},[2032,2196],[1908,6330,6332,6335],{"className":6331},[1951,2196],[1908,6333,2141],{"className":6334,"style":2163},[1951,1952,2196],[1908,6336,6338],{"className":6337},[2167],[1908,6339,6341,6362],{"className":6340},[2171,2172],[1908,6342,6344,6359],{"className":6343},[2176],[1908,6345,6347],{"className":6346,"style":6298},[2180],[1908,6348,6350,6353],{"style":6349},"top:-2.357em;margin-left:-0.0576em;margin-right:0.0714em;",[1908,6351],{"className":6352,"style":6305},[2188],[1908,6354,6356],{"className":6355},[2193,6309,6310,2196],[1908,6357,2107],{"className":6358},[1951,1952,2196],[1908,6360,2204],{"className":6361},[2203],[1908,6363,6365],{"className":6364},[2176],[1908,6366,6368],{"className":6367,"style":6323},[2180],[1908,6369],{},[1908,6371,6373,6376],{"style":6372},"top:-3em;",[1908,6374],{"className":6375,"style":6273},[2188],[1908,6377,6378],{},[1908,6379,6069],{"className":6380},[6245],[1908,6382,2204],{"className":6383},[2203],[1908,6385,6387],{"className":6386},[2176],[1908,6388,6391],{"className":6389,"style":6390},[2180],"height:0.8444em;",[1908,6392],{},[1908,6394],{"className":6395,"style":2057},[2027],[1908,6397,6399,6402],{"className":6398},[1951],[1908,6400,2235],{"className":6401},[1951,1952],[1908,6403,6405],{"className":6404},[2167],[1908,6406,6408,6428],{"className":6407},[2171,2172],[1908,6409,6411,6425],{"className":6410},[2176],[1908,6412,6414],{"className":6413,"style":2181},[2180],[1908,6415,6416,6419],{"style":2308},[1908,6417],{"className":6418,"style":2189},[2188],[1908,6420,6422],{"className":6421},[2193,2194,2195,2196],[1908,6423,2107],{"className":6424},[1951,1952,2196],[1908,6426,2204],{"className":6427},[2203],[1908,6429,6431],{"className":6430},[2176],[1908,6432,6434],{"className":6433,"style":2211},[2180],[1908,6435],{},[1908,6437,2566],{"className":6438},[2046],[1908,6440,6442,6445],{"className":6441},[1951],[1908,6443,2561],{"className":6444},[1951,1952],[1908,6446,6448],{"className":6447},[2167],[1908,6449,6451,6471],{"className":6450},[2171,2172],[1908,6452,6454,6468],{"className":6453},[2176],[1908,6455,6457],{"className":6456,"style":2181},[2180],[1908,6458,6459,6462],{"style":2308},[1908,6460],{"className":6461,"style":2189},[2188],[1908,6463,6465],{"className":6464},[2193,2194,2195,2196],[1908,6466,2107],{"className":6467},[1951,1952,2196],[1908,6469,2204],{"className":6470},[2203],[1908,6472,6474],{"className":6473},[2176],[1908,6475,6477],{"className":6476,"style":2211},[2180],[1908,6478],{},[1908,6480,1991],{"className":6481},[2053],[1908,6483],{"className":6484,"style":2057},[2027],[1908,6486,6488,6491],{"className":6487},[1951],[1908,6489,2561],{"className":6490},[1951,1952],[1908,6492,6494],{"className":6493},[2167],[1908,6495,6497,6523],{"className":6496},[2171,2172],[1908,6498,6500,6520],{"className":6499},[2176],[1908,6501,6503],{"className":6502,"style":2181},[2180],[1908,6504,6505,6508],{"style":2308},[1908,6506],{"className":6507,"style":2189},[2188],[1908,6509,6511],{"className":6510},[2193,2194,2195,2196],[1908,6512,6514,6517],{"className":6513},[1951,2196],[1908,6515,2828],{"className":6516},[1951,2196],[1908,6518,2107],{"className":6519},[1951,1952,2196],[1908,6521,2204],{"className":6522},[2203],[1908,6524,6526],{"className":6525},[2176],[1908,6527,6529],{"className":6528,"style":2945},[2180],[1908,6530],{},[1908,6532,2595],{"className":6533},[2086],[1798,6535,6536,6537,6769,6770,6798],{},"纳什均衡满足：",[1908,6538,6540,6586],{"className":6539},[1911],[1908,6541,6543],{"className":6542},[1915],[1917,6544,6545],{"xmlns":1919},[1921,6546,6547,6583],{},[1924,6548,6549,6557,6559,6561,6567,6569,6581],{},[3540,6550,6551,6553,6555],{},[1927,6552,2561],{},[1927,6554,2107],{},[1978,6556,3548],{},[1978,6558,5489],{},[1927,6560,6033],{},[2137,6562,6563,6565],{},[1927,6564,2274],{},[1927,6566,2107],{},[1978,6568,2566],{"stretchy":1983},[3540,6570,6571,6573,6579],{},[1927,6572,2561],{},[1924,6574,6575,6577],{},[1978,6576,2828],{},[1927,6578,2107],{},[1978,6580,3548],{},[1978,6582,2595],{"stretchy":1983},[1931,6584,6585],{"encoding":1933},"s_i^* \\in BR_i(s_{-i}^*)",[1908,6587,6589,6655],{"className":6588,"ariaHidden":1938},[1937],[1908,6590,6592,6595,6646,6649,6652],{"className":6591},[1942],[1908,6593],{"className":6594,"style":3561},[1946],[1908,6596,6598,6601],{"className":6597},[1951],[1908,6599,2561],{"className":6600},[1951,1952],[1908,6602,6604],{"className":6603},[2167],[1908,6605,6607,6638],{"className":6606},[2171,2172],[1908,6608,6610,6635],{"className":6609},[2176],[1908,6611,6613,6624],{"className":6612,"style":3580},[2180],[1908,6614,6615,6618],{"style":3583},[1908,6616],{"className":6617,"style":2189},[2188],[1908,6619,6621],{"className":6620},[2193,2194,2195,2196],[1908,6622,2107],{"className":6623},[1951,1952,2196],[1908,6625,6626,6629],{"style":3595},[1908,6627],{"className":6628,"style":2189},[2188],[1908,6630,6632],{"className":6631},[2193,2194,2195,2196],[1908,6633,3548],{"className":6634},[2392,2196],[1908,6636,2204],{"className":6637},[2203],[1908,6639,6641],{"className":6640},[2176],[1908,6642,6644],{"className":6643,"style":3614},[2180],[1908,6645],{},[1908,6647],{"className":6648,"style":2028},[2027],[1908,6650,5489],{"className":6651},[2032],[1908,6653],{"className":6654,"style":2028},[2027],[1908,6656,6658,6662,6665,6705,6708,6766],{"className":6657},[1942],[1908,6659],{"className":6660,"style":6661},[1946],"height:1.067em;vertical-align:-0.317em;",[1908,6663,6033],{"className":6664,"style":6131},[1951,1952],[1908,6666,6668,6671],{"className":6667},[1951],[1908,6669,2274],{"className":6670,"style":6138},[1951,1952],[1908,6672,6674],{"className":6673},[2167],[1908,6675,6677,6697],{"className":6676},[2171,2172],[1908,6678,6680,6694],{"className":6679},[2176],[1908,6681,6683],{"className":6682,"style":2181},[2180],[1908,6684,6685,6688],{"style":6153},[1908,6686],{"className":6687,"style":2189},[2188],[1908,6689,6691],{"className":6690},[2193,2194,2195,2196],[1908,6692,2107],{"className":6693},[1951,1952,2196],[1908,6695,2204],{"className":6696},[2203],[1908,6698,6700],{"className":6699},[2176],[1908,6701,6703],{"className":6702,"style":2211},[2180],[1908,6704],{},[1908,6706,2566],{"className":6707},[2046],[1908,6709,6711,6714],{"className":6710},[1951],[1908,6712,2561],{"className":6713},[1951,1952],[1908,6715,6717],{"className":6716},[2167],[1908,6718,6720,6757],{"className":6719},[2171,2172],[1908,6721,6723,6754],{"className":6722},[2176],[1908,6724,6726,6743],{"className":6725,"style":3580},[2180],[1908,6727,6728,6731],{"style":3583},[1908,6729],{"className":6730,"style":2189},[2188],[1908,6732,6734],{"className":6733},[2193,2194,2195,2196],[1908,6735,6737,6740],{"className":6736},[1951,2196],[1908,6738,2828],{"className":6739},[1951,2196],[1908,6741,2107],{"className":6742},[1951,1952,2196],[1908,6744,6745,6748],{"style":3595},[1908,6746],{"className":6747,"style":2189},[2188],[1908,6749,6751],{"className":6750},[2193,2194,2195,2196],[1908,6752,3548],{"className":6753},[2392,2196],[1908,6755,2204],{"className":6756},[2203],[1908,6758,6760],{"className":6759},[2176],[1908,6761,6764],{"className":6762,"style":6763},[2180],"height:0.317em;",[1908,6765],{},[1908,6767,2595],{"className":6768},[2086],"对所有",[1908,6771,6773,6786],{"className":6772},[1911],[1908,6774,6776],{"className":6775},[1915],[1917,6777,6778],{"xmlns":1919},[1921,6779,6780,6784],{},[1924,6781,6782],{},[1927,6783,2107],{},[1931,6785,2107],{"encoding":1933},[1908,6787,6789],{"className":6788,"ariaHidden":1938},[1937],[1908,6790,6792,6795],{"className":6791},[1942],[1908,6793],{"className":6794,"style":2119},[1946],[1908,6796,2107],{"className":6797},[1951,1952],"。",[1798,6800,6801],{},[1857,6802,6803],{},"例题: 协调博弈 (Coordination Game)",[3421,6805,6806,6818],{},[3424,6807,6808],{},[3427,6809,6810,6812,6815],{},[3430,6811],{},[3430,6813,6814],{},"参与者2：歌剧(O)",[3430,6816,6817],{},"参与者2：足球(F)",[3439,6819,6820,6833],{},[3427,6821,6822,6827,6830],{},[3444,6823,6824],{},[1857,6825,6826],{},"参与者1：歌剧(O)",[3444,6828,6829],{},"(2, 1)",[3444,6831,6832],{},"(0, 0)",[3427,6834,6835,6840,6842],{},[3444,6836,6837],{},[1857,6838,6839],{},"参与者1：足球(F)",[3444,6841,6832],{},[3444,6843,6844],{},"(1, 2)",[1798,6846,6847,1860],{},[1857,6848,6849],{},"分析",[1805,6851,6852,6855,6858],{},[1808,6853,6854],{},"如果2选O，1的最优反应是O（2 > 0）",[1808,6856,6857],{},"如果2选F，1的最优反应是F（1 > 0）",[1808,6859,6860],{},"对称地分析参与者2",[1798,6862,6863,6866],{},[1857,6864,6865],{},"纳什均衡",": (O, O)和(F, F)——两个纯策略纳什均衡！",[1798,6868,6869,6872],{},[1857,6870,6871],{},"问题",": 如果存在多重均衡，参与者如何协调？这引出了均衡选择和焦点(focal point)的概念。",[1897,6874,6876],{"id":6875},"_24-剔除严格劣策略-iesds","2.4 剔除严格劣策略 (IESDS)",[1798,6878,6879,1860],{},[1857,6880,6881],{},"迭代剔除严格劣策略 (Iterated Elimination of Strictly Dominated Strategies)",[1875,6883,6884,6887,6890],{},[1808,6885,6886],{},"找到所有严格劣策略并剔除",[1808,6888,6889],{},"在剩余策略集中，重复步骤1",[1808,6891,6892],{},"直到无法剔除为止",[1798,6894,6895,1860],{},[1857,6896,6897],{},"性质",[1805,6899,6900,6903,6906,6909],{},[1808,6901,6902],{},"IESDS的顺序不影响最终结果",[1808,6904,6905],{},"如果IESDS后只剩一个策略组合，它必然是唯一的纳什均衡",[1808,6907,6908],{},"纳什均衡一定能在IESDS中幸存",[1808,6910,6911],{},"但IESDS可能无法找到所有纳什均衡",[1798,6913,6914],{},[1857,6915,6916],{},"例题: 智猪博弈",[3421,6918,6919,6931],{},[3424,6920,6921],{},[3427,6922,6923,6925,6928],{},[3430,6924],{},[3430,6926,6927],{},"小猪：按(P)",[3430,6929,6930],{},"小猪：等(W)",[3439,6932,6933,6946],{},[3427,6934,6935,6940,6943],{},[3444,6936,6937],{},[1857,6938,6939],{},"大猪：按(P)",[3444,6941,6942],{},"(4, 1)",[3444,6944,6945],{},"(-1, 4)",[3427,6947,6948,6953,6956],{},[3444,6949,6950],{},[1857,6951,6952],{},"大猪：等(W)",[3444,6954,6955],{},"(6, -1)",[3444,6957,6832],{},[1798,6959,6960,1860],{},[1857,6961,6849],{},[1805,6963,6964,6975,6978],{},[1808,6965,6966,6967],{},"对小猪：无论大猪如何选择，等待(W)都优于按按钮(P)\n",[1805,6968,6969,6972],{},[1808,6970,6971],{},"如果大猪按：W得4 > P得1",[1808,6973,6974],{},"如果大猪等：W得0 > P得-1",[1808,6976,6977],{},"W是小猪的占优策略，剔除P",[1808,6979,6980],{},"给定小猪选W，大猪选P（得6 > 0）",[1798,6982,6983,6986],{},[1857,6984,6985],{},"唯一纳什均衡",": (P, W)——大猪劳动，小猪搭便车",[1897,6988,6990],{"id":6989},"_25-纳什均衡的存在性","2.5 纳什均衡的存在性",[1798,6992,6993,6996,6997,7066],{},[1857,6994,6995],{},"纳什定理 (Nash, 1950)",": 如果策略集",[1908,6998,7000,7017],{"className":6999},[1911],[1908,7001,7003],{"className":7002},[1915],[1917,7004,7005],{"xmlns":1919},[1921,7006,7007,7015],{},[1924,7008,7009],{},[2137,7010,7011,7013],{},[1927,7012,2141],{},[1927,7014,2107],{},[1931,7016,2146],{"encoding":1933},[1908,7018,7020],{"className":7019,"ariaHidden":1938},[1937],[1908,7021,7023,7026],{"className":7022},[1942],[1908,7024],{"className":7025,"style":2156},[1946],[1908,7027,7029,7032],{"className":7028},[1951],[1908,7030,2141],{"className":7031,"style":2163},[1951,1952],[1908,7033,7035],{"className":7034},[2167],[1908,7036,7038,7058],{"className":7037},[2171,2172],[1908,7039,7041,7055],{"className":7040},[2176],[1908,7042,7044],{"className":7043,"style":2181},[2180],[1908,7045,7046,7049],{"style":2184},[1908,7047],{"className":7048,"style":2189},[2188],[1908,7050,7052],{"className":7051},[2193,2194,2195,2196],[1908,7053,2107],{"className":7054},[1951,1952,2196],[1908,7056,2204],{"className":7057},[2203],[1908,7059,7061],{"className":7060},[2176],[1908,7062,7064],{"className":7063,"style":2211},[2180],[1908,7065],{},"都是有限的，则至少存在一个纳什均衡（可能是混合策略）。",[1798,7068,7069,7072],{},[1857,7070,7071],{},"更一般的存在性定理 (Kakutani不动点定理)",": 如果：",[1875,7074,7075,7148,7221],{},[1808,7076,7077,7078,7147],{},"策略集",[1908,7079,7081,7098],{"className":7080},[1911],[1908,7082,7084],{"className":7083},[1915],[1917,7085,7086],{"xmlns":1919},[1921,7087,7088,7096],{},[1924,7089,7090],{},[2137,7091,7092,7094],{},[1927,7093,2141],{},[1927,7095,2107],{},[1931,7097,2146],{"encoding":1933},[1908,7099,7101],{"className":7100,"ariaHidden":1938},[1937],[1908,7102,7104,7107],{"className":7103},[1942],[1908,7105],{"className":7106,"style":2156},[1946],[1908,7108,7110,7113],{"className":7109},[1951],[1908,7111,2141],{"className":7112,"style":2163},[1951,1952],[1908,7114,7116],{"className":7115},[2167],[1908,7117,7119,7139],{"className":7118},[2171,2172],[1908,7120,7122,7136],{"className":7121},[2176],[1908,7123,7125],{"className":7124,"style":2181},[2180],[1908,7126,7127,7130],{"style":2184},[1908,7128],{"className":7129,"style":2189},[2188],[1908,7131,7133],{"className":7132},[2193,2194,2195,2196],[1908,7134,2107],{"className":7135},[1951,1952,2196],[1908,7137,2204],{"className":7138},[2203],[1908,7140,7142],{"className":7141},[2176],[1908,7143,7145],{"className":7144,"style":2211},[2180],[1908,7146],{},"是欧几里得空间的非空紧凸子集",[1808,7149,2218,7150,7220],{},[1908,7151,7153,7171],{"className":7152},[1911],[1908,7154,7156],{"className":7155},[1915],[1917,7157,7158],{"xmlns":1919},[1921,7159,7160,7168],{},[1924,7161,7162],{},[2137,7163,7164,7166],{},[1927,7165,2235],{},[1927,7167,2107],{},[1931,7169,7170],{"encoding":1933},"u_i",[1908,7172,7174],{"className":7173,"ariaHidden":1938},[1937],[1908,7175,7177,7180],{"className":7176},[1942],[1908,7178],{"className":7179,"style":2287},[1946],[1908,7181,7183,7186],{"className":7182},[1951],[1908,7184,2235],{"className":7185},[1951,1952],[1908,7187,7189],{"className":7188},[2167],[1908,7190,7192,7212],{"className":7191},[2171,2172],[1908,7193,7195,7209],{"className":7194},[2176],[1908,7196,7198],{"className":7197,"style":2181},[2180],[1908,7199,7200,7203],{"style":2308},[1908,7201],{"className":7202,"style":2189},[2188],[1908,7204,7206],{"className":7205},[2193,2194,2195,2196],[1908,7207,2107],{"className":7208},[1951,1952,2196],[1908,7210,2204],{"className":7211},[2203],[1908,7213,7215],{"className":7214},[2176],[1908,7216,7218],{"className":7217,"style":2211},[2180],[1908,7219],{},"连续",[1808,7222,7223,7412,7413,7482],{},[1908,7224,7226,7265],{"className":7225},[1911],[1908,7227,7229],{"className":7228},[1915],[1917,7230,7231],{"xmlns":1919},[1921,7232,7233,7263],{},[1924,7234,7235,7241,7243,7249,7251,7261],{},[2137,7236,7237,7239],{},[1927,7238,2235],{},[1927,7240,2107],{},[1978,7242,2566],{"stretchy":1983},[2137,7244,7245,7247],{},[1927,7246,2561],{},[1927,7248,2107],{},[1978,7250,1991],{"separator":1938},[2137,7252,7253,7255],{},[1927,7254,2561],{},[1924,7256,7257,7259],{},[1978,7258,2828],{},[1927,7260,2107],{},[1978,7262,2595],{"stretchy":1983},[1931,7264,3263],{"encoding":1933},[1908,7266,7268],{"className":7267,"ariaHidden":1938},[1937],[1908,7269,7271,7274,7314,7317,7357,7360,7363,7409],{"className":7270},[1942],[1908,7272],{"className":7273,"style":2042},[1946],[1908,7275,7277,7280],{"className":7276},[1951],[1908,7278,2235],{"className":7279},[1951,1952],[1908,7281,7283],{"className":7282},[2167],[1908,7284,7286,7306],{"className":7285},[2171,2172],[1908,7287,7289,7303],{"className":7288},[2176],[1908,7290,7292],{"className":7291,"style":2181},[2180],[1908,7293,7294,7297],{"style":2308},[1908,7295],{"className":7296,"style":2189},[2188],[1908,7298,7300],{"className":7299},[2193,2194,2195,2196],[1908,7301,2107],{"className":7302},[1951,1952,2196],[1908,7304,2204],{"className":7305},[2203],[1908,7307,7309],{"className":7308},[2176],[1908,7310,7312],{"className":7311,"style":2211},[2180],[1908,7313],{},[1908,7315,2566],{"className":7316},[2046],[1908,7318,7320,7323],{"className":7319},[1951],[1908,7321,2561],{"className":7322},[1951,1952],[1908,7324,7326],{"className":7325},[2167],[1908,7327,7329,7349],{"className":7328},[2171,2172],[1908,7330,7332,7346],{"className":7331},[2176],[1908,7333,7335],{"className":7334,"style":2181},[2180],[1908,7336,7337,7340],{"style":2308},[1908,7338],{"className":7339,"style":2189},[2188],[1908,7341,7343],{"className":7342},[2193,2194,2195,2196],[1908,7344,2107],{"className":7345},[1951,1952,2196],[1908,7347,2204],{"className":7348},[2203],[1908,7350,7352],{"className":7351},[2176],[1908,7353,7355],{"className":7354,"style":2211},[2180],[1908,7356],{},[1908,7358,1991],{"className":7359},[2053],[1908,7361],{"className":7362,"style":2057},[2027],[1908,7364,7366,7369],{"className":7365},[1951],[1908,7367,2561],{"className":7368},[1951,1952],[1908,7370,7372],{"className":7371},[2167],[1908,7373,7375,7401],{"className":7374},[2171,2172],[1908,7376,7378,7398],{"className":7377},[2176],[1908,7379,7381],{"className":7380,"style":2181},[2180],[1908,7382,7383,7386],{"style":2308},[1908,7384],{"className":7385,"style":2189},[2188],[1908,7387,7389],{"className":7388},[2193,2194,2195,2196],[1908,7390,7392,7395],{"className":7391},[1951,2196],[1908,7393,2828],{"className":7394},[1951,2196],[1908,7396,2107],{"className":7397},[1951,1952,2196],[1908,7399,2204],{"className":7400},[2203],[1908,7402,7404],{"className":7403},[2176],[1908,7405,7407],{"className":7406,"style":2945},[2180],[1908,7408],{},[1908,7410,2595],{"className":7411},[2086],"关于",[1908,7414,7416,7433],{"className":7415},[1911],[1908,7417,7419],{"className":7418},[1915],[1917,7420,7421],{"xmlns":1919},[1921,7422,7423,7431],{},[1924,7424,7425],{},[2137,7426,7427,7429],{},[1927,7428,2561],{},[1927,7430,2107],{},[1931,7432,4415],{"encoding":1933},[1908,7434,7436],{"className":7435,"ariaHidden":1938},[1937],[1908,7437,7439,7442],{"className":7438},[1942],[1908,7440],{"className":7441,"style":2287},[1946],[1908,7443,7445,7448],{"className":7444},[1951],[1908,7446,2561],{"className":7447},[1951,1952],[1908,7449,7451],{"className":7450},[2167],[1908,7452,7454,7474],{"className":7453},[2171,2172],[1908,7455,7457,7471],{"className":7456},[2176],[1908,7458,7460],{"className":7459,"style":2181},[2180],[1908,7461,7462,7465],{"style":2308},[1908,7463],{"className":7464,"style":2189},[2188],[1908,7466,7468],{"className":7467},[2193,2194,2195,2196],[1908,7469,2107],{"className":7470},[1951,1952,2196],[1908,7472,2204],{"className":7473},[2203],[1908,7475,7477],{"className":7476},[2176],[1908,7478,7480],{"className":7479,"style":2211},[2180],[1908,7481],{},"拟凹",[1798,7484,7485],{},"则纯策略纳什均衡存在。",[1890,7487],{},[1794,7489,7491],{"id":7490},"_3-混合策略纳什均衡","3. 混合策略纳什均衡",[1897,7493,7495],{"id":7494},"_31-混合策略的定义","3.1 混合策略的定义",[1798,7497,7498,7501],{},[1857,7499,7500],{},"纯策略",": 确定性地选择某个行动",[1798,7503,7504,7507],{},[1857,7505,7506],{},"混合策略",": 在纯策略上的概率分布",[1908,7509,7511],{"className":7510},[3912],[1908,7512,7514,7548],{"className":7513},[1911],[1908,7515,7517],{"className":7516},[1915],[1917,7518,7519],{"xmlns":1919,"display":3921},[1921,7520,7521,7545],{},[1924,7522,7523,7530,7532,7535,7537,7543],{},[2137,7524,7525,7528],{},[1927,7526,7527],{},"σ",[1927,7529,2107],{},[1978,7531,5489],{},[1927,7533,7534],{"mathvariant":3638},"Δ",[1978,7536,2566],{"stretchy":1983},[2137,7538,7539,7541],{},[1927,7540,2141],{},[1927,7542,2107],{},[1978,7544,2595],{"stretchy":1983},[1931,7546,7547],{"encoding":1933},"\\sigma_i \\in \\Delta(S_i)",[1908,7549,7551,7609],{"className":7550,"ariaHidden":1938},[1937],[1908,7552,7554,7558,7600,7603,7606],{"className":7553},[1942],[1908,7555],{"className":7556,"style":7557},[1946],"height:0.6891em;vertical-align:-0.15em;",[1908,7559,7561,7565],{"className":7560},[1951],[1908,7562,7527],{"className":7563,"style":7564},[1951,1952],"margin-right:0.0359em;",[1908,7566,7568],{"className":7567},[2167],[1908,7569,7571,7592],{"className":7570},[2171,2172],[1908,7572,7574,7589],{"className":7573},[2176],[1908,7575,7577],{"className":7576,"style":2181},[2180],[1908,7578,7580,7583],{"style":7579},"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;",[1908,7581],{"className":7582,"style":2189},[2188],[1908,7584,7586],{"className":7585},[2193,2194,2195,2196],[1908,7587,2107],{"className":7588},[1951,1952,2196],[1908,7590,2204],{"className":7591},[2203],[1908,7593,7595],{"className":7594},[2176],[1908,7596,7598],{"className":7597,"style":2211},[2180],[1908,7599],{},[1908,7601],{"className":7602,"style":2028},[2027],[1908,7604,5489],{"className":7605},[2032],[1908,7607],{"className":7608,"style":2028},[2027],[1908,7610,7612,7615,7618,7621,7661],{"className":7611},[1942],[1908,7613],{"className":7614,"style":2042},[1946],[1908,7616,7534],{"className":7617},[1951],[1908,7619,2566],{"className":7620},[2046],[1908,7622,7624,7627],{"className":7623},[1951],[1908,7625,2141],{"className":7626,"style":2163},[1951,1952],[1908,7628,7630],{"className":7629},[2167],[1908,7631,7633,7653],{"className":7632},[2171,2172],[1908,7634,7636,7650],{"className":7635},[2176],[1908,7637,7639],{"className":7638,"style":2181},[2180],[1908,7640,7641,7644],{"style":2184},[1908,7642],{"className":7643,"style":2189},[2188],[1908,7645,7647],{"className":7646},[2193,2194,2195,2196],[1908,7648,2107],{"className":7649},[1951,1952,2196],[1908,7651,2204],{"className":7652},[2203],[1908,7654,7656],{"className":7655},[2176],[1908,7657,7659],{"className":7658,"style":2211},[2180],[1908,7660],{},[1908,7662,2595],{"className":7663},[2086],[1798,7665,7666,7667,7752,7753,7822],{},"其中",[1908,7668,7670,7694],{"className":7669},[1911],[1908,7671,7673],{"className":7672},[1915],[1917,7674,7675],{"xmlns":1919},[1921,7676,7677,7691],{},[1924,7678,7679,7681,7683,7689],{},[1927,7680,7534],{"mathvariant":3638},[1978,7682,2566],{"stretchy":1983},[2137,7684,7685,7687],{},[1927,7686,2141],{},[1927,7688,2107],{},[1978,7690,2595],{"stretchy":1983},[1931,7692,7693],{"encoding":1933},"\\Delta(S_i)",[1908,7695,7697],{"className":7696,"ariaHidden":1938},[1937],[1908,7698,7700,7703,7706,7709,7749],{"className":7699},[1942],[1908,7701],{"className":7702,"style":2042},[1946],[1908,7704,7534],{"className":7705},[1951],[1908,7707,2566],{"className":7708},[2046],[1908,7710,7712,7715],{"className":7711},[1951],[1908,7713,2141],{"className":7714,"style":2163},[1951,1952],[1908,7716,7718],{"className":7717},[2167],[1908,7719,7721,7741],{"className":7720},[2171,2172],[1908,7722,7724,7738],{"className":7723},[2176],[1908,7725,7727],{"className":7726,"style":2181},[2180],[1908,7728,7729,7732],{"style":2184},[1908,7730],{"className":7731,"style":2189},[2188],[1908,7733,7735],{"className":7734},[2193,2194,2195,2196],[1908,7736,2107],{"className":7737},[1951,1952,2196],[1908,7739,2204],{"className":7740},[2203],[1908,7742,7744],{"className":7743},[2176],[1908,7745,7747],{"className":7746,"style":2211},[2180],[1908,7748],{},[1908,7750,2595],{"className":7751},[2086],"是",[1908,7754,7756,7773],{"className":7755},[1911],[1908,7757,7759],{"className":7758},[1915],[1917,7760,7761],{"xmlns":1919},[1921,7762,7763,7771],{},[1924,7764,7765],{},[2137,7766,7767,7769],{},[1927,7768,2141],{},[1927,7770,2107],{},[1931,7772,2146],{"encoding":1933},[1908,7774,7776],{"className":7775,"ariaHidden":1938},[1937],[1908,7777,7779,7782],{"className":7778},[1942],[1908,7780],{"className":7781,"style":2156},[1946],[1908,7783,7785,7788],{"className":7784},[1951],[1908,7786,2141],{"className":7787,"style":2163},[1951,1952],[1908,7789,7791],{"className":7790},[2167],[1908,7792,7794,7814],{"className":7793},[2171,2172],[1908,7795,7797,7811],{"className":7796},[2176],[1908,7798,7800],{"className":7799,"style":2181},[2180],[1908,7801,7802,7805],{"style":2184},[1908,7803],{"className":7804,"style":2189},[2188],[1908,7806,7808],{"className":7807},[2193,2194,2195,2196],[1908,7809,2107],{"className":7810},[1951,1952,2196],[1908,7812,2204],{"className":7813},[2203],[1908,7815,7817],{"className":7816},[2176],[1908,7818,7820],{"className":7819,"style":2211},[2180],[1908,7821],{},"上所有概率分布的集合。",[1798,7824,7825,1961,7827,7953,7954,7982,7983,8052],{},[1857,7826,2541],{},[1908,7828,7830,7858],{"className":7829},[1911],[1908,7831,7833],{"className":7832},[1915],[1917,7834,7835],{"xmlns":1919},[1921,7836,7837,7855],{},[1924,7838,7839,7845,7847,7853],{},[2137,7840,7841,7843],{},[1927,7842,7527],{},[1927,7844,2107],{},[1978,7846,2566],{"stretchy":1983},[2137,7848,7849,7851],{},[1927,7850,2561],{},[1927,7852,2107],{},[1978,7854,2595],{"stretchy":1983},[1931,7856,7857],{"encoding":1933},"\\sigma_i(s_i)",[1908,7859,7861],{"className":7860,"ariaHidden":1938},[1937],[1908,7862,7864,7867,7907,7910,7950],{"className":7863},[1942],[1908,7865],{"className":7866,"style":2042},[1946],[1908,7868,7870,7873],{"className":7869},[1951],[1908,7871,7527],{"className":7872,"style":7564},[1951,1952],[1908,7874,7876],{"className":7875},[2167],[1908,7877,7879,7899],{"className":7878},[2171,2172],[1908,7880,7882,7896],{"className":7881},[2176],[1908,7883,7885],{"className":7884,"style":2181},[2180],[1908,7886,7887,7890],{"style":7579},[1908,7888],{"className":7889,"style":2189},[2188],[1908,7891,7893],{"className":7892},[2193,2194,2195,2196],[1908,7894,2107],{"className":7895},[1951,1952,2196],[1908,7897,2204],{"className":7898},[2203],[1908,7900,7902],{"className":7901},[2176],[1908,7903,7905],{"className":7904,"style":2211},[2180],[1908,7906],{},[1908,7908,2566],{"className":7909},[2046],[1908,7911,7913,7916],{"className":7912},[1951],[1908,7914,2561],{"className":7915},[1951,1952],[1908,7917,7919],{"className":7918},[2167],[1908,7920,7922,7942],{"className":7921},[2171,2172],[1908,7923,7925,7939],{"className":7924},[2176],[1908,7926,7928],{"className":7927,"style":2181},[2180],[1908,7929,7930,7933],{"style":2308},[1908,7931],{"className":7932,"style":2189},[2188],[1908,7934,7936],{"className":7935},[2193,2194,2195,2196],[1908,7937,2107],{"className":7938},[1951,1952,2196],[1908,7940,2204],{"className":7941},[2203],[1908,7943,7945],{"className":7944},[2176],[1908,7946,7948],{"className":7947,"style":2211},[2180],[1908,7949],{},[1908,7951,2595],{"className":7952},[2086],"表示参与者",[1908,7955,7957,7970],{"className":7956},[1911],[1908,7958,7960],{"className":7959},[1915],[1917,7961,7962],{"xmlns":1919},[1921,7963,7964,7968],{},[1924,7965,7966],{},[1927,7967,2107],{},[1931,7969,2107],{"encoding":1933},[1908,7971,7973],{"className":7972,"ariaHidden":1938},[1937],[1908,7974,7976,7979],{"className":7975},[1942],[1908,7977],{"className":7978,"style":2119},[1946],[1908,7980,2107],{"className":7981},[1951,1952],"选择纯策略",[1908,7984,7986,8003],{"className":7985},[1911],[1908,7987,7989],{"className":7988},[1915],[1917,7990,7991],{"xmlns":1919},[1921,7992,7993,8001],{},[1924,7994,7995],{},[2137,7996,7997,7999],{},[1927,7998,2561],{},[1927,8000,2107],{},[1931,8002,4415],{"encoding":1933},[1908,8004,8006],{"className":8005,"ariaHidden":1938},[1937],[1908,8007,8009,8012],{"className":8008},[1942],[1908,8010],{"className":8011,"style":2287},[1946],[1908,8013,8015,8018],{"className":8014},[1951],[1908,8016,2561],{"className":8017},[1951,1952],[1908,8019,8021],{"className":8020},[2167],[1908,8022,8024,8044],{"className":8023},[2171,2172],[1908,8025,8027,8041],{"className":8026},[2176],[1908,8028,8030],{"className":8029,"style":2181},[2180],[1908,8031,8032,8035],{"style":2308},[1908,8033],{"className":8034,"style":2189},[2188],[1908,8036,8038],{"className":8037},[2193,2194,2195,2196],[1908,8039,2107],{"className":8040},[1951,1952,2196],[1908,8042,2204],{"className":8043},[2203],[1908,8045,8047],{"className":8046},[2176],[1908,8048,8050],{"className":8049,"style":2211},[2180],[1908,8051],{},"的概率。",[1897,8054,8056],{"id":8055},"_32-期望支付","3.2 期望支付",[1798,8058,8059,8060,8232,8233,8261],{},"给定混合策略组合",[1908,8061,8063,8101],{"className":8062},[1911],[1908,8064,8066],{"className":8065},[1915],[1917,8067,8068],{"xmlns":1919},[1921,8069,8070,8098],{},[1924,8071,8072,8074,8076,8078,8084,8086,8088,8090,8096],{},[1927,8073,7527],{},[1978,8075,1980],{},[1978,8077,2566],{"stretchy":1983},[2137,8079,8080,8082],{},[1927,8081,7527],{},[1986,8083,1988],{},[1978,8085,1991],{"separator":1938},[1978,8087,1999],{},[1978,8089,1991],{"separator":1938},[2137,8091,8092,8094],{},[1927,8093,7527],{},[1927,8095,1929],{},[1978,8097,2595],{"stretchy":1983},[1931,8099,8100],{"encoding":1933},"\\sigma = (\\sigma_1, \\ldots, \\sigma_n)",[1908,8102,8104,8122],{"className":8103,"ariaHidden":1938},[1937],[1908,8105,8107,8110,8113,8116,8119],{"className":8106},[1942],[1908,8108],{"className":8109,"style":1947},[1946],[1908,8111,7527],{"className":8112,"style":7564},[1951,1952],[1908,8114],{"className":8115,"style":2028},[2027],[1908,8117,1980],{"className":8118},[2032],[1908,8120],{"className":8121,"style":2028},[2027],[1908,8123,8125,8128,8131,8171,8174,8177,8180,8183,8186,8189,8229],{"className":8124},[1942],[1908,8126],{"className":8127,"style":2042},[1946],[1908,8129,2566],{"className":8130},[2046],[1908,8132,8134,8137],{"className":8133},[1951],[1908,8135,7527],{"className":8136,"style":7564},[1951,1952],[1908,8138,8140],{"className":8139},[2167],[1908,8141,8143,8163],{"className":8142},[2171,2172],[1908,8144,8146,8160],{"className":8145},[2176],[1908,8147,8149],{"className":8148,"style":2362},[2180],[1908,8150,8151,8154],{"style":7579},[1908,8152],{"className":8153,"style":2189},[2188],[1908,8155,8157],{"className":8156},[2193,2194,2195,2196],[1908,8158,1988],{"className":8159},[1951,2196],[1908,8161,2204],{"className":8162},[2203],[1908,8164,8166],{"className":8165},[2176],[1908,8167,8169],{"className":8168,"style":2211},[2180],[1908,8170],{},[1908,8172,1991],{"className":8173},[2053],[1908,8175],{"className":8176,"style":2057},[2027],[1908,8178,1999],{"className":8179},[2070],[1908,8181],{"className":8182,"style":2057},[2027],[1908,8184,1991],{"className":8185},[2053],[1908,8187],{"className":8188,"style":2057},[2027],[1908,8190,8192,8195],{"className":8191},[1951],[1908,8193,7527],{"className":8194,"style":7564},[1951,1952],[1908,8196,8198],{"className":8197},[2167],[1908,8199,8201,8221],{"className":8200},[2171,2172],[1908,8202,8204,8218],{"className":8203},[2176],[1908,8205,8207],{"className":8206,"style":2494},[2180],[1908,8208,8209,8212],{"style":7579},[1908,8210],{"className":8211,"style":2189},[2188],[1908,8213,8215],{"className":8214},[2193,2194,2195,2196],[1908,8216,1929],{"className":8217},[1951,1952,2196],[1908,8219,2204],{"className":8220},[2203],[1908,8222,8224],{"className":8223},[2176],[1908,8225,8227],{"className":8226,"style":2211},[2180],[1908,8228],{},[1908,8230,2595],{"className":8231},[2086],"，参与者",[1908,8234,8236,8249],{"className":8235},[1911],[1908,8237,8239],{"className":8238},[1915],[1917,8240,8241],{"xmlns":1919},[1921,8242,8243,8247],{},[1924,8244,8245],{},[1927,8246,2107],{},[1931,8248,2107],{"encoding":1933},[1908,8250,8252],{"className":8251,"ariaHidden":1938},[1937],[1908,8253,8255,8258],{"className":8254},[1942],[1908,8256],{"className":8257,"style":2119},[1946],[1908,8259,2107],{"className":8260},[1951,1952],"的期望支付：",[1908,8263,8265],{"className":8264},[3912],[1908,8266,8268,8352],{"className":8267},[1911],[1908,8269,8271],{"className":8270},[1915],[1917,8272,8273],{"xmlns":1919,"display":3921},[1921,8274,8275,8349],{},[1924,8276,8277,8283,8285,8287,8289,8291,8304,8310,8312,8314,8316,8333,8339,8341,8347],{},[2137,8278,8279,8281],{},[1927,8280,2235],{},[1927,8282,2107],{},[1978,8284,2566],{"stretchy":1983},[1927,8286,7527],{},[1978,8288,2595],{"stretchy":1983},[1978,8290,1980],{},[6063,8292,8293,8296],{},[1978,8294,8295],{},"∑",[1924,8297,8298,8300,8302],{},[1927,8299,2561],{},[1978,8301,5489],{},[1927,8303,2141],{},[2137,8305,8306,8308],{},[1927,8307,2235],{},[1927,8309,2107],{},[1978,8311,2566],{"stretchy":1983},[1927,8313,2561],{},[1978,8315,2595],{"stretchy":1983},[8317,8318,8319,8322,8331],"munderover",{},[1978,8320,8321],{},"∏",[1924,8323,8324,8327,8329],{},[1927,8325,8326],{},"j",[1978,8328,1980],{},[1986,8330,1988],{},[1927,8332,1929],{},[2137,8334,8335,8337],{},[1927,8336,7527],{},[1927,8338,8326],{},[1978,8340,2566],{"stretchy":1983},[2137,8342,8343,8345],{},[1927,8344,2561],{},[1927,8346,8326],{},[1978,8348,2595],{"stretchy":1983},[1931,8350,8351],{"encoding":1933},"u_i(\\sigma) = \\sum_{s \\in S} u_i(s) \\prod_{j=1}^n \\sigma_j(s_j)",[1908,8353,8355,8419],{"className":8354,"ariaHidden":1938},[1937],[1908,8356,8358,8361,8401,8404,8407,8410,8413,8416],{"className":8357},[1942],[1908,8359],{"className":8360,"style":2042},[1946],[1908,8362,8364,8367],{"className":8363},[1951],[1908,8365,2235],{"className":8366},[1951,1952],[1908,8368,8370],{"className":8369},[2167],[1908,8371,8373,8393],{"className":8372},[2171,2172],[1908,8374,8376,8390],{"className":8375},[2176],[1908,8377,8379],{"className":8378,"style":2181},[2180],[1908,8380,8381,8384],{"style":2308},[1908,8382],{"className":8383,"style":2189},[2188],[1908,8385,8387],{"className":8386},[2193,2194,2195,2196],[1908,8388,2107],{"className":8389},[1951,1952,2196],[1908,8391,2204],{"className":8392},[2203],[1908,8394,8396],{"className":8395},[2176],[1908,8397,8399],{"className":8398,"style":2211},[2180],[1908,8400],{},[1908,8402,2566],{"className":8403},[2046],[1908,8405,7527],{"className":8406,"style":7564},[1951,1952],[1908,8408,2595],{"className":8409},[2086],[1908,8411],{"className":8412,"style":2028},[2027],[1908,8414,1980],{"className":8415},[2032],[1908,8417],{"className":8418,"style":2028},[2027],[1908,8420,8422,8426,8486,8489,8529,8532,8535,8538,8541,8610,8613,8654,8657,8697],{"className":8421},[1942],[1908,8423],{"className":8424,"style":8425},[1946],"height:3.0652em;vertical-align:-1.4138em;",[1908,8427,8429],{"className":8428},[6245,6257],[1908,8430,8432,8477],{"className":8431},[2171,2172],[1908,8433,8435,8474],{"className":8434},[2176],[1908,8436,8439,8461],{"className":8437,"style":8438},[2180],"height:1.05em;",[1908,8440,8442,8446],{"style":8441},"top:-1.8557em;margin-left:0em;",[1908,8443],{"className":8444,"style":8445},[2188],"height:3.05em;",[1908,8447,8449],{"className":8448},[2193,2194,2195,2196],[1908,8450,8452,8455,8458],{"className":8451},[1951,2196],[1908,8453,2561],{"className":8454},[1951,1952,2196],[1908,8456,5489],{"className":8457},[2032,2196],[1908,8459,2141],{"className":8460,"style":2163},[1951,1952,2196],[1908,8462,8464,8467],{"style":8463},"top:-3.05em;",[1908,8465],{"className":8466,"style":8445},[2188],[1908,8468,8469],{},[1908,8470,8295],{"className":8471},[6245,8472,8473],"op-symbol","large-op",[1908,8475,2204],{"className":8476},[2203],[1908,8478,8480],{"className":8479},[2176],[1908,8481,8484],{"className":8482,"style":8483},[2180],"height:1.3217em;",[1908,8485],{},[1908,8487],{"className":8488,"style":2057},[2027],[1908,8490,8492,8495],{"className":8491},[1951],[1908,8493,2235],{"className":8494},[1951,1952],[1908,8496,8498],{"className":8497},[2167],[1908,8499,8501,8521],{"className":8500},[2171,2172],[1908,8502,8504,8518],{"className":8503},[2176],[1908,8505,8507],{"className":8506,"style":2181},[2180],[1908,8508,8509,8512],{"style":2308},[1908,8510],{"className":8511,"style":2189},[2188],[1908,8513,8515],{"className":8514},[2193,2194,2195,2196],[1908,8516,2107],{"className":8517},[1951,1952,2196],[1908,8519,2204],{"className":8520},[2203],[1908,8522,8524],{"className":8523},[2176],[1908,8525,8527],{"className":8526,"style":2211},[2180],[1908,8528],{},[1908,8530,2566],{"className":8531},[2046],[1908,8533,2561],{"className":8534},[1951,1952],[1908,8536,2595],{"className":8537},[2086],[1908,8539],{"className":8540,"style":2057},[2027],[1908,8542,8544],{"className":8543},[6245,6257],[1908,8545,8547,8601],{"className":8546},[2171,2172],[1908,8548,8550,8598],{"className":8549},[2176],[1908,8551,8554,8576,8586],{"className":8552,"style":8553},[2180],"height:1.6514em;",[1908,8555,8557,8560],{"style":8556},"top:-1.8723em;margin-left:0em;",[1908,8558],{"className":8559,"style":8445},[2188],[1908,8561,8563],{"className":8562},[2193,2194,2195,2196],[1908,8564,8566,8570,8573],{"className":8565},[1951,2196],[1908,8567,8326],{"className":8568,"style":8569},[1951,1952,2196],"margin-right:0.0572em;",[1908,8571,1980],{"className":8572},[2032,2196],[1908,8574,1988],{"className":8575},[1951,2196],[1908,8577,8578,8581],{"style":8463},[1908,8579],{"className":8580,"style":8445},[2188],[1908,8582,8583],{},[1908,8584,8321],{"className":8585},[6245,8472,8473],[1908,8587,8589,8592],{"style":8588},"top:-4.3em;margin-left:0em;",[1908,8590],{"className":8591,"style":8445},[2188],[1908,8593,8595],{"className":8594},[2193,2194,2195,2196],[1908,8596,1929],{"className":8597},[1951,1952,2196],[1908,8599,2204],{"className":8600},[2203],[1908,8602,8604],{"className":8603},[2176],[1908,8605,8608],{"className":8606,"style":8607},[2180],"height:1.4138em;",[1908,8609],{},[1908,8611],{"className":8612,"style":2057},[2027],[1908,8614,8616,8619],{"className":8615},[1951],[1908,8617,7527],{"className":8618,"style":7564},[1951,1952],[1908,8620,8622],{"className":8621},[2167],[1908,8623,8625,8645],{"className":8624},[2171,2172],[1908,8626,8628,8642],{"className":8627},[2176],[1908,8629,8631],{"className":8630,"style":2181},[2180],[1908,8632,8633,8636],{"style":7579},[1908,8634],{"className":8635,"style":2189},[2188],[1908,8637,8639],{"className":8638},[2193,2194,2195,2196],[1908,8640,8326],{"className":8641,"style":8569},[1951,1952,2196],[1908,8643,2204],{"className":8644},[2203],[1908,8646,8648],{"className":8647},[2176],[1908,8649,8652],{"className":8650,"style":8651},[2180],"height:0.2861em;",[1908,8653],{},[1908,8655,2566],{"className":8656},[2046],[1908,8658,8660,8663],{"className":8659},[1951],[1908,8661,2561],{"className":8662},[1951,1952],[1908,8664,8666],{"className":8665},[2167],[1908,8667,8669,8689],{"className":8668},[2171,2172],[1908,8670,8672,8686],{"className":8671},[2176],[1908,8673,8675],{"className":8674,"style":2181},[2180],[1908,8676,8677,8680],{"style":2308},[1908,8678],{"className":8679,"style":2189},[2188],[1908,8681,8683],{"className":8682},[2193,2194,2195,2196],[1908,8684,8326],{"className":8685,"style":8569},[1951,1952,2196],[1908,8687,2204],{"className":8688},[2203],[1908,8690,8692],{"className":8691},[2176],[1908,8693,8695],{"className":8694,"style":8651},[2180],[1908,8696],{},[1908,8698,2595],{"className":8699},[2086],[1897,8701,8703],{"id":8702},"_33-混合策略纳什均衡","3.3 混合策略纳什均衡",[1798,8705,8706,8708,8709,8768,8769,3908],{},[1857,8707,1905],{},": 混合策略组合",[1908,8710,8712,8730],{"className":8711},[1911],[1908,8713,8715],{"className":8714},[1915],[1917,8716,8717],{"xmlns":1919},[1921,8718,8719,8727],{},[1924,8720,8721],{},[5080,8722,8723,8725],{},[1927,8724,7527],{},[1978,8726,3548],{},[1931,8728,8729],{"encoding":1933},"\\sigma^*",[1908,8731,8733],{"className":8732,"ariaHidden":1938},[1937],[1908,8734,8736,8739],{"className":8735},[1942],[1908,8737],{"className":8738,"style":3580},[1946],[1908,8740,8742,8745],{"className":8741},[1951],[1908,8743,7527],{"className":8744,"style":7564},[1951,1952],[1908,8746,8748],{"className":8747},[2167],[1908,8749,8751],{"className":8750},[2171],[1908,8752,8754],{"className":8753},[2176],[1908,8755,8757],{"className":8756,"style":3580},[2180],[1908,8758,8759,8762],{"style":3595},[1908,8760],{"className":8761,"style":2189},[2188],[1908,8763,8765],{"className":8764},[2193,2194,2195,2196],[1908,8766,3548],{"className":8767},[2392,2196],"是纳什均衡，如果对每个",[1908,8770,8772,8785],{"className":8771},[1911],[1908,8773,8775],{"className":8774},[1915],[1917,8776,8777],{"xmlns":1919},[1921,8778,8779,8783],{},[1924,8780,8781],{},[1927,8782,2107],{},[1931,8784,2107],{"encoding":1933},[1908,8786,8788],{"className":8787,"ariaHidden":1938},[1937],[1908,8789,8791,8794],{"className":8790},[1942],[1908,8792],{"className":8793,"style":2119},[1946],[1908,8795,2107],{"className":8796},[1951,1952],[1908,8798,8800],{"className":8799},[3912],[1908,8801,8803,8905],{"className":8802},[1911],[1908,8804,8806],{"className":8805},[1915],[1917,8807,8808],{"xmlns":1919,"display":3921},[1921,8809,8810,8902],{},[1924,8811,8812,8818,8820,8828,8830,8842,8844,8846,8852,8854,8860,8862,8874,8876,8878,8880,8882,8888,8890,8892,8894,8900],{},[2137,8813,8814,8816],{},[1927,8815,2235],{},[1927,8817,2107],{},[1978,8819,2566],{"stretchy":1983},[3540,8821,8822,8824,8826],{},[1927,8823,7527],{},[1927,8825,2107],{},[1978,8827,3548],{},[1978,8829,1991],{"separator":1938},[3540,8831,8832,8834,8840],{},[1927,8833,7527],{},[1924,8835,8836,8838],{},[1978,8837,2828],{},[1927,8839,2107],{},[1978,8841,3548],{},[1978,8843,2595],{"stretchy":1983},[1978,8845,4373],{},[2137,8847,8848,8850],{},[1927,8849,2235],{},[1927,8851,2107],{},[1978,8853,2566],{"stretchy":1983},[2137,8855,8856,8858],{},[1927,8857,7527],{},[1927,8859,2107],{},[1978,8861,1991],{"separator":1938},[3540,8863,8864,8866,8872],{},[1927,8865,7527],{},[1924,8867,8868,8870],{},[1978,8869,2828],{},[1927,8871,2107],{},[1978,8873,3548],{},[1978,8875,2595],{"stretchy":1983},[1978,8877,1991],{"separator":1938},[2027,8879],{"width":5477},[1927,8881,5480],{"mathvariant":3638},[2137,8883,8884,8886],{},[1927,8885,7527],{},[1927,8887,2107],{},[1978,8889,5489],{},[1927,8891,7534],{"mathvariant":3638},[1978,8893,2566],{"stretchy":1983},[2137,8895,8896,8898],{},[1927,8897,2141],{},[1927,8899,2107],{},[1978,8901,2595],{"stretchy":1983},[1931,8903,8904],{"encoding":1933},"u_i(\\sigma_i^*, \\sigma_{-i}^*) \\ge u_i(\\sigma_i, \\sigma_{-i}^*), \\quad \\forall \\sigma_i \\in \\Delta(S_i)",[1908,8906,8908,9084,9300],{"className":8907,"ariaHidden":1938},[1937],[1908,8909,8911,8914,8954,8957,9009,9012,9015,9072,9075,9078,9081],{"className":8910},[1942],[1908,8912],{"className":8913,"style":5508},[1946],[1908,8915,8917,8920],{"className":8916},[1951],[1908,8918,2235],{"className":8919},[1951,1952],[1908,8921,8923],{"className":8922},[2167],[1908,8924,8926,8946],{"className":8925},[2171,2172],[1908,8927,8929,8943],{"className":8928},[2176],[1908,8930,8932],{"className":8931,"style":2181},[2180],[1908,8933,8934,8937],{"style":2308},[1908,8935],{"className":8936,"style":2189},[2188],[1908,8938,8940],{"className":8939},[2193,2194,2195,2196],[1908,8941,2107],{"className":8942},[1951,1952,2196],[1908,8944,2204],{"className":8945},[2203],[1908,8947,8949],{"className":8948},[2176],[1908,8950,8952],{"className":8951,"style":2211},[2180],[1908,8953],{},[1908,8955,2566],{"className":8956},[2046],[1908,8958,8960,8963],{"className":8959},[1951],[1908,8961,7527],{"className":8962,"style":7564},[1951,1952],[1908,8964,8966],{"className":8965},[2167],[1908,8967,8969,9001],{"className":8968},[2171,2172],[1908,8970,8972,8998],{"className":8971},[2176],[1908,8973,8975,8987],{"className":8974,"style":4062},[2180],[1908,8976,8978,8981],{"style":8977},"top:-2.453em;margin-left:-0.0359em;margin-right:0.05em;",[1908,8979],{"className":8980,"style":2189},[2188],[1908,8982,8984],{"className":8983},[2193,2194,2195,2196],[1908,8985,2107],{"className":8986},[1951,1952,2196],[1908,8988,8989,8992],{"style":4077},[1908,8990],{"className":8991,"style":2189},[2188],[1908,8993,8995],{"className":8994},[2193,2194,2195,2196],[1908,8996,3548],{"className":8997},[2392,2196],[1908,8999,2204],{"className":9000},[2203],[1908,9002,9004],{"className":9003},[2176],[1908,9005,9007],{"className":9006,"style":4096},[2180],[1908,9008],{},[1908,9010,1991],{"className":9011},[2053],[1908,9013],{"className":9014,"style":2057},[2027],[1908,9016,9018,9021],{"className":9017},[1951],[1908,9019,7527],{"className":9020,"style":7564},[1951,1952],[1908,9022,9024],{"className":9023},[2167],[1908,9025,9027,9064],{"className":9026},[2171,2172],[1908,9028,9030,9061],{"className":9029},[2176],[1908,9031,9033,9050],{"className":9032,"style":4062},[2180],[1908,9034,9035,9038],{"style":8977},[1908,9036],{"className":9037,"style":2189},[2188],[1908,9039,9041],{"className":9040},[2193,2194,2195,2196],[1908,9042,9044,9047],{"className":9043},[1951,2196],[1908,9045,2828],{"className":9046},[1951,2196],[1908,9048,2107],{"className":9049},[1951,1952,2196],[1908,9051,9052,9055],{"style":4077},[1908,9053],{"className":9054,"style":2189},[2188],[1908,9056,9058],{"className":9057},[2193,2194,2195,2196],[1908,9059,3548],{"className":9060},[2392,2196],[1908,9062,2204],{"className":9063},[2203],[1908,9065,9067],{"className":9066},[2176],[1908,9068,9070],{"className":9069,"style":5664},[2180],[1908,9071],{},[1908,9073,2595],{"className":9074},[2086],[1908,9076],{"className":9077,"style":2028},[2027],[1908,9079,4373],{"className":9080},[2032],[1908,9082],{"className":9083,"style":2028},[2027],[1908,9085,9087,9090,9130,9133,9173,9176,9179,9236,9239,9242,9245,9248,9251,9291,9294,9297],{"className":9086},[1942],[1908,9088],{"className":9089,"style":5508},[1946],[1908,9091,9093,9096],{"className":9092},[1951],[1908,9094,2235],{"className":9095},[1951,1952],[1908,9097,9099],{"className":9098},[2167],[1908,9100,9102,9122],{"className":9101},[2171,2172],[1908,9103,9105,9119],{"className":9104},[2176],[1908,9106,9108],{"className":9107,"style":2181},[2180],[1908,9109,9110,9113],{"style":2308},[1908,9111],{"className":9112,"style":2189},[2188],[1908,9114,9116],{"className":9115},[2193,2194,2195,2196],[1908,9117,2107],{"className":9118},[1951,1952,2196],[1908,9120,2204],{"className":9121},[2203],[1908,9123,9125],{"className":9124},[2176],[1908,9126,9128],{"className":9127,"style":2211},[2180],[1908,9129],{},[1908,9131,2566],{"className":9132},[2046],[1908,9134,9136,9139],{"className":9135},[1951],[1908,9137,7527],{"className":9138,"style":7564},[1951,1952],[1908,9140,9142],{"className":9141},[2167],[1908,9143,9145,9165],{"className":9144},[2171,2172],[1908,9146,9148,9162],{"className":9147},[2176],[1908,9149,9151],{"className":9150,"style":2181},[2180],[1908,9152,9153,9156],{"style":7579},[1908,9154],{"className":9155,"style":2189},[2188],[1908,9157,9159],{"className":9158},[2193,2194,2195,2196],[1908,9160,2107],{"className":9161},[1951,1952,2196],[1908,9163,2204],{"className":9164},[2203],[1908,9166,9168],{"className":9167},[2176],[1908,9169,9171],{"className":9170,"style":2211},[2180],[1908,9172],{},[1908,9174,1991],{"className":9175},[2053],[1908,9177],{"className":9178,"style":2057},[2027],[1908,9180,9182,9185],{"className":9181},[1951],[1908,9183,7527],{"className":9184,"style":7564},[1951,1952],[1908,9186,9188],{"className":9187},[2167],[1908,9189,9191,9228],{"className":9190},[2171,2172],[1908,9192,9194,9225],{"className":9193},[2176],[1908,9195,9197,9214],{"className":9196,"style":4062},[2180],[1908,9198,9199,9202],{"style":8977},[1908,9200],{"className":9201,"style":2189},[2188],[1908,9203,9205],{"className":9204},[2193,2194,2195,2196],[1908,9206,9208,9211],{"className":9207},[1951,2196],[1908,9209,2828],{"className":9210},[1951,2196],[1908,9212,2107],{"className":9213},[1951,1952,2196],[1908,9215,9216,9219],{"style":4077},[1908,9217],{"className":9218,"style":2189},[2188],[1908,9220,9222],{"className":9221},[2193,2194,2195,2196],[1908,9223,3548],{"className":9224},[2392,2196],[1908,9226,2204],{"className":9227},[2203],[1908,9229,9231],{"className":9230},[2176],[1908,9232,9234],{"className":9233,"style":5664},[2180],[1908,9235],{},[1908,9237,2595],{"className":9238},[2086],[1908,9240,1991],{"className":9241},[2053],[1908,9243],{"className":9244,"style":5840},[2027],[1908,9246],{"className":9247,"style":2057},[2027],[1908,9249,5480],{"className":9250},[1951],[1908,9252,9254,9257],{"className":9253},[1951],[1908,9255,7527],{"className":9256,"style":7564},[1951,1952],[1908,9258,9260],{"className":9259},[2167],[1908,9261,9263,9283],{"className":9262},[2171,2172],[1908,9264,9266,9280],{"className":9265},[2176],[1908,9267,9269],{"className":9268,"style":2181},[2180],[1908,9270,9271,9274],{"style":7579},[1908,9272],{"className":9273,"style":2189},[2188],[1908,9275,9277],{"className":9276},[2193,2194,2195,2196],[1908,9278,2107],{"className":9279},[1951,1952,2196],[1908,9281,2204],{"className":9282},[2203],[1908,9284,9286],{"className":9285},[2176],[1908,9287,9289],{"className":9288,"style":2211},[2180],[1908,9290],{},[1908,9292],{"className":9293,"style":2028},[2027],[1908,9295,5489],{"className":9296},[2032],[1908,9298],{"className":9299,"style":2028},[2027],[1908,9301,9303,9306,9309,9312,9352],{"className":9302},[1942],[1908,9304],{"className":9305,"style":2042},[1946],[1908,9307,7534],{"className":9308},[1951],[1908,9310,2566],{"className":9311},[2046],[1908,9313,9315,9318],{"className":9314},[1951],[1908,9316,2141],{"className":9317,"style":2163},[1951,1952],[1908,9319,9321],{"className":9320},[2167],[1908,9322,9324,9344],{"className":9323},[2171,2172],[1908,9325,9327,9341],{"className":9326},[2176],[1908,9328,9330],{"className":9329,"style":2181},[2180],[1908,9331,9332,9335],{"style":2184},[1908,9333],{"className":9334,"style":2189},[2188],[1908,9336,9338],{"className":9337},[2193,2194,2195,2196],[1908,9339,2107],{"className":9340},[1951,1952,2196],[1908,9342,2204],{"className":9343},[2203],[1908,9345,9347],{"className":9346},[2176],[1908,9348,9350],{"className":9349,"style":2211},[2180],[1908,9351],{},[1908,9353,2595],{"className":9354},[2086],[1798,9356,9357,9360,9361,9389,9390,9418],{},[1857,9358,9359],{},"关键引理（无差异原则）",": 在混合策略纳什均衡中，如果参与者",[1908,9362,9364,9377],{"className":9363},[1911],[1908,9365,9367],{"className":9366},[1915],[1917,9368,9369],{"xmlns":1919},[1921,9370,9371,9375],{},[1924,9372,9373],{},[1927,9374,2107],{},[1931,9376,2107],{"encoding":1933},[1908,9378,9380],{"className":9379,"ariaHidden":1938},[1937],[1908,9381,9383,9386],{"className":9382},[1942],[1908,9384],{"className":9385,"style":2119},[1946],[1908,9387,2107],{"className":9388},[1951,1952],"以正概率选择某个纯策略，那么该纯策略必须是其最优反应之一，即给予",[1908,9391,9393,9406],{"className":9392},[1911],[1908,9394,9396],{"className":9395},[1915],[1917,9397,9398],{"xmlns":1919},[1921,9399,9400,9404],{},[1924,9401,9402],{},[1927,9403,2107],{},[1931,9405,2107],{"encoding":1933},[1908,9407,9409],{"className":9408,"ariaHidden":1938},[1937],[1908,9410,9412,9415],{"className":9411},[1942],[1908,9413],{"className":9414,"style":2119},[1946],[1908,9416,2107],{"className":9417},[1951,1952],"相同的期望支付。",[1798,9420,9421,9424],{},[1857,9422,9423],{},"推论",": 在混合策略均衡中，参与者在其支持集（正概率纯策略集合）中的所有策略间无差异。",[1897,9426,9428],{"id":9427},"_34-求解混合策略均衡","3.4 求解混合策略均衡",[1798,9430,9431],{},[1857,9432,9433],{},"例题: 性别战争\u002F协调博弈",[3421,9435,9436,9448],{},[3424,9437,9438],{},[3427,9439,9440,9442,9445],{},[3430,9441],{},[3430,9443,9444],{},"女：歌剧(O)",[3430,9446,9447],{},"女：足球(F)",[3439,9449,9450,9461],{},[3427,9451,9452,9457,9459],{},[3444,9453,9454],{},[1857,9455,9456],{},"男：歌剧(O)",[3444,9458,6829],{},[3444,9460,6832],{},[3427,9462,9463,9468,9470],{},[3444,9464,9465],{},[1857,9466,9467],{},"男：足球(F)",[3444,9469,6832],{},[3444,9471,6844],{},[1798,9473,9474],{},"已找到两个纯策略均衡：(O, O)和(F, F)。是否存在混合策略均衡？",[1798,9476,9477,1860],{},[1857,9478,9479],{},"求解步骤",[1798,9481,9482,9483,9512,9513,6798],{},"设男选O的概率为",[1908,9484,9486,9499],{"className":9485},[1911],[1908,9487,9489],{"className":9488},[1915],[1917,9490,9491],{"xmlns":1919},[1921,9492,9493,9497],{},[1924,9494,9495],{},[1927,9496,1798],{},[1931,9498,1798],{"encoding":1933},[1908,9500,9502],{"className":9501,"ariaHidden":1938},[1937],[1908,9503,9505,9509],{"className":9504},[1942],[1908,9506],{"className":9507,"style":9508},[1946],"height:0.625em;vertical-align:-0.1944em;",[1908,9510,1798],{"className":9511},[1951,1952],"，女选O的概率为",[1908,9514,9516,9530],{"className":9515},[1911],[1908,9517,9519],{"className":9518},[1915],[1917,9520,9521],{"xmlns":1919},[1921,9522,9523,9528],{},[1924,9524,9525],{},[1927,9526,9527],{},"q",[1931,9529,9527],{"encoding":1933},[1908,9531,9533],{"className":9532,"ariaHidden":1938},[1937],[1908,9534,9536,9539],{"className":9535},[1942],[1908,9537],{"className":9538,"style":9508},[1946],[1908,9540,9527],{"className":9541,"style":7564},[1951,1952],[1798,9543,9544,9547],{},[1857,9545,9546],{},"使女无差异","（她才愿意混合）:",[1908,9549,9551],{"className":9550},[3912],[1908,9552,9554,9596],{"className":9553},[1911],[1908,9555,9557],{"className":9556},[1915],[1917,9558,9559],{"xmlns":1919,"display":3921},[1921,9560,9561,9593],{},[1924,9562,9563,9571,9573,9576,9578,9580,9586,9588,9591],{},[2137,9564,9565,9567],{},[1927,9566,2235],{},[9568,9569,9570],"mtext",{},"女",[1978,9572,2566],{"stretchy":1983},[1927,9574,9575],{},"O",[1978,9577,2595],{"stretchy":1983},[1978,9579,1980],{},[2137,9581,9582,9584],{},[1927,9583,2235],{},[9568,9585,9570],{},[1978,9587,2566],{"stretchy":1983},[1927,9589,9590],{},"F",[1978,9592,2595],{"stretchy":1983},[1931,9594,9595],{"encoding":1933},"u_{\\text{女}}(O) = u_{\\text{女}}(F)",[1908,9597,9599,9673],{"className":9598,"ariaHidden":1938},[1937],[1908,9600,9602,9605,9654,9657,9661,9664,9667,9670],{"className":9601},[1942],[1908,9603],{"className":9604,"style":2042},[1946],[1908,9606,9608,9611],{"className":9607},[1951],[1908,9609,2235],{"className":9610},[1951,1952],[1908,9612,9614],{"className":9613},[2167],[1908,9615,9617,9646],{"className":9616},[2171,2172],[1908,9618,9620,9643],{"className":9619},[2176],[1908,9621,9624],{"className":9622,"style":9623},[2180],"height:0.3283em;",[1908,9625,9626,9629],{"style":2308},[1908,9627],{"className":9628,"style":2189},[2188],[1908,9630,9632],{"className":9631},[2193,2194,2195,2196],[1908,9633,9635],{"className":9634},[1951,2196],[1908,9636,9639],{"className":9637},[1951,9638,2196],"text",[1908,9640,9570],{"className":9641},[1951,9642,2196],"cjk_fallback",[1908,9644,2204],{"className":9645},[2203],[1908,9647,9649],{"className":9648},[2176],[1908,9650,9652],{"className":9651,"style":2211},[2180],[1908,9653],{},[1908,9655,2566],{"className":9656},[2046],[1908,9658,9575],{"className":9659,"style":9660},[1951,1952],"margin-right:0.0278em;",[1908,9662,2595],{"className":9663},[2086],[1908,9665],{"className":9666,"style":2028},[2027],[1908,9668,1980],{"className":9669},[2032],[1908,9671],{"className":9672,"style":2028},[2027],[1908,9674,9676,9679,9725,9728,9732],{"className":9675},[1942],[1908,9677],{"className":9678,"style":2042},[1946],[1908,9680,9682,9685],{"className":9681},[1951],[1908,9683,2235],{"className":9684},[1951,1952],[1908,9686,9688],{"className":9687},[2167],[1908,9689,9691,9717],{"className":9690},[2171,2172],[1908,9692,9694,9714],{"className":9693},[2176],[1908,9695,9697],{"className":9696,"style":9623},[2180],[1908,9698,9699,9702],{"style":2308},[1908,9700],{"className":9701,"style":2189},[2188],[1908,9703,9705],{"className":9704},[2193,2194,2195,2196],[1908,9706,9708],{"className":9707},[1951,2196],[1908,9709,9711],{"className":9710},[1951,9638,2196],[1908,9712,9570],{"className":9713},[1951,9642,2196],[1908,9715,2204],{"className":9716},[2203],[1908,9718,9720],{"className":9719},[2176],[1908,9721,9723],{"className":9722,"style":2211},[2180],[1908,9724],{},[1908,9726,2566],{"className":9727},[2046],[1908,9729,9590],{"className":9730,"style":9731},[1951,1952],"margin-right:0.1389em;",[1908,9733,2595],{"className":9734},[2086],[1908,9736,9738],{"className":9737},[3912],[1908,9739,9741,9801],{"className":9740},[1911],[1908,9742,9744],{"className":9743},[1915],[1917,9745,9746],{"xmlns":1919,"display":3921},[1921,9747,9748,9798],{},[1924,9749,9750,9752,9755,9757,9759,9762,9764,9766,9768,9770,9772,9774,9776,9778,9780,9782,9784,9786,9788,9790,9792,9794,9796],{},[1986,9751,1988],{},[1978,9753,9754],{},"⋅",[1927,9756,1798],{},[1978,9758,2871],{},[1986,9760,9761],{},"0",[1978,9763,9754],{},[1978,9765,2566],{"stretchy":1983},[1986,9767,1988],{},[1978,9769,2828],{},[1927,9771,1798],{},[1978,9773,2595],{"stretchy":1983},[1978,9775,1980],{},[1986,9777,9761],{},[1978,9779,9754],{},[1927,9781,1798],{},[1978,9783,2871],{},[1986,9785,1994],{},[1978,9787,9754],{},[1978,9789,2566],{"stretchy":1983},[1986,9791,1988],{},[1978,9793,2828],{},[1927,9795,1798],{},[1978,9797,2595],{"stretchy":1983},[1931,9799,9800],{"encoding":1933},"1 \\cdot p + 0 \\cdot (1-p) = 0 \\cdot p + 2 \\cdot (1-p)",[1908,9802,9804,9823,9842,9860,9881,9902,9920,9938,9956,9977],{"className":9803,"ariaHidden":1938},[1937],[1908,9805,9807,9811,9814,9817,9820],{"className":9806},[1942],[1908,9808],{"className":9809,"style":9810},[1946],"height:0.6444em;",[1908,9812,1988],{"className":9813},[1951],[1908,9815],{"className":9816,"style":2388},[2027],[1908,9818,9754],{"className":9819},[2392],[1908,9821],{"className":9822,"style":2388},[2027],[1908,9824,9826,9830,9833,9836,9839],{"className":9825},[1942],[1908,9827],{"className":9828,"style":9829},[1946],"height:0.7778em;vertical-align:-0.1944em;",[1908,9831,1798],{"className":9832},[1951,1952],[1908,9834],{"className":9835,"style":2388},[2027],[1908,9837,2871],{"className":9838},[2392],[1908,9840],{"className":9841,"style":2388},[2027],[1908,9843,9845,9848,9851,9854,9857],{"className":9844},[1942],[1908,9846],{"className":9847,"style":9810},[1946],[1908,9849,9761],{"className":9850},[1951],[1908,9852],{"className":9853,"style":2388},[2027],[1908,9855,9754],{"className":9856},[2392],[1908,9858],{"className":9859,"style":2388},[2027],[1908,9861,9863,9866,9869,9872,9875,9878],{"className":9862},[1942],[1908,9864],{"className":9865,"style":2042},[1946],[1908,9867,2566],{"className":9868},[2046],[1908,9870,1988],{"className":9871},[1951],[1908,9873],{"className":9874,"style":2388},[2027],[1908,9876,2828],{"className":9877},[2392],[1908,9879],{"className":9880,"style":2388},[2027],[1908,9882,9884,9887,9890,9893,9896,9899],{"className":9883},[1942],[1908,9885],{"className":9886,"style":2042},[1946],[1908,9888,1798],{"className":9889},[1951,1952],[1908,9891,2595],{"className":9892},[2086],[1908,9894],{"className":9895,"style":2028},[2027],[1908,9897,1980],{"className":9898},[2032],[1908,9900],{"className":9901,"style":2028},[2027],[1908,9903,9905,9908,9911,9914,9917],{"className":9904},[1942],[1908,9906],{"className":9907,"style":9810},[1946],[1908,9909,9761],{"className":9910},[1951],[1908,9912],{"className":9913,"style":2388},[2027],[1908,9915,9754],{"className":9916},[2392],[1908,9918],{"className":9919,"style":2388},[2027],[1908,9921,9923,9926,9929,9932,9935],{"className":9922},[1942],[1908,9924],{"className":9925,"style":9829},[1946],[1908,9927,1798],{"className":9928},[1951,1952],[1908,9930],{"className":9931,"style":2388},[2027],[1908,9933,2871],{"className":9934},[2392],[1908,9936],{"className":9937,"style":2388},[2027],[1908,9939,9941,9944,9947,9950,9953],{"className":9940},[1942],[1908,9942],{"className":9943,"style":9810},[1946],[1908,9945,1994],{"className":9946},[1951],[1908,9948],{"className":9949,"style":2388},[2027],[1908,9951,9754],{"className":9952},[2392],[1908,9954],{"className":9955,"style":2388},[2027],[1908,9957,9959,9962,9965,9968,9971,9974],{"className":9958},[1942],[1908,9960],{"className":9961,"style":2042},[1946],[1908,9963,2566],{"className":9964},[2046],[1908,9966,1988],{"className":9967},[1951],[1908,9969],{"className":9970,"style":2388},[2027],[1908,9972,2828],{"className":9973},[2392],[1908,9975],{"className":9976,"style":2388},[2027],[1908,9978,9980,9983,9986],{"className":9979},[1942],[1908,9981],{"className":9982,"style":2042},[1946],[1908,9984,1798],{"className":9985},[1951,1952],[1908,9987,2595],{"className":9988},[2086],[1908,9990,9992],{"className":9991},[3912],[1908,9993,9995,10023],{"className":9994},[1911],[1908,9996,9998],{"className":9997},[1915],[1917,9999,10000],{"xmlns":1919,"display":3921},[1921,10001,10002,10020],{},[1924,10003,10004,10006,10008,10010,10012,10014,10016,10018],{},[1927,10005,1798],{},[1978,10007,1980],{},[1986,10009,1994],{},[1978,10011,2566],{"stretchy":1983},[1986,10013,1988],{},[1978,10015,2828],{},[1927,10017,1798],{},[1978,10019,2595],{"stretchy":1983},[1931,10021,10022],{"encoding":1933},"p = 2(1-p)",[1908,10024,10026,10044,10068],{"className":10025,"ariaHidden":1938},[1937],[1908,10027,10029,10032,10035,10038,10041],{"className":10028},[1942],[1908,10030],{"className":10031,"style":9508},[1946],[1908,10033,1798],{"className":10034},[1951,1952],[1908,10036],{"className":10037,"style":2028},[2027],[1908,10039,1980],{"className":10040},[2032],[1908,10042],{"className":10043,"style":2028},[2027],[1908,10045,10047,10050,10053,10056,10059,10062,10065],{"className":10046},[1942],[1908,10048],{"className":10049,"style":2042},[1946],[1908,10051,1994],{"className":10052},[1951],[1908,10054,2566],{"className":10055},[2046],[1908,10057,1988],{"className":10058},[1951],[1908,10060],{"className":10061,"style":2388},[2027],[1908,10063,2828],{"className":10064},[2392],[1908,10066],{"className":10067,"style":2388},[2027],[1908,10069,10071,10074,10077],{"className":10070},[1942],[1908,10072],{"className":10073,"style":2042},[1946],[1908,10075,1798],{"className":10076},[1951,1952],[1908,10078,2595],{"className":10079},[2086],[1908,10081,10083],{"className":10082},[3912],[1908,10084,10086,10110],{"className":10085},[1911],[1908,10087,10089],{"className":10088},[1915],[1917,10090,10091],{"xmlns":1919,"display":3921},[1921,10092,10093,10107],{},[1924,10094,10095,10097,10099,10101,10104],{},[1927,10096,1798],{},[1978,10098,1980],{},[1986,10100,1994],{},[1927,10102,10103],{"mathvariant":3638},"\u002F",[1986,10105,10106],{},"3",[1931,10108,10109],{"encoding":1933},"p = 2\u002F3",[1908,10111,10113,10131],{"className":10112,"ariaHidden":1938},[1937],[1908,10114,10116,10119,10122,10125,10128],{"className":10115},[1942],[1908,10117],{"className":10118,"style":9508},[1946],[1908,10120,1798],{"className":10121},[1951,1952],[1908,10123],{"className":10124,"style":2028},[2027],[1908,10126,1980],{"className":10127},[2032],[1908,10129],{"className":10130,"style":2028},[2027],[1908,10132,10134,10137],{"className":10133},[1942],[1908,10135],{"className":10136,"style":2042},[1946],[1908,10138,10140],{"className":10139},[1951],"2\u002F3",[1798,10142,10143,1860],{},[1857,10144,10145],{},"使男无差异",[1908,10147,10149],{"className":10148},[3912],[1908,10150,10152,10191],{"className":10151},[1911],[1908,10153,10155],{"className":10154},[1915],[1917,10156,10157],{"xmlns":1919,"display":3921},[1921,10158,10159,10188],{},[1924,10160,10161,10168,10170,10172,10174,10176,10182,10184,10186],{},[2137,10162,10163,10165],{},[1927,10164,2235],{},[9568,10166,10167],{},"男",[1978,10169,2566],{"stretchy":1983},[1927,10171,9575],{},[1978,10173,2595],{"stretchy":1983},[1978,10175,1980],{},[2137,10177,10178,10180],{},[1927,10179,2235],{},[9568,10181,10167],{},[1978,10183,2566],{"stretchy":1983},[1927,10185,9590],{},[1978,10187,2595],{"stretchy":1983},[1931,10189,10190],{"encoding":1933},"u_{\\text{男}}(O) = u_{\\text{男}}(F)",[1908,10192,10194,10264],{"className":10193,"ariaHidden":1938},[1937],[1908,10195,10197,10200,10246,10249,10252,10255,10258,10261],{"className":10196},[1942],[1908,10198],{"className":10199,"style":2042},[1946],[1908,10201,10203,10206],{"className":10202},[1951],[1908,10204,2235],{"className":10205},[1951,1952],[1908,10207,10209],{"className":10208},[2167],[1908,10210,10212,10238],{"className":10211},[2171,2172],[1908,10213,10215,10235],{"className":10214},[2176],[1908,10216,10218],{"className":10217,"style":9623},[2180],[1908,10219,10220,10223],{"style":2308},[1908,10221],{"className":10222,"style":2189},[2188],[1908,10224,10226],{"className":10225},[2193,2194,2195,2196],[1908,10227,10229],{"className":10228},[1951,2196],[1908,10230,10232],{"className":10231},[1951,9638,2196],[1908,10233,10167],{"className":10234},[1951,9642,2196],[1908,10236,2204],{"className":10237},[2203],[1908,10239,10241],{"className":10240},[2176],[1908,10242,10244],{"className":10243,"style":2211},[2180],[1908,10245],{},[1908,10247,2566],{"className":10248},[2046],[1908,10250,9575],{"className":10251,"style":9660},[1951,1952],[1908,10253,2595],{"className":10254},[2086],[1908,10256],{"className":10257,"style":2028},[2027],[1908,10259,1980],{"className":10260},[2032],[1908,10262],{"className":10263,"style":2028},[2027],[1908,10265,10267,10270,10316,10319,10322],{"className":10266},[1942],[1908,10268],{"className":10269,"style":2042},[1946],[1908,10271,10273,10276],{"className":10272},[1951],[1908,10274,2235],{"className":10275},[1951,1952],[1908,10277,10279],{"className":10278},[2167],[1908,10280,10282,10308],{"className":10281},[2171,2172],[1908,10283,10285,10305],{"className":10284},[2176],[1908,10286,10288],{"className":10287,"style":9623},[2180],[1908,10289,10290,10293],{"style":2308},[1908,10291],{"className":10292,"style":2189},[2188],[1908,10294,10296],{"className":10295},[2193,2194,2195,2196],[1908,10297,10299],{"className":10298},[1951,2196],[1908,10300,10302],{"className":10301},[1951,9638,2196],[1908,10303,10167],{"className":10304},[1951,9642,2196],[1908,10306,2204],{"className":10307},[2203],[1908,10309,10311],{"className":10310},[2176],[1908,10312,10314],{"className":10313,"style":2211},[2180],[1908,10315],{},[1908,10317,2566],{"className":10318},[2046],[1908,10320,9590],{"className":10321,"style":9731},[1951,1952],[1908,10323,2595],{"className":10324},[2086],[1908,10326,10328],{"className":10327},[3912],[1908,10329,10331,10389],{"className":10330},[1911],[1908,10332,10334],{"className":10333},[1915],[1917,10335,10336],{"xmlns":1919,"display":3921},[1921,10337,10338,10386],{},[1924,10339,10340,10342,10344,10346,10348,10350,10352,10354,10356,10358,10360,10362,10364,10366,10368,10370,10372,10374,10376,10378,10380,10382,10384],{},[1986,10341,1994],{},[1978,10343,9754],{},[1927,10345,9527],{},[1978,10347,2871],{},[1986,10349,9761],{},[1978,10351,9754],{},[1978,10353,2566],{"stretchy":1983},[1986,10355,1988],{},[1978,10357,2828],{},[1927,10359,9527],{},[1978,10361,2595],{"stretchy":1983},[1978,10363,1980],{},[1986,10365,9761],{},[1978,10367,9754],{},[1927,10369,9527],{},[1978,10371,2871],{},[1986,10373,1988],{},[1978,10375,9754],{},[1978,10377,2566],{"stretchy":1983},[1986,10379,1988],{},[1978,10381,2828],{},[1927,10383,9527],{},[1978,10385,2595],{"stretchy":1983},[1931,10387,10388],{"encoding":1933},"2 \\cdot q + 0 \\cdot (1-q) = 0 \\cdot q + 1 \\cdot (1-q)",[1908,10390,10392,10410,10428,10446,10467,10488,10506,10524,10542,10563],{"className":10391,"ariaHidden":1938},[1937],[1908,10393,10395,10398,10401,10404,10407],{"className":10394},[1942],[1908,10396],{"className":10397,"style":9810},[1946],[1908,10399,1994],{"className":10400},[1951],[1908,10402],{"className":10403,"style":2388},[2027],[1908,10405,9754],{"className":10406},[2392],[1908,10408],{"className":10409,"style":2388},[2027],[1908,10411,10413,10416,10419,10422,10425],{"className":10412},[1942],[1908,10414],{"className":10415,"style":9829},[1946],[1908,10417,9527],{"className":10418,"style":7564},[1951,1952],[1908,10420],{"className":10421,"style":2388},[2027],[1908,10423,2871],{"className":10424},[2392],[1908,10426],{"className":10427,"style":2388},[2027],[1908,10429,10431,10434,10437,10440,10443],{"className":10430},[1942],[1908,10432],{"className":10433,"style":9810},[1946],[1908,10435,9761],{"className":10436},[1951],[1908,10438],{"className":10439,"style":2388},[2027],[1908,10441,9754],{"className":10442},[2392],[1908,10444],{"className":10445,"style":2388},[2027],[1908,10447,10449,10452,10455,10458,10461,10464],{"className":10448},[1942],[1908,10450],{"className":10451,"style":2042},[1946],[1908,10453,2566],{"className":10454},[2046],[1908,10456,1988],{"className":10457},[1951],[1908,10459],{"className":10460,"style":2388},[2027],[1908,10462,2828],{"className":10463},[2392],[1908,10465],{"className":10466,"style":2388},[2027],[1908,10468,10470,10473,10476,10479,10482,10485],{"className":10469},[1942],[1908,10471],{"className":10472,"style":2042},[1946],[1908,10474,9527],{"className":10475,"style":7564},[1951,1952],[1908,10477,2595],{"className":10478},[2086],[1908,10480],{"className":10481,"style":2028},[2027],[1908,10483,1980],{"className":10484},[2032],[1908,10486],{"className":10487,"style":2028},[2027],[1908,10489,10491,10494,10497,10500,10503],{"className":10490},[1942],[1908,10492],{"className":10493,"style":9810},[1946],[1908,10495,9761],{"className":10496},[1951],[1908,10498],{"className":10499,"style":2388},[2027],[1908,10501,9754],{"className":10502},[2392],[1908,10504],{"className":10505,"style":2388},[2027],[1908,10507,10509,10512,10515,10518,10521],{"className":10508},[1942],[1908,10510],{"className":10511,"style":9829},[1946],[1908,10513,9527],{"className":10514,"style":7564},[1951,1952],[1908,10516],{"className":10517,"style":2388},[2027],[1908,10519,2871],{"className":10520},[2392],[1908,10522],{"className":10523,"style":2388},[2027],[1908,10525,10527,10530,10533,10536,10539],{"className":10526},[1942],[1908,10528],{"className":10529,"style":9810},[1946],[1908,10531,1988],{"className":10532},[1951],[1908,10534],{"className":10535,"style":2388},[2027],[1908,10537,9754],{"className":10538},[2392],[1908,10540],{"className":10541,"style":2388},[2027],[1908,10543,10545,10548,10551,10554,10557,10560],{"className":10544},[1942],[1908,10546],{"className":10547,"style":2042},[1946],[1908,10549,2566],{"className":10550},[2046],[1908,10552,1988],{"className":10553},[1951],[1908,10555],{"className":10556,"style":2388},[2027],[1908,10558,2828],{"className":10559},[2392],[1908,10561],{"className":10562,"style":2388},[2027],[1908,10564,10566,10569,10572],{"className":10565},[1942],[1908,10567],{"className":10568,"style":2042},[1946],[1908,10570,9527],{"className":10571,"style":7564},[1951,1952],[1908,10573,2595],{"className":10574},[2086],[1908,10576,10578],{"className":10577},[3912],[1908,10579,10581,10605],{"className":10580},[1911],[1908,10582,10584],{"className":10583},[1915],[1917,10585,10586],{"xmlns":1919,"display":3921},[1921,10587,10588,10602],{},[1924,10589,10590,10592,10594,10596,10598,10600],{},[1986,10591,1994],{},[1927,10593,9527],{},[1978,10595,1980],{},[1986,10597,1988],{},[1978,10599,2828],{},[1927,10601,9527],{},[1931,10603,10604],{"encoding":1933},"2q = 1 - q",[1908,10606,10608,10630,10649],{"className":10607,"ariaHidden":1938},[1937],[1908,10609,10611,10615,10618,10621,10624,10627],{"className":10610},[1942],[1908,10612],{"className":10613,"style":10614},[1946],"height:0.8389em;vertical-align:-0.1944em;",[1908,10616,1994],{"className":10617},[1951],[1908,10619,9527],{"className":10620,"style":7564},[1951,1952],[1908,10622],{"className":10623,"style":2028},[2027],[1908,10625,1980],{"className":10626},[2032],[1908,10628],{"className":10629,"style":2028},[2027],[1908,10631,10633,10637,10640,10643,10646],{"className":10632},[1942],[1908,10634],{"className":10635,"style":10636},[1946],"height:0.7278em;vertical-align:-0.0833em;",[1908,10638,1988],{"className":10639},[1951],[1908,10641],{"className":10642,"style":2388},[2027],[1908,10644,2828],{"className":10645},[2392],[1908,10647],{"className":10648,"style":2388},[2027],[1908,10650,10652,10655],{"className":10651},[1942],[1908,10653],{"className":10654,"style":9508},[1946],[1908,10656,9527],{"className":10657,"style":7564},[1951,1952],[1908,10659,10661],{"className":10660},[3912],[1908,10662,10664,10686],{"className":10663},[1911],[1908,10665,10667],{"className":10666},[1915],[1917,10668,10669],{"xmlns":1919,"display":3921},[1921,10670,10671,10683],{},[1924,10672,10673,10675,10677,10679,10681],{},[1927,10674,9527],{},[1978,10676,1980],{},[1986,10678,1988],{},[1927,10680,10103],{"mathvariant":3638},[1986,10682,10106],{},[1931,10684,10685],{"encoding":1933},"q = 1\u002F3",[1908,10687,10689,10707],{"className":10688,"ariaHidden":1938},[1937],[1908,10690,10692,10695,10698,10701,10704],{"className":10691},[1942],[1908,10693],{"className":10694,"style":9508},[1946],[1908,10696,9527],{"className":10697,"style":7564},[1951,1952],[1908,10699],{"className":10700,"style":2028},[2027],[1908,10702,1980],{"className":10703},[2032],[1908,10705],{"className":10706,"style":2028},[2027],[1908,10708,10710,10713],{"className":10709},[1942],[1908,10711],{"className":10712,"style":2042},[1946],[1908,10714,10716],{"className":10715},[1951],"1\u002F3",[1798,10718,10719,10722],{},[1857,10720,10721],{},"混合策略纳什均衡",": 男选O的概率2\u002F3，女选O的概率1\u002F3。",[1798,10724,10725,1860],{},[1857,10726,10727],{},"期望支付",[1908,10729,10731],{"className":10730},[3912],[1908,10732,10734,10783],{"className":10733},[1911],[1908,10735,10737],{"className":10736},[1915],[1917,10738,10739],{"xmlns":1919,"display":3921},[1921,10740,10741,10780],{},[1924,10742,10743,10749,10751,10753,10755,10762,10764,10770,10772],{},[2137,10744,10745,10747],{},[1927,10746,2235],{},[9568,10748,10167],{},[1978,10750,1980],{},[1986,10752,1994],{},[1978,10754,2248],{},[10756,10757,10758,10760],"mfrac",{},[1986,10759,1988],{},[1986,10761,10106],{},[1978,10763,2248],{},[10756,10765,10766,10768],{},[1986,10767,1994],{},[1986,10769,10106],{},[1978,10771,1980],{},[10756,10773,10774,10777],{},[1986,10775,10776],{},"4",[1986,10778,10779],{},"9",[1931,10781,10782],{"encoding":1933},"u_{\\text{男}} = 2 \\times \\frac{1}{3} \\times \\frac{2}{3} = \\frac{4}{9}",[1908,10784,10786,10847,10865,10951,11028],{"className":10785,"ariaHidden":1938},[1937],[1908,10787,10789,10792,10838,10841,10844],{"className":10788},[1942],[1908,10790],{"className":10791,"style":2287},[1946],[1908,10793,10795,10798],{"className":10794},[1951],[1908,10796,2235],{"className":10797},[1951,1952],[1908,10799,10801],{"className":10800},[2167],[1908,10802,10804,10830],{"className":10803},[2171,2172],[1908,10805,10807,10827],{"className":10806},[2176],[1908,10808,10810],{"className":10809,"style":9623},[2180],[1908,10811,10812,10815],{"style":2308},[1908,10813],{"className":10814,"style":2189},[2188],[1908,10816,10818],{"className":10817},[2193,2194,2195,2196],[1908,10819,10821],{"className":10820},[1951,2196],[1908,10822,10824],{"className":10823},[1951,9638,2196],[1908,10825,10167],{"className":10826},[1951,9642,2196],[1908,10828,2204],{"className":10829},[2203],[1908,10831,10833],{"className":10832},[2176],[1908,10834,10836],{"className":10835,"style":2211},[2180],[1908,10837],{},[1908,10839],{"className":10840,"style":2028},[2027],[1908,10842,1980],{"className":10843},[2032],[1908,10845],{"className":10846,"style":2028},[2027],[1908,10848,10850,10853,10856,10859,10862],{"className":10849},[1942],[1908,10851],{"className":10852,"style":10636},[1946],[1908,10854,1994],{"className":10855},[1951],[1908,10857],{"className":10858,"style":2388},[2027],[1908,10860,2248],{"className":10861},[2392],[1908,10863],{"className":10864,"style":2388},[2027],[1908,10866,10868,10872,10942,10945,10948],{"className":10867},[1942],[1908,10869],{"className":10870,"style":10871},[1946],"height:2.0074em;vertical-align:-0.686em;",[1908,10873,10875,10879,10939],{"className":10874},[1951],[1908,10876],{"className":10877},[2046,10878],"nulldelimiter",[1908,10880,10882],{"className":10881},[10756],[1908,10883,10885,10930],{"className":10884},[2171,2172],[1908,10886,10888,10927],{"className":10887},[2176],[1908,10889,10892,10904,10915],{"className":10890,"style":10891},[2180],"height:1.3214em;",[1908,10893,10895,10898],{"style":10894},"top:-2.314em;",[1908,10896],{"className":10897,"style":6273},[2188],[1908,10899,10901],{"className":10900},[1951],[1908,10902,10106],{"className":10903},[1951],[1908,10905,10907,10910],{"style":10906},"top:-3.23em;",[1908,10908],{"className":10909,"style":6273},[2188],[1908,10911],{"className":10912,"style":10914},[10913],"frac-line","border-bottom-width:0.04em;",[1908,10916,10918,10921],{"style":10917},"top:-3.677em;",[1908,10919],{"className":10920,"style":6273},[2188],[1908,10922,10924],{"className":10923},[1951],[1908,10925,1988],{"className":10926},[1951],[1908,10928,2204],{"className":10929},[2203],[1908,10931,10933],{"className":10932},[2176],[1908,10934,10937],{"className":10935,"style":10936},[2180],"height:0.686em;",[1908,10938],{},[1908,10940],{"className":10941},[2086,10878],[1908,10943],{"className":10944,"style":2388},[2027],[1908,10946,2248],{"className":10947},[2392],[1908,10949],{"className":10950,"style":2388},[2027],[1908,10952,10954,10957,11019,11022,11025],{"className":10953},[1942],[1908,10955],{"className":10956,"style":10871},[1946],[1908,10958,10960,10963,11016],{"className":10959},[1951],[1908,10961],{"className":10962},[2046,10878],[1908,10964,10966],{"className":10965},[10756],[1908,10967,10969,11008],{"className":10968},[2171,2172],[1908,10970,10972,11005],{"className":10971},[2176],[1908,10973,10975,10986,10994],{"className":10974,"style":10891},[2180],[1908,10976,10977,10980],{"style":10894},[1908,10978],{"className":10979,"style":6273},[2188],[1908,10981,10983],{"className":10982},[1951],[1908,10984,10106],{"className":10985},[1951],[1908,10987,10988,10991],{"style":10906},[1908,10989],{"className":10990,"style":6273},[2188],[1908,10992],{"className":10993,"style":10914},[10913],[1908,10995,10996,10999],{"style":10917},[1908,10997],{"className":10998,"style":6273},[2188],[1908,11000,11002],{"className":11001},[1951],[1908,11003,1994],{"className":11004},[1951],[1908,11006,2204],{"className":11007},[2203],[1908,11009,11011],{"className":11010},[2176],[1908,11012,11014],{"className":11013,"style":10936},[2180],[1908,11015],{},[1908,11017],{"className":11018},[2086,10878],[1908,11020],{"className":11021,"style":2028},[2027],[1908,11023,1980],{"className":11024},[2032],[1908,11026],{"className":11027,"style":2028},[2027],[1908,11029,11031,11034],{"className":11030},[1942],[1908,11032],{"className":11033,"style":10871},[1946],[1908,11035,11037,11040,11093],{"className":11036},[1951],[1908,11038],{"className":11039},[2046,10878],[1908,11041,11043],{"className":11042},[10756],[1908,11044,11046,11085],{"className":11045},[2171,2172],[1908,11047,11049,11082],{"className":11048},[2176],[1908,11050,11052,11063,11071],{"className":11051,"style":10891},[2180],[1908,11053,11054,11057],{"style":10894},[1908,11055],{"className":11056,"style":6273},[2188],[1908,11058,11060],{"className":11059},[1951],[1908,11061,10779],{"className":11062},[1951],[1908,11064,11065,11068],{"style":10906},[1908,11066],{"className":11067,"style":6273},[2188],[1908,11069],{"className":11070,"style":10914},[10913],[1908,11072,11073,11076],{"style":10917},[1908,11074],{"className":11075,"style":6273},[2188],[1908,11077,11079],{"className":11078},[1951],[1908,11080,10776],{"className":11081},[1951],[1908,11083,2204],{"className":11084},[2203],[1908,11086,11088],{"className":11087},[2176],[1908,11089,11091],{"className":11090,"style":10936},[2180],[1908,11092],{},[1908,11094],{"className":11095},[2086,10878],[1908,11097,11099],{"className":11098},[3912],[1908,11100,11102,11148],{"className":11101},[1911],[1908,11103,11105],{"className":11104},[1915],[1917,11106,11107],{"xmlns":1919,"display":3921},[1921,11108,11109,11145],{},[1924,11110,11111,11117,11119,11121,11123,11129,11131,11137,11139],{},[2137,11112,11113,11115],{},[1927,11114,2235],{},[9568,11116,9570],{},[1978,11118,1980],{},[1986,11120,1988],{},[1978,11122,2248],{},[10756,11124,11125,11127],{},[1986,11126,1988],{},[1986,11128,10106],{},[1978,11130,2248],{},[10756,11132,11133,11135],{},[1986,11134,1994],{},[1986,11136,10106],{},[1978,11138,1980],{},[10756,11140,11141,11143],{},[1986,11142,1994],{},[1986,11144,10779],{},[1931,11146,11147],{"encoding":1933},"u_{\\text{女}} = 1 \\times \\frac{1}{3} \\times \\frac{2}{3} = \\frac{2}{9}",[1908,11149,11151,11212,11230,11307,11384],{"className":11150,"ariaHidden":1938},[1937],[1908,11152,11154,11157,11203,11206,11209],{"className":11153},[1942],[1908,11155],{"className":11156,"style":2287},[1946],[1908,11158,11160,11163],{"className":11159},[1951],[1908,11161,2235],{"className":11162},[1951,1952],[1908,11164,11166],{"className":11165},[2167],[1908,11167,11169,11195],{"className":11168},[2171,2172],[1908,11170,11172,11192],{"className":11171},[2176],[1908,11173,11175],{"className":11174,"style":9623},[2180],[1908,11176,11177,11180],{"style":2308},[1908,11178],{"className":11179,"style":2189},[2188],[1908,11181,11183],{"className":11182},[2193,2194,2195,2196],[1908,11184,11186],{"className":11185},[1951,2196],[1908,11187,11189],{"className":11188},[1951,9638,2196],[1908,11190,9570],{"className":11191},[1951,9642,2196],[1908,11193,2204],{"className":11194},[2203],[1908,11196,11198],{"className":11197},[2176],[1908,11199,11201],{"className":11200,"style":2211},[2180],[1908,11202],{},[1908,11204],{"className":11205,"style":2028},[2027],[1908,11207,1980],{"className":11208},[2032],[1908,11210],{"className":11211,"style":2028},[2027],[1908,11213,11215,11218,11221,11224,11227],{"className":11214},[1942],[1908,11216],{"className":11217,"style":10636},[1946],[1908,11219,1988],{"className":11220},[1951],[1908,11222],{"className":11223,"style":2388},[2027],[1908,11225,2248],{"className":11226},[2392],[1908,11228],{"className":11229,"style":2388},[2027],[1908,11231,11233,11236,11298,11301,11304],{"className":11232},[1942],[1908,11234],{"className":11235,"style":10871},[1946],[1908,11237,11239,11242,11295],{"className":11238},[1951],[1908,11240],{"className":11241},[2046,10878],[1908,11243,11245],{"className":11244},[10756],[1908,11246,11248,11287],{"className":11247},[2171,2172],[1908,11249,11251,11284],{"className":11250},[2176],[1908,11252,11254,11265,11273],{"className":11253,"style":10891},[2180],[1908,11255,11256,11259],{"style":10894},[1908,11257],{"className":11258,"style":6273},[2188],[1908,11260,11262],{"className":11261},[1951],[1908,11263,10106],{"className":11264},[1951],[1908,11266,11267,11270],{"style":10906},[1908,11268],{"className":11269,"style":6273},[2188],[1908,11271],{"className":11272,"style":10914},[10913],[1908,11274,11275,11278],{"style":10917},[1908,11276],{"className":11277,"style":6273},[2188],[1908,11279,11281],{"className":11280},[1951],[1908,11282,1988],{"className":11283},[1951],[1908,11285,2204],{"className":11286},[2203],[1908,11288,11290],{"className":11289},[2176],[1908,11291,11293],{"className":11292,"style":10936},[2180],[1908,11294],{},[1908,11296],{"className":11297},[2086,10878],[1908,11299],{"className":11300,"style":2388},[2027],[1908,11302,2248],{"className":11303},[2392],[1908,11305],{"className":11306,"style":2388},[2027],[1908,11308,11310,11313,11375,11378,11381],{"className":11309},[1942],[1908,11311],{"className":11312,"style":10871},[1946],[1908,11314,11316,11319,11372],{"className":11315},[1951],[1908,11317],{"className":11318},[2046,10878],[1908,11320,11322],{"className":11321},[10756],[1908,11323,11325,11364],{"className":11324},[2171,2172],[1908,11326,11328,11361],{"className":11327},[2176],[1908,11329,11331,11342,11350],{"className":11330,"style":10891},[2180],[1908,11332,11333,11336],{"style":10894},[1908,11334],{"className":11335,"style":6273},[2188],[1908,11337,11339],{"className":11338},[1951],[1908,11340,10106],{"className":11341},[1951],[1908,11343,11344,11347],{"style":10906},[1908,11345],{"className":11346,"style":6273},[2188],[1908,11348],{"className":11349,"style":10914},[10913],[1908,11351,11352,11355],{"style":10917},[1908,11353],{"className":11354,"style":6273},[2188],[1908,11356,11358],{"className":11357},[1951],[1908,11359,1994],{"className":11360},[1951],[1908,11362,2204],{"className":11363},[2203],[1908,11365,11367],{"className":11366},[2176],[1908,11368,11370],{"className":11369,"style":10936},[2180],[1908,11371],{},[1908,11373],{"className":11374},[2086,10878],[1908,11376],{"className":11377,"style":2028},[2027],[1908,11379,1980],{"className":11380},[2032],[1908,11382],{"className":11383,"style":2028},[2027],[1908,11385,11387,11390],{"className":11386},[1942],[1908,11388],{"className":11389,"style":10871},[1946],[1908,11391,11393,11396,11449],{"className":11392},[1951],[1908,11394],{"className":11395},[2046,10878],[1908,11397,11399],{"className":11398},[10756],[1908,11400,11402,11441],{"className":11401},[2171,2172],[1908,11403,11405,11438],{"className":11404},[2176],[1908,11406,11408,11419,11427],{"className":11407,"style":10891},[2180],[1908,11409,11410,11413],{"style":10894},[1908,11411],{"className":11412,"style":6273},[2188],[1908,11414,11416],{"className":11415},[1951],[1908,11417,10779],{"className":11418},[1951],[1908,11420,11421,11424],{"style":10906},[1908,11422],{"className":11423,"style":6273},[2188],[1908,11425],{"className":11426,"style":10914},[10913],[1908,11428,11429,11432],{"style":10917},[1908,11430],{"className":11431,"style":6273},[2188],[1908,11433,11435],{"className":11434},[1951],[1908,11436,1994],{"className":11437},[1951],[1908,11439,2204],{"className":11440},[2203],[1908,11442,11444],{"className":11443},[2176],[1908,11445,11447],{"className":11446,"style":10936},[2180],[1908,11448],{},[1908,11450],{"className":11451},[2086,10878],[1798,11453,11454],{},"注意这比两个纯策略均衡都要差！混合策略均衡反映了协调失败的风险。",[1897,11456,11458],{"id":11457},"_35-经典案例石头剪刀布","3.5 经典案例：石头剪刀布",[3421,11460,11461,11476],{},[3424,11462,11463],{},[3427,11464,11465,11467,11470,11473],{},[3430,11466],{},[3430,11468,11469],{},"石头",[3430,11471,11472],{},"剪刀",[3430,11474,11475],{},"布",[3439,11477,11478,11492,11504],{},[3427,11479,11480,11484,11486,11489],{},[3444,11481,11482],{},[1857,11483,11469],{},[3444,11485,6832],{},[3444,11487,11488],{},"(1, -1)",[3444,11490,11491],{},"(-1, 1)",[3427,11493,11494,11498,11500,11502],{},[3444,11495,11496],{},[1857,11497,11472],{},[3444,11499,11491],{},[3444,11501,6832],{},[3444,11503,11488],{},[3427,11505,11506,11510,11512,11514],{},[3444,11507,11508],{},[1857,11509,11475],{},[3444,11511,11488],{},[3444,11513,11491],{},[3444,11515,6832],{},[1798,11517,11518,11521],{},[1857,11519,11520],{},"观察",": 不存在纯策略纳什均衡（任何策略组合都有人想偏离）",[1798,11523,11524,11527,11528,11560],{},[1857,11525,11526],{},"对称混合策略均衡",": 每个参与者以",[1908,11529,11531,11548],{"className":11530},[1911],[1908,11532,11534],{"className":11533},[1915],[1917,11535,11536],{"xmlns":1919},[1921,11537,11538,11546],{},[1924,11539,11540,11542,11544],{},[1986,11541,1988],{},[1927,11543,10103],{"mathvariant":3638},[1986,11545,10106],{},[1931,11547,10716],{"encoding":1933},[1908,11549,11551],{"className":11550,"ariaHidden":1938},[1937],[1908,11552,11554,11557],{"className":11553},[1942],[1908,11555],{"className":11556,"style":2042},[1946],[1908,11558,10716],{"className":11559},[1951],"概率选择每个策略",[1798,11562,11563,11566],{},[1857,11564,11565],{},"验证",": 给定对手均匀随机，自己的期望支付对所有策略都是0，因此无差异，无偏离动机。",[1890,11568],{},[1794,11570,11572],{"id":11571},"_4-动态博弈与扩展式","4. 动态博弈与扩展式",[1897,11574,11576],{"id":11575},"_41-扩展式博弈-extensive-form-game","4.1 扩展式博弈 (Extensive Form Game)",[1798,11578,11579,11582],{},[1857,11580,11581],{},"表示方法",": 博弈树",[1798,11584,11585,1860],{},[1857,11586,11587],{},"要素",[1875,11589,11590,11596,11602,11608],{},[1808,11591,11592,11595],{},[1857,11593,11594],{},"节点",": 决策点",[1808,11597,11598,11601],{},[1857,11599,11600],{},"分支",": 可选择的行动",[1808,11603,11604,11607],{},[1857,11605,11606],{},"信息集",": 参与者无法区分的节点集合",[1808,11609,11610,11613],{},[1857,11611,11612],{},"终端节点",": 博弈结束，标注支付",[1798,11615,11616,11619,11620,11623],{},[1857,11617,11618],{},"完美信息",": 所有信息集都是单点（参与者知道历史）\n",[1857,11621,11622],{},"不完美信息",": 存在非单点信息集",[1897,11625,11627],{"id":11626},"_42-逆向归纳法-backward-induction","4.2 逆向归纳法 (Backward Induction)",[1798,11629,11630,11633],{},[1857,11631,11632],{},"适用条件",": 有限、完美信息博弈",[1798,11635,11636,1860],{},[1857,11637,11638],{},"算法",[1875,11640,11641,11644,11647,11650,11653],{},[1808,11642,11643],{},"从最后一个决策节点开始",[1808,11645,11646],{},"确定该节点的最优行动",[1808,11648,11649],{},"用该最优行动的支付替代该子博弈",[1808,11651,11652],{},"向前移动到前一个决策节点",[1808,11654,11655],{},"重复直到初始节点",[1798,11657,11658],{},[1857,11659,11660],{},"例题: 进入博弈 (Entry Game)",[11662,11663,11667],"pre",{"className":11664,"code":11666,"language":9638},[11665],"language-text","         进入者\n        \u002F      \\\n      进入      不进入\n      \u002F          \\\n   在位者        (0, 2)\n   \u002F    \\\n 战斗   容纳\n  \u002F      \\\n(-1,-1)  (1,1)\n",[11668,11669,11666],"code",{"__ignoreMap":10},[1798,11671,11672,1860],{},[1857,11673,11674],{},"逆向归纳",[1805,11676,11677,11680],{},[1808,11678,11679],{},"最后节点：在位者选择\"容纳\"（1 > -1）",[1808,11681,11682],{},"回到初始节点：进入者预期到容纳，选择\"进入\"（1 > 0）",[1798,11684,11685,11688],{},[1857,11686,11687],{},"子博弈精炼纳什均衡 (SPNE)",": (进入, 容纳)",[1798,11690,11691,11694],{},[1857,11692,11693],{},"关键洞见",": \"战斗\"是不可信威胁——虽然在位者威胁说\"你进入我就战斗\"，但一旦进入真的发生，容纳才是最优反应。SPNE排除了这种基于不可信威胁的均衡。",[1897,11696,11698],{"id":11697},"_43-子博弈精炼纳什均衡","4.3 子博弈精炼纳什均衡",[1798,11700,11701,11704],{},[1857,11702,11703],{},"子博弈",": 从某个单点信息集开始的博弈树的一部分，本身构成一个完整的博弈。",[1798,11706,11707,11709],{},[1857,11708,1905],{},": 策略组合是SPNE，如果它在每个子博弈中都构成纳什均衡。",[1798,11711,11712,11715],{},[1857,11713,11714],{},"意义",": SPNE要求策略在博弈的任何阶段都是可信的，即使那个阶段在均衡路径之外（\"离轨威胁\"也必须可信）。",[1798,11717,11718,1860],{},[1857,11719,6897],{},[1875,11721,11722,11725,11728,11731],{},[1808,11723,11724],{},"每个SPNE都是纳什均衡",[1808,11726,11727],{},"反之不成立（纳什均衡可能包含不可信威胁）",[1808,11729,11730],{},"有限完美信息博弈必然存在纯策略SPNE",[1808,11732,11733],{},"SPNE可以通过逆向归纳找到",[1897,11735,11737],{"id":11736},"_44-蜈蚣博弈-centipede-game","4.4 蜈蚣博弈 (Centipede Game)",[11662,11739,11742],{"className":11740,"code":11741,"language":9638},[11665],"  1     2     1     2\n  ↓     ↓     ↓     ↓\n下→(1,0) 下→(0,2) 下→(3,1) 下→(2,4)\n继续→  继续→  继续→  继续→ (终点)(4,3)\n",[11668,11743,11741],{"__ignoreMap":10},[1798,11745,11746,1860],{},[1857,11747,11748],{},"逆向归纳解",[1805,11750,11751,11754,11757,11760],{},[1808,11752,11753],{},"最后节点：参与者2选\"下\"（4 > 3）",[1808,11755,11756],{},"倒数第二：参与者1预期到这点，选\"下\"（3 > 2）",[1808,11758,11759],{},"继续倒推……",[1808,11761,11762,11765],{},[1857,11763,11764],{},"结论",": 参与者1在第一步就选\"下\"，得到(1, 0)",[1798,11767,11768,11771],{},[1857,11769,11770],{},"悖论",": 如果双方都\"继续\"，可以到达(4, 3)，对双方都更好！",[1798,11773,11774,11777],{},[1857,11775,11776],{},"实验证据",": 实验中，参与者很少在第一步就选\"下\"，往往会合作几轮。",[1798,11779,11780,1860],{},[1857,11781,11782],{},"解释",[1875,11784,11785,11788,11791,11794],{},[1808,11786,11787],{},"有限理性",[1808,11789,11790],{},"对对方理性的怀疑",[1808,11792,11793],{},"利他偏好",[1808,11795,11796],{},"声誉考虑（即使是单次博弈）",[1798,11798,11799],{},"这展示了逆向归纳法的局限性。",[1890,11801],{},[1794,11803,11805],{"id":11804},"_5-重复博弈","5. 重复博弈",[1897,11807,11809],{"id":11808},"_51-有限重复博弈","5.1 有限重复博弈",[1798,11811,11812,11815,11816,11845,11846,11875,11876,11904],{},[1857,11813,11814],{},"设定",": 阶段博弈",[1908,11817,11819,11833],{"className":11818},[1911],[1908,11820,11822],{"className":11821},[1915],[1917,11823,11824],{"xmlns":1919},[1921,11825,11826,11831],{},[1924,11827,11828],{},[1927,11829,11830],{},"G",[1931,11832,11830],{"encoding":1933},[1908,11834,11836],{"className":11835,"ariaHidden":1938},[1937],[1908,11837,11839,11842],{"className":11838},[1942],[1908,11840],{"className":11841,"style":2019},[1946],[1908,11843,11830],{"className":11844},[1951,1952],"重复",[1908,11847,11849,11863],{"className":11848},[1911],[1908,11850,11852],{"className":11851},[1915],[1917,11853,11854],{"xmlns":1919},[1921,11855,11856,11861],{},[1924,11857,11858],{},[1927,11859,11860],{},"T",[1931,11862,11860],{"encoding":1933},[1908,11864,11866],{"className":11865,"ariaHidden":1938},[1937],[1908,11867,11869,11872],{"className":11868},[1942],[1908,11870],{"className":11871,"style":2019},[1946],[1908,11873,11860],{"className":11874,"style":9731},[1951,1952],"次，",[1908,11877,11879,11892],{"className":11878},[1911],[1908,11880,11882],{"className":11881},[1915],[1917,11883,11884],{"xmlns":1919},[1921,11885,11886,11890],{},[1924,11887,11888],{},[1927,11889,11860],{},[1931,11891,11860],{"encoding":1933},[1908,11893,11895],{"className":11894,"ariaHidden":1938},[1937],[1908,11896,11898,11901],{"className":11897},[1942],[1908,11899],{"className":11900,"style":2019},[1946],[1908,11902,11860],{"className":11903,"style":9731},[1951,1952],"有限且为共同知识。",[1798,11906,11907,11910,11911,11939,11940,11999,12000,6798],{},[1857,11908,11909],{},"定理",": 如果阶段博弈",[1908,11912,11914,11927],{"className":11913},[1911],[1908,11915,11917],{"className":11916},[1915],[1917,11918,11919],{"xmlns":1919},[1921,11920,11921,11925],{},[1924,11922,11923],{},[1927,11924,11830],{},[1931,11926,11830],{"encoding":1933},[1908,11928,11930],{"className":11929,"ariaHidden":1938},[1937],[1908,11931,11933,11936],{"className":11932},[1942],[1908,11934],{"className":11935,"style":2019},[1946],[1908,11937,11830],{"className":11938},[1951,1952],"有唯一纳什均衡",[1908,11941,11943,11961],{"className":11942},[1911],[1908,11944,11946],{"className":11945},[1915],[1917,11947,11948],{"xmlns":1919},[1921,11949,11950,11958],{},[1924,11951,11952],{},[5080,11953,11954,11956],{},[1927,11955,2561],{},[1978,11957,3548],{},[1931,11959,11960],{"encoding":1933},"s^*",[1908,11962,11964],{"className":11963,"ariaHidden":1938},[1937],[1908,11965,11967,11970],{"className":11966},[1942],[1908,11968],{"className":11969,"style":3580},[1946],[1908,11971,11973,11976],{"className":11972},[1951],[1908,11974,2561],{"className":11975},[1951,1952],[1908,11977,11979],{"className":11978},[2167],[1908,11980,11982],{"className":11981},[2171],[1908,11983,11985],{"className":11984},[2176],[1908,11986,11988],{"className":11987,"style":3580},[2180],[1908,11989,11990,11993],{"style":3595},[1908,11991],{"className":11992,"style":2189},[2188],[1908,11994,11996],{"className":11995},[2193,2194,2195,2196],[1908,11997,3548],{"className":11998},[2392,2196],"，则有限重复博弈的唯一SPNE是每期都选择",[1908,12001,12003,12020],{"className":12002},[1911],[1908,12004,12006],{"className":12005},[1915],[1917,12007,12008],{"xmlns":1919},[1921,12009,12010,12018],{},[1924,12011,12012],{},[5080,12013,12014,12016],{},[1927,12015,2561],{},[1978,12017,3548],{},[1931,12019,11960],{"encoding":1933},[1908,12021,12023],{"className":12022,"ariaHidden":1938},[1937],[1908,12024,12026,12029],{"className":12025},[1942],[1908,12027],{"className":12028,"style":3580},[1946],[1908,12030,12032,12035],{"className":12031},[1951],[1908,12033,2561],{"className":12034},[1951,1952],[1908,12036,12038],{"className":12037},[2167],[1908,12039,12041],{"className":12040},[2171],[1908,12042,12044],{"className":12043},[2176],[1908,12045,12047],{"className":12046,"style":3580},[2180],[1908,12048,12049,12052],{"style":3595},[1908,12050],{"className":12051,"style":2189},[2188],[1908,12053,12055],{"className":12054},[2193,2194,2195,2196],[1908,12056,3548],{"className":12057},[2392,2196],[1798,12059,12060,12063],{},[1857,12061,12062],{},"证明","（逆向归纳）:",[1805,12065,12066,12156,12357],{},[1808,12067,12068,12069,12097,12098],{},"第",[1908,12070,12072,12085],{"className":12071},[1911],[1908,12073,12075],{"className":12074},[1915],[1917,12076,12077],{"xmlns":1919},[1921,12078,12079,12083],{},[1924,12080,12081],{},[1927,12082,11860],{},[1931,12084,11860],{"encoding":1933},[1908,12086,12088],{"className":12087,"ariaHidden":1938},[1937],[1908,12089,12091,12094],{"className":12090},[1942],[1908,12092],{"className":12093,"style":2019},[1946],[1908,12095,11860],{"className":12096,"style":9731},[1951,1952],"期：这是最后一期，选择阶段博弈的纳什均衡",[1908,12099,12101,12118],{"className":12100},[1911],[1908,12102,12104],{"className":12103},[1915],[1917,12105,12106],{"xmlns":1919},[1921,12107,12108,12116],{},[1924,12109,12110],{},[5080,12111,12112,12114],{},[1927,12113,2561],{},[1978,12115,3548],{},[1931,12117,11960],{"encoding":1933},[1908,12119,12121],{"className":12120,"ariaHidden":1938},[1937],[1908,12122,12124,12127],{"className":12123},[1942],[1908,12125],{"className":12126,"style":3580},[1946],[1908,12128,12130,12133],{"className":12129},[1951],[1908,12131,2561],{"className":12132},[1951,1952],[1908,12134,12136],{"className":12135},[2167],[1908,12137,12139],{"className":12138},[2171],[1908,12140,12142],{"className":12141},[2176],[1908,12143,12145],{"className":12144,"style":3580},[2180],[1908,12146,12147,12150],{"style":3595},[1908,12148],{"className":12149,"style":2189},[2188],[1908,12151,12153],{"className":12152},[2193,2194,2195,2196],[1908,12154,3548],{"className":12155},[2392,2196],[1808,12157,12068,12158,12210,12211,12239,12240,12298,12299],{},[1908,12159,12161,12179],{"className":12160},[1911],[1908,12162,12164],{"className":12163},[1915],[1917,12165,12166],{"xmlns":1919},[1921,12167,12168,12176],{},[1924,12169,12170,12172,12174],{},[1927,12171,11860],{},[1978,12173,2828],{},[1986,12175,1988],{},[1931,12177,12178],{"encoding":1933},"T-1",[1908,12180,12182,12201],{"className":12181,"ariaHidden":1938},[1937],[1908,12183,12185,12189,12192,12195,12198],{"className":12184},[1942],[1908,12186],{"className":12187,"style":12188},[1946],"height:0.7667em;vertical-align:-0.0833em;",[1908,12190,11860],{"className":12191,"style":9731},[1951,1952],[1908,12193],{"className":12194,"style":2388},[2027],[1908,12196,2828],{"className":12197},[2392],[1908,12199],{"className":12200,"style":2388},[2027],[1908,12202,12204,12207],{"className":12203},[1942],[1908,12205],{"className":12206,"style":9810},[1946],[1908,12208,1988],{"className":12209},[1951],"期：由于第",[1908,12212,12214,12227],{"className":12213},[1911],[1908,12215,12217],{"className":12216},[1915],[1917,12218,12219],{"xmlns":1919},[1921,12220,12221,12225],{},[1924,12222,12223],{},[1927,12224,11860],{},[1931,12226,11860],{"encoding":1933},[1908,12228,12230],{"className":12229,"ariaHidden":1938},[1937],[1908,12231,12233,12236],{"className":12232},[1942],[1908,12234],{"className":12235,"style":2019},[1946],[1908,12237,11860],{"className":12238,"style":9731},[1951,1952],"期的行动已确定为",[1908,12241,12243,12260],{"className":12242},[1911],[1908,12244,12246],{"className":12245},[1915],[1917,12247,12248],{"xmlns":1919},[1921,12249,12250,12258],{},[1924,12251,12252],{},[5080,12253,12254,12256],{},[1927,12255,2561],{},[1978,12257,3548],{},[1931,12259,11960],{"encoding":1933},[1908,12261,12263],{"className":12262,"ariaHidden":1938},[1937],[1908,12264,12266,12269],{"className":12265},[1942],[1908,12267],{"className":12268,"style":3580},[1946],[1908,12270,12272,12275],{"className":12271},[1951],[1908,12273,2561],{"className":12274},[1951,1952],[1908,12276,12278],{"className":12277},[2167],[1908,12279,12281],{"className":12280},[2171],[1908,12282,12284],{"className":12283},[2176],[1908,12285,12287],{"className":12286,"style":3580},[2180],[1908,12288,12289,12292],{"style":3595},[1908,12290],{"className":12291,"style":2189},[2188],[1908,12293,12295],{"className":12294},[2193,2194,2195,2196],[1908,12296,3548],{"className":12297},[2392,2196],"，当前期的偏离不影响未来，因此选择",[1908,12300,12302,12319],{"className":12301},[1911],[1908,12303,12305],{"className":12304},[1915],[1917,12306,12307],{"xmlns":1919},[1921,12308,12309,12317],{},[1924,12310,12311],{},[5080,12312,12313,12315],{},[1927,12314,2561],{},[1978,12316,3548],{},[1931,12318,11960],{"encoding":1933},[1908,12320,12322],{"className":12321,"ariaHidden":1938},[1937],[1908,12323,12325,12328],{"className":12324},[1942],[1908,12326],{"className":12327,"style":3580},[1946],[1908,12329,12331,12334],{"className":12330},[1951],[1908,12332,2561],{"className":12333},[1951,1952],[1908,12335,12337],{"className":12336},[2167],[1908,12338,12340],{"className":12339},[2171],[1908,12341,12343],{"className":12342},[2176],[1908,12344,12346],{"className":12345,"style":3580},[2180],[1908,12347,12348,12351],{"style":3595},[1908,12349],{"className":12350,"style":2189},[2188],[1908,12352,12354],{"className":12353},[2193,2194,2195,2196],[1908,12355,3548],{"className":12356},[2392,2196],[1808,12358,12359],{},"依此类推……",[1798,12361,12362,12365],{},[1857,12363,12364],{},"应用",": 有限重复的囚徒困境中，唯一SPNE是每期都背叛。",[1897,12367,12369],{"id":12368},"_52-无限重复博弈","5.2 无限重复博弈",[1798,12371,12372,11815,12374,12402,12403,6798],{},[1857,12373,11814],{},[1908,12375,12377,12390],{"className":12376},[1911],[1908,12378,12380],{"className":12379},[1915],[1917,12381,12382],{"xmlns":1919},[1921,12383,12384,12388],{},[1924,12385,12386],{},[1927,12387,11830],{},[1931,12389,11830],{"encoding":1933},[1908,12391,12393],{"className":12392,"ariaHidden":1938},[1937],[1908,12394,12396,12399],{"className":12395},[1942],[1908,12397],{"className":12398,"style":2019},[1946],[1908,12400,11830],{"className":12401},[1951,1952],"无限次重复，参与者折现因子为",[1908,12404,12406,12433],{"className":12405},[1911],[1908,12407,12409],{"className":12408},[1915],[1917,12410,12411],{"xmlns":1919},[1921,12412,12413,12430],{},[1924,12414,12415,12418,12420,12422,12424,12426,12428],{},[1927,12416,12417],{},"δ",[1978,12419,5489],{},[1978,12421,2566],{"stretchy":1983},[1986,12423,9761],{},[1978,12425,1991],{"separator":1938},[1986,12427,1988],{},[1978,12429,2595],{"stretchy":1983},[1931,12431,12432],{"encoding":1933},"\\delta \\in (0, 1)",[1908,12434,12436,12456],{"className":12435,"ariaHidden":1938},[1937],[1908,12437,12439,12443,12447,12450,12453],{"className":12438},[1942],[1908,12440],{"className":12441,"style":12442},[1946],"height:0.7335em;vertical-align:-0.0391em;",[1908,12444,12417],{"className":12445,"style":12446},[1951,1952],"margin-right:0.0379em;",[1908,12448],{"className":12449,"style":2028},[2027],[1908,12451,5489],{"className":12452},[2032],[1908,12454],{"className":12455,"style":2028},[2027],[1908,12457,12459,12462,12465,12468,12471,12474,12477],{"className":12458},[1942],[1908,12460],{"className":12461,"style":2042},[1946],[1908,12463,2566],{"className":12464},[2046],[1908,12466,9761],{"className":12467},[1951],[1908,12469,1991],{"className":12470},[2053],[1908,12472],{"className":12473,"style":2057},[2027],[1908,12475,1988],{"className":12476},[1951],[1908,12478,2595],{"className":12479},[2086],[1798,12481,12482,1860],{},[1857,12483,12484],{},"总支付",[1908,12486,12488],{"className":12487},[3912],[1908,12489,12491,12541],{"className":12490},[1911],[1908,12492,12494],{"className":12493},[1915],[1917,12495,12496],{"xmlns":1919,"display":3921},[1921,12497,12498,12538],{},[1924,12499,12500,12516,12522,12528,12530,12536],{},[8317,12501,12502,12504,12513],{},[1978,12503,8295],{},[1924,12505,12506,12509,12511],{},[1927,12507,12508],{},"t",[1978,12510,1980],{},[1986,12512,9761],{},[1927,12514,12515],{"mathvariant":3638},"∞",[5080,12517,12518,12520],{},[1927,12519,12417],{},[1927,12521,12508],{},[2137,12523,12524,12526],{},[1927,12525,2235],{},[1927,12527,2107],{},[1978,12529,2566],{"stretchy":1983},[5080,12531,12532,12534],{},[1927,12533,2561],{},[1927,12535,12508],{},[1978,12537,2595],{"stretchy":1983},[1931,12539,12540],{"encoding":1933},"\\sum_{t=0}^{\\infty} \\delta^t u_i(s^t)",[1908,12542,12544],{"className":12543,"ariaHidden":1938},[1937],[1908,12545,12547,12551,12620,12623,12653,12693,12696,12725],{"className":12546},[1942],[1908,12548],{"className":12549,"style":12550},[1946],"height:2.9185em;vertical-align:-1.2671em;",[1908,12552,12554],{"className":12553},[6245,6257],[1908,12555,12557,12611],{"className":12556},[2171,2172],[1908,12558,12560,12608],{"className":12559},[2176],[1908,12561,12563,12584,12594],{"className":12562,"style":8553},[2180],[1908,12564,12566,12569],{"style":12565},"top:-1.8829em;margin-left:0em;",[1908,12567],{"className":12568,"style":8445},[2188],[1908,12570,12572],{"className":12571},[2193,2194,2195,2196],[1908,12573,12575,12578,12581],{"className":12574},[1951,2196],[1908,12576,12508],{"className":12577},[1951,1952,2196],[1908,12579,1980],{"className":12580},[2032,2196],[1908,12582,9761],{"className":12583},[1951,2196],[1908,12585,12586,12589],{"style":8463},[1908,12587],{"className":12588,"style":8445},[2188],[1908,12590,12591],{},[1908,12592,8295],{"className":12593},[6245,8472,8473],[1908,12595,12596,12599],{"style":8588},[1908,12597],{"className":12598,"style":8445},[2188],[1908,12600,12602],{"className":12601},[2193,2194,2195,2196],[1908,12603,12605],{"className":12604},[1951,2196],[1908,12606,12515],{"className":12607},[1951,2196],[1908,12609,2204],{"className":12610},[2203],[1908,12612,12614],{"className":12613},[2176],[1908,12615,12618],{"className":12616,"style":12617},[2180],"height:1.2671em;",[1908,12619],{},[1908,12621],{"className":12622,"style":2057},[2027],[1908,12624,12626,12629],{"className":12625},[1951],[1908,12627,12417],{"className":12628,"style":12446},[1951,1952],[1908,12630,12632],{"className":12631},[2167],[1908,12633,12635],{"className":12634},[2171],[1908,12636,12638],{"className":12637},[2176],[1908,12639,12642],{"className":12640,"style":12641},[2180],"height:0.8436em;",[1908,12643,12644,12647],{"style":4077},[1908,12645],{"className":12646,"style":2189},[2188],[1908,12648,12650],{"className":12649},[2193,2194,2195,2196],[1908,12651,12508],{"className":12652},[1951,1952,2196],[1908,12654,12656,12659],{"className":12655},[1951],[1908,12657,2235],{"className":12658},[1951,1952],[1908,12660,12662],{"className":12661},[2167],[1908,12663,12665,12685],{"className":12664},[2171,2172],[1908,12666,12668,12682],{"className":12667},[2176],[1908,12669,12671],{"className":12670,"style":2181},[2180],[1908,12672,12673,12676],{"style":2308},[1908,12674],{"className":12675,"style":2189},[2188],[1908,12677,12679],{"className":12678},[2193,2194,2195,2196],[1908,12680,2107],{"className":12681},[1951,1952,2196],[1908,12683,2204],{"className":12684},[2203],[1908,12686,12688],{"className":12687},[2176],[1908,12689,12691],{"className":12690,"style":2211},[2180],[1908,12692],{},[1908,12694,2566],{"className":12695},[2046],[1908,12697,12699,12702],{"className":12698},[1951],[1908,12700,2561],{"className":12701},[1951,1952],[1908,12703,12705],{"className":12704},[2167],[1908,12706,12708],{"className":12707},[2171],[1908,12709,12711],{"className":12710},[2176],[1908,12712,12714],{"className":12713,"style":12641},[2180],[1908,12715,12716,12719],{"style":4077},[1908,12717],{"className":12718,"style":2189},[2188],[1908,12720,12722],{"className":12721},[2193,2194,2195,2196],[1908,12723,12508],{"className":12724},[1951,1952,2196],[1908,12726,2595],{"className":12727},[2086],[1798,12729,7666,12730,12790,12791,12820],{},[1908,12731,12733,12751],{"className":12732},[1911],[1908,12734,12736],{"className":12735},[1915],[1917,12737,12738],{"xmlns":1919},[1921,12739,12740,12748],{},[1924,12741,12742],{},[5080,12743,12744,12746],{},[1927,12745,2561],{},[1927,12747,12508],{},[1931,12749,12750],{"encoding":1933},"s^t",[1908,12752,12754],{"className":12753,"ariaHidden":1938},[1937],[1908,12755,12757,12761],{"className":12756},[1942],[1908,12758],{"className":12759,"style":12760},[1946],"height:0.7936em;",[1908,12762,12764,12767],{"className":12763},[1951],[1908,12765,2561],{"className":12766},[1951,1952],[1908,12768,12770],{"className":12769},[2167],[1908,12771,12773],{"className":12772},[2171],[1908,12774,12776],{"className":12775},[2176],[1908,12777,12779],{"className":12778,"style":12760},[2180],[1908,12780,12781,12784],{"style":3595},[1908,12782],{"className":12783,"style":2189},[2188],[1908,12785,12787],{"className":12786},[2193,2194,2195,2196],[1908,12788,12508],{"className":12789},[1951,1952,2196],"是第",[1908,12792,12794,12807],{"className":12793},[1911],[1908,12795,12797],{"className":12796},[1915],[1917,12798,12799],{"xmlns":1919},[1921,12800,12801,12805],{},[1924,12802,12803],{},[1927,12804,12508],{},[1931,12806,12508],{"encoding":1933},[1908,12808,12810],{"className":12809,"ariaHidden":1938},[1937],[1908,12811,12813,12817],{"className":12812},[1942],[1908,12814],{"className":12815,"style":12816},[1946],"height:0.6151em;",[1908,12818,12508],{"className":12819},[1951,1952],"期的策略组合。",[1798,12822,12823,12826],{},[1857,12824,12825],{},"策略",": 现在是整个历史的函数，可以是条件性的（\"如果你昨天背叛，我今天就惩罚你\"）。",[1897,12828,12830],{"id":12829},"_53-触发策略-trigger-strategies","5.3 触发策略 (Trigger Strategies)",[1798,12832,12833,1860],{},[1857,12834,12835],{},"冷酷触发策略 (Grim Trigger)",[1805,12837,12838,12841,12844],{},[1808,12839,12840],{},"第一期选择合作",[1808,12842,12843],{},"只要历史上都是合作，继续合作",[1808,12845,12846],{},"一旦观察到任何人背叛，永远背叛",[1798,12848,12849,1860],{},[1857,12850,12851],{},"一次性惩罚策略",[1805,12853,12854,12857,12860],{},[1808,12855,12856],{},"第一期合作",[1808,12858,12859],{},"如果对方上期合作，本期合作",[1808,12861,12862],{},"如果对方上期背叛，本期背叛，之后回到合作",[1897,12864,12866],{"id":12865},"_54-民间定理-folk-theorem","5.4 民间定理 (Folk Theorem)",[1798,12868,12869,12872],{},[1857,12870,12871],{},"可行支付",": 阶段博弈中某策略组合的支付向量",[1798,12874,12875,12878],{},[1857,12876,12877],{},"个体理性支付",": 参与者能通过自己的minimax策略保证的最低支付",[1798,12880,12881,12884,12885,12915],{},[1857,12882,12883],{},"民间定理（简化版）",": 对于折现因子足够接近1（",[1908,12886,12888,12902],{"className":12887},[1911],[1908,12889,12891],{"className":12890},[1915],[1917,12892,12893],{"xmlns":1919},[1921,12894,12895,12899],{},[1924,12896,12897],{},[1927,12898,12417],{},[1931,12900,12901],{"encoding":1933},"\\delta",[1908,12903,12905],{"className":12904,"ariaHidden":1938},[1937],[1908,12906,12908,12912],{"className":12907},[1942],[1908,12909],{"className":12910,"style":12911},[1946],"height:0.6944em;",[1908,12913,12417],{"className":12914,"style":12446},[1951,1952],"充分大），任何满足以下条件的可行支付都可以作为某个子博弈精炼纳什均衡的平均支付：",[1875,12917,12918,12921],{},[1808,12919,12920],{},"严格高于个体理性水平",[1808,12922,12923],{},"可以通过某策略组合实现",[1798,12925,12926,1860],{},[1857,12927,5946],{},[1805,12929,12930,12962],{},[1808,12931,12932,12933,12961],{},"未来足够重要（",[1908,12934,12936,12949],{"className":12935},[1911],[1908,12937,12939],{"className":12938},[1915],[1917,12940,12941],{"xmlns":1919},[1921,12942,12943,12947],{},[1924,12944,12945],{},[1927,12946,12417],{},[1931,12948,12901],{"encoding":1933},[1908,12950,12952],{"className":12951,"ariaHidden":1938},[1937],[1908,12953,12955,12958],{"className":12954},[1942],[1908,12956],{"className":12957,"style":12911},[1946],[1908,12959,12417],{"className":12960,"style":12446},[1951,1952],"接近1）时，偏离的短期收益被未来惩罚抵消",[1808,12963,12964],{},"可以用惩罚阶段来支撑合作",[1798,12966,12967,12969],{},[1857,12968,12364],{},": 解释卡特尔、隐性合谋等现象",[1897,12971,12973],{"id":12972},"_55-无限重复囚徒困境中的合作","5.5 无限重复囚徒困境中的合作",[1798,12975,12976,1860],{},[1857,12977,12978],{},"囚徒困境",[3421,12980,12981,12993],{},[3424,12982,12983],{},[3427,12984,12985,12987,12990],{},[3430,12986],{},[3430,12988,12989],{},"合作(C)",[3430,12991,12992],{},"背叛(D)",[3439,12994,12995,13007],{},[3427,12996,12997,13001,13004],{},[3444,12998,12999],{},[1857,13000,12989],{},[3444,13002,13003],{},"(3, 3)",[3444,13005,13006],{},"(0, 4)",[3427,13008,13009,13013,13016],{},[3444,13010,13011],{},[1857,13012,12992],{},[3444,13014,13015],{},"(4, 0)",[3444,13017,13018],{},"(1, 1)",[1798,13020,13021,1860],{},[1857,13022,13023],{},"冷酷触发策略支撑的合作",[1798,13025,13026],{},"如果两人都采用冷酷触发策略：",[1805,13028,13029,13147],{},[1808,13030,13031,13032],{},"合作路径支付: ",[1908,13033,13035,13059],{"className":13034},[1911],[1908,13036,13038],{"className":13037},[1915],[1917,13039,13040],{"xmlns":1919},[1921,13041,13042,13056],{},[1924,13043,13044],{},[10756,13045,13046,13048],{},[1986,13047,10106],{},[1924,13049,13050,13052,13054],{},[1986,13051,1988],{},[1978,13053,2828],{},[1927,13055,12417],{},[1931,13057,13058],{"encoding":1933},"\\frac{3}{1-\\delta}",[1908,13060,13062],{"className":13061,"ariaHidden":1938},[1937],[1908,13063,13065,13069],{"className":13064},[1942],[1908,13066],{"className":13067,"style":13068},[1946],"height:1.2484em;vertical-align:-0.4033em;",[1908,13070,13072,13075,13144],{"className":13071},[1951],[1908,13073],{"className":13074},[2046,10878],[1908,13076,13078],{"className":13077},[10756],[1908,13079,13081,13135],{"className":13080},[2171,2172],[1908,13082,13084,13132],{"className":13083},[2176],[1908,13085,13088,13109,13117],{"className":13086,"style":13087},[2180],"height:0.8451em;",[1908,13089,13091,13094],{"style":13090},"top:-2.655em;",[1908,13092],{"className":13093,"style":6273},[2188],[1908,13095,13097],{"className":13096},[2193,2194,2195,2196],[1908,13098,13100,13103,13106],{"className":13099},[1951,2196],[1908,13101,1988],{"className":13102},[1951,2196],[1908,13104,2828],{"className":13105},[2392,2196],[1908,13107,12417],{"className":13108,"style":12446},[1951,1952,2196],[1908,13110,13111,13114],{"style":10906},[1908,13112],{"className":13113,"style":6273},[2188],[1908,13115],{"className":13116,"style":10914},[10913],[1908,13118,13120,13123],{"style":13119},"top:-3.394em;",[1908,13121],{"className":13122,"style":6273},[2188],[1908,13124,13126],{"className":13125},[2193,2194,2195,2196],[1908,13127,13129],{"className":13128},[1951,2196],[1908,13130,10106],{"className":13131},[1951,2196],[1908,13133,2204],{"className":13134},[2203],[1908,13136,13138],{"className":13137},[2176],[1908,13139,13142],{"className":13140,"style":13141},[2180],"height:0.4033em;",[1908,13143],{},[1908,13145],{"className":13146},[2086,10878],[1808,13148,13149,13150],{},"偏离到背叛: 当期得4，之后永远得1，总支付",[1908,13151,13153,13181],{"className":13152},[1911],[1908,13154,13156],{"className":13155},[1915],[1917,13157,13158],{"xmlns":1919},[1921,13159,13160,13178],{},[1924,13161,13162,13164,13166],{},[1986,13163,10776],{},[1978,13165,2871],{},[10756,13167,13168,13170],{},[1927,13169,12417],{},[1924,13171,13172,13174,13176],{},[1986,13173,1988],{},[1978,13175,2828],{},[1927,13177,12417],{},[1931,13179,13180],{"encoding":1933},"4 + \\frac{\\delta}{1-\\delta}",[1908,13182,13184,13202],{"className":13183,"ariaHidden":1938},[1937],[1908,13185,13187,13190,13193,13196,13199],{"className":13186},[1942],[1908,13188],{"className":13189,"style":10636},[1946],[1908,13191,10776],{"className":13192},[1951],[1908,13194],{"className":13195,"style":2388},[2027],[1908,13197,2871],{"className":13198},[2392],[1908,13200],{"className":13201,"style":2388},[2027],[1908,13203,13205,13209],{"className":13204},[1942],[1908,13206],{"className":13207,"style":13208},[1946],"height:1.2834em;vertical-align:-0.4033em;",[1908,13210,13212,13215,13281],{"className":13211},[1951],[1908,13213],{"className":13214},[2046,10878],[1908,13216,13218],{"className":13217},[10756],[1908,13219,13221,13273],{"className":13220},[2171,2172],[1908,13222,13224,13270],{"className":13223},[2176],[1908,13225,13228,13248,13256],{"className":13226,"style":13227},[2180],"height:0.8801em;",[1908,13229,13230,13233],{"style":13090},[1908,13231],{"className":13232,"style":6273},[2188],[1908,13234,13236],{"className":13235},[2193,2194,2195,2196],[1908,13237,13239,13242,13245],{"className":13238},[1951,2196],[1908,13240,1988],{"className":13241},[1951,2196],[1908,13243,2828],{"className":13244},[2392,2196],[1908,13246,12417],{"className":13247,"style":12446},[1951,1952,2196],[1908,13249,13250,13253],{"style":10906},[1908,13251],{"className":13252,"style":6273},[2188],[1908,13254],{"className":13255,"style":10914},[10913],[1908,13257,13258,13261],{"style":13119},[1908,13259],{"className":13260,"style":6273},[2188],[1908,13262,13264],{"className":13263},[2193,2194,2195,2196],[1908,13265,13267],{"className":13266},[1951,2196],[1908,13268,12417],{"className":13269,"style":12446},[1951,1952,2196],[1908,13271,2204],{"className":13272},[2203],[1908,13274,13276],{"className":13275},[2176],[1908,13277,13279],{"className":13278,"style":13141},[2180],[1908,13280],{},[1908,13282],{"className":13283},[2086,10878],[1798,13285,13286,1860],{},[1857,13287,13288],{},"不偏离条件",[1908,13290,13292],{"className":13291},[3912],[1908,13293,13295,13337],{"className":13294},[1911],[1908,13296,13298],{"className":13297},[1915],[1917,13299,13300],{"xmlns":1919,"display":3921},[1921,13301,13302,13334],{},[1924,13303,13304,13316,13318,13320,13322],{},[10756,13305,13306,13308],{},[1986,13307,10106],{},[1924,13309,13310,13312,13314],{},[1986,13311,1988],{},[1978,13313,2828],{},[1927,13315,12417],{},[1978,13317,4373],{},[1986,13319,10776],{},[1978,13321,2871],{},[10756,13323,13324,13326],{},[1927,13325,12417],{},[1924,13327,13328,13330,13332],{},[1986,13329,1988],{},[1978,13331,2828],{},[1927,13333,12417],{},[1931,13335,13336],{"encoding":1933},"\\frac{3}{1-\\delta} \\ge 4 + \\frac{\\delta}{1-\\delta}",[1908,13338,13340,13431,13449],{"className":13339,"ariaHidden":1938},[1937],[1908,13341,13343,13347,13422,13425,13428],{"className":13342},[1942],[1908,13344],{"className":13345,"style":13346},[1946],"height:2.0908em;vertical-align:-0.7693em;",[1908,13348,13350,13353,13419],{"className":13349},[1951],[1908,13351],{"className":13352},[2046,10878],[1908,13354,13356],{"className":13355},[10756],[1908,13357,13359,13410],{"className":13358},[2171,2172],[1908,13360,13362,13407],{"className":13361},[2176],[1908,13363,13365,13388,13396],{"className":13364,"style":10891},[2180],[1908,13366,13367,13370],{"style":10894},[1908,13368],{"className":13369,"style":6273},[2188],[1908,13371,13373,13376,13379,13382,13385],{"className":13372},[1951],[1908,13374,1988],{"className":13375},[1951],[1908,13377],{"className":13378,"style":2388},[2027],[1908,13380,2828],{"className":13381},[2392],[1908,13383],{"className":13384,"style":2388},[2027],[1908,13386,12417],{"className":13387,"style":12446},[1951,1952],[1908,13389,13390,13393],{"style":10906},[1908,13391],{"className":13392,"style":6273},[2188],[1908,13394],{"className":13395,"style":10914},[10913],[1908,13397,13398,13401],{"style":10917},[1908,13399],{"className":13400,"style":6273},[2188],[1908,13402,13404],{"className":13403},[1951],[1908,13405,10106],{"className":13406},[1951],[1908,13408,2204],{"className":13409},[2203],[1908,13411,13413],{"className":13412},[2176],[1908,13414,13417],{"className":13415,"style":13416},[2180],"height:0.7693em;",[1908,13418],{},[1908,13420],{"className":13421},[2086,10878],[1908,13423],{"className":13424,"style":2028},[2027],[1908,13426,4373],{"className":13427},[2032],[1908,13429],{"className":13430,"style":2028},[2027],[1908,13432,13434,13437,13440,13443,13446],{"className":13433},[1942],[1908,13435],{"className":13436,"style":10636},[1946],[1908,13438,10776],{"className":13439},[1951],[1908,13441],{"className":13442,"style":2388},[2027],[1908,13444,2871],{"className":13445},[2392],[1908,13447],{"className":13448,"style":2388},[2027],[1908,13450,13452,13456],{"className":13451},[1942],[1908,13453],{"className":13454,"style":13455},[1946],"height:2.1408em;vertical-align:-0.7693em;",[1908,13457,13459,13462,13528],{"className":13458},[1951],[1908,13460],{"className":13461},[2046,10878],[1908,13463,13465],{"className":13464},[10756],[1908,13466,13468,13520],{"className":13467},[2171,2172],[1908,13469,13471,13517],{"className":13470},[2176],[1908,13472,13475,13498,13506],{"className":13473,"style":13474},[2180],"height:1.3714em;",[1908,13476,13477,13480],{"style":10894},[1908,13478],{"className":13479,"style":6273},[2188],[1908,13481,13483,13486,13489,13492,13495],{"className":13482},[1951],[1908,13484,1988],{"className":13485},[1951],[1908,13487],{"className":13488,"style":2388},[2027],[1908,13490,2828],{"className":13491},[2392],[1908,13493],{"className":13494,"style":2388},[2027],[1908,13496,12417],{"className":13497,"style":12446},[1951,1952],[1908,13499,13500,13503],{"style":10906},[1908,13501],{"className":13502,"style":6273},[2188],[1908,13504],{"className":13505,"style":10914},[10913],[1908,13507,13508,13511],{"style":10917},[1908,13509],{"className":13510,"style":6273},[2188],[1908,13512,13514],{"className":13513},[1951],[1908,13515,12417],{"className":13516,"style":12446},[1951,1952],[1908,13518,2204],{"className":13519},[2203],[1908,13521,13523],{"className":13522},[2176],[1908,13524,13526],{"className":13525,"style":13416},[2180],[1908,13527],{},[1908,13529],{"className":13530},[2086,10878],[1908,13532,13534],{"className":13533},[3912],[1908,13535,13537,13569],{"className":13536},[1911],[1908,13538,13540],{"className":13539},[1915],[1917,13541,13542],{"xmlns":1919,"display":3921},[1921,13543,13544,13566],{},[1924,13545,13546,13548,13550,13552,13554,13556,13558,13560,13562,13564],{},[1986,13547,10106],{},[1978,13549,4373],{},[1986,13551,10776],{},[1978,13553,2566],{"stretchy":1983},[1986,13555,1988],{},[1978,13557,2828],{},[1927,13559,12417],{},[1978,13561,2595],{"stretchy":1983},[1978,13563,2871],{},[1927,13565,12417],{},[1931,13567,13568],{"encoding":1933},"3 \\ge 4(1-\\delta) + \\delta",[1908,13570,13572,13591,13615,13636],{"className":13571,"ariaHidden":1938},[1937],[1908,13573,13575,13579,13582,13585,13588],{"className":13574},[1942],[1908,13576],{"className":13577,"style":13578},[1946],"height:0.7804em;vertical-align:-0.136em;",[1908,13580,10106],{"className":13581},[1951],[1908,13583],{"className":13584,"style":2028},[2027],[1908,13586,4373],{"className":13587},[2032],[1908,13589],{"className":13590,"style":2028},[2027],[1908,13592,13594,13597,13600,13603,13606,13609,13612],{"className":13593},[1942],[1908,13595],{"className":13596,"style":2042},[1946],[1908,13598,10776],{"className":13599},[1951],[1908,13601,2566],{"className":13602},[2046],[1908,13604,1988],{"className":13605},[1951],[1908,13607],{"className":13608,"style":2388},[2027],[1908,13610,2828],{"className":13611},[2392],[1908,13613],{"className":13614,"style":2388},[2027],[1908,13616,13618,13621,13624,13627,13630,13633],{"className":13617},[1942],[1908,13619],{"className":13620,"style":2042},[1946],[1908,13622,12417],{"className":13623,"style":12446},[1951,1952],[1908,13625,2595],{"className":13626},[2086],[1908,13628],{"className":13629,"style":2388},[2027],[1908,13631,2871],{"className":13632},[2392],[1908,13634],{"className":13635,"style":2388},[2027],[1908,13637,13639,13642],{"className":13638},[1942],[1908,13640],{"className":13641,"style":12911},[1946],[1908,13643,12417],{"className":13644,"style":12446},[1951,1952],[1908,13646,13648],{"className":13647},[3912],[1908,13649,13651,13675],{"className":13650},[1911],[1908,13652,13654],{"className":13653},[1915],[1917,13655,13656],{"xmlns":1919,"display":3921},[1921,13657,13658,13672],{},[1924,13659,13660,13662,13664,13666,13668,13670],{},[1986,13661,10106],{},[1978,13663,4373],{},[1986,13665,10776],{},[1978,13667,2828],{},[1986,13669,10106],{},[1927,13671,12417],{},[1931,13673,13674],{"encoding":1933},"3 \\ge 4 - 3\\delta",[1908,13676,13678,13696,13714],{"className":13677,"ariaHidden":1938},[1937],[1908,13679,13681,13684,13687,13690,13693],{"className":13680},[1942],[1908,13682],{"className":13683,"style":13578},[1946],[1908,13685,10106],{"className":13686},[1951],[1908,13688],{"className":13689,"style":2028},[2027],[1908,13691,4373],{"className":13692},[2032],[1908,13694],{"className":13695,"style":2028},[2027],[1908,13697,13699,13702,13705,13708,13711],{"className":13698},[1942],[1908,13700],{"className":13701,"style":10636},[1946],[1908,13703,10776],{"className":13704},[1951],[1908,13706],{"className":13707,"style":2388},[2027],[1908,13709,2828],{"className":13710},[2392],[1908,13712],{"className":13713,"style":2388},[2027],[1908,13715,13717,13720,13723],{"className":13716},[1942],[1908,13718],{"className":13719,"style":12911},[1946],[1908,13721,10106],{"className":13722},[1951],[1908,13724,12417],{"className":13725,"style":12446},[1951,1952],[1908,13727,13729],{"className":13728},[3912],[1908,13730,13732,13754],{"className":13731},[1911],[1908,13733,13735],{"className":13734},[1915],[1917,13736,13737],{"xmlns":1919,"display":3921},[1921,13738,13739,13751],{},[1924,13740,13741,13743,13745],{},[1927,13742,12417],{},[1978,13744,4373],{},[10756,13746,13747,13749],{},[1986,13748,1988],{},[1986,13750,10106],{},[1931,13752,13753],{"encoding":1933},"\\delta \\ge \\frac{1}{3}",[1908,13755,13757,13776],{"className":13756,"ariaHidden":1938},[1937],[1908,13758,13760,13764,13767,13770,13773],{"className":13759},[1942],[1908,13761],{"className":13762,"style":13763},[1946],"height:0.8304em;vertical-align:-0.136em;",[1908,13765,12417],{"className":13766,"style":12446},[1951,1952],[1908,13768],{"className":13769,"style":2028},[2027],[1908,13771,4373],{"className":13772},[2032],[1908,13774],{"className":13775,"style":2028},[2027],[1908,13777,13779,13782],{"className":13778},[1942],[1908,13780],{"className":13781,"style":10871},[1946],[1908,13783,13785,13788,13841],{"className":13784},[1951],[1908,13786],{"className":13787},[2046,10878],[1908,13789,13791],{"className":13790},[10756],[1908,13792,13794,13833],{"className":13793},[2171,2172],[1908,13795,13797,13830],{"className":13796},[2176],[1908,13798,13800,13811,13819],{"className":13799,"style":10891},[2180],[1908,13801,13802,13805],{"style":10894},[1908,13803],{"className":13804,"style":6273},[2188],[1908,13806,13808],{"className":13807},[1951],[1908,13809,10106],{"className":13810},[1951],[1908,13812,13813,13816],{"style":10906},[1908,13814],{"className":13815,"style":6273},[2188],[1908,13817],{"className":13818,"style":10914},[10913],[1908,13820,13821,13824],{"style":10917},[1908,13822],{"className":13823,"style":6273},[2188],[1908,13825,13827],{"className":13826},[1951],[1908,13828,1988],{"className":13829},[1951],[1908,13831,2204],{"className":13832},[2203],[1908,13834,13836],{"className":13835},[2176],[1908,13837,13839],{"className":13838,"style":10936},[2180],[1908,13840],{},[1908,13842],{"className":13843},[2086,10878],[1798,13845,13846,13848,13849,13904],{},[1857,13847,11764],{},": 只要",[1908,13850,13852,13874],{"className":13851},[1911],[1908,13853,13855],{"className":13854},[1915],[1917,13856,13857],{"xmlns":1919},[1921,13858,13859,13871],{},[1924,13860,13861,13863,13865,13867,13869],{},[1927,13862,12417],{},[1978,13864,4373],{},[1986,13866,1988],{},[1927,13868,10103],{"mathvariant":3638},[1986,13870,10106],{},[1931,13872,13873],{"encoding":1933},"\\delta \\ge 1\u002F3",[1908,13875,13877,13895],{"className":13876,"ariaHidden":1938},[1937],[1908,13878,13880,13883,13886,13889,13892],{"className":13879},[1942],[1908,13881],{"className":13882,"style":13763},[1946],[1908,13884,12417],{"className":13885,"style":12446},[1951,1952],[1908,13887],{"className":13888,"style":2028},[2027],[1908,13890,4373],{"className":13891},[2032],[1908,13893],{"className":13894,"style":2028},[2027],[1908,13896,13898,13901],{"className":13897},[1942],[1908,13899],{"className":13900,"style":2042},[1946],[1908,13902,10716],{"className":13903},[1951],"（未来足够重要），双方合作是SPNE！",[1798,13906,13907,1860],{},[1857,13908,13909],{},"经济学含义",[1805,13911,13912,13915,13947],{},[1808,13913,13914],{},"长期关系促进合作",[1808,13916,13917,13918,13946],{},"频繁互动（",[1908,13919,13921,13934],{"className":13920},[1911],[1908,13922,13924],{"className":13923},[1915],[1917,13925,13926],{"xmlns":1919},[1921,13927,13928,13932],{},[1924,13929,13930],{},[1927,13931,12417],{},[1931,13933,12901],{"encoding":1933},[1908,13935,13937],{"className":13936,"ariaHidden":1938},[1937],[1908,13938,13940,13943],{"className":13939},[1942],[1908,13941],{"className":13942,"style":12911},[1946],[1908,13944,12417],{"className":13945,"style":12446},[1951,1952],"高）有助于维持隐性合约",[1808,13948,13949,13950,13978],{},"一次性交易（",[1908,13951,13953,13966],{"className":13952},[1911],[1908,13954,13956],{"className":13955},[1915],[1917,13957,13958],{"xmlns":1919},[1921,13959,13960,13964],{},[1924,13961,13962],{},[1927,13963,12417],{},[1931,13965,12901],{"encoding":1933},[1908,13967,13969],{"className":13968,"ariaHidden":1938},[1937],[1908,13970,13972,13975],{"className":13971},[1942],[1908,13973],{"className":13974,"style":12911},[1946],[1908,13976,12417],{"className":13977,"style":12446},[1951,1952],"低）更可能出现机会主义",[1890,13980],{},[1794,13982,13984],{"id":13983},"_6-完整例题","6. 完整例题",[1897,13986,13988],{"id":13987},"例题1-求解混合策略均衡","例题1: 求解混合策略均衡",[1798,13990,13991,13994],{},[1857,13992,13993],{},"题目",": 求以下博弈的所有纳什均衡（纯策略和混合策略）",[3421,13996,13997,14008],{},[3424,13998,13999],{},[3427,14000,14001,14003,14006],{},[3430,14002],{},[3430,14004,14005],{},"L",[3430,14007,2274],{},[3439,14009,14010,14022],{},[3427,14011,14012,14017,14020],{},[3444,14013,14014],{},[1857,14015,14016],{},"U",[3444,14018,14019],{},"(3, 1)",[3444,14021,6832],{},[3427,14023,14024,14029,14032],{},[3444,14025,14026],{},[1857,14027,14028],{},"D",[3444,14030,14031],{},"(1, 0)",[3444,14033,14034],{},"(2, 2)",[1798,14036,14037,1860],{},[1857,14038,14039],{},"解答",[1798,14041,14042],{},[1857,14043,14044],{},"(1) 纯策略纳什均衡",[1798,14046,14047],{},"检查每个策略组合：",[1805,14049,14050,14053,14056,14059],{},[1808,14051,14052],{},"(U, L): 给定L，U是最优（3>1）；给定U，L是最优（1>0）✓",[1808,14054,14055],{},"(U, R): 给定R，D是最优（2>0）✗",[1808,14057,14058],{},"(D, L): 给定L，U是最优（3>1）✗",[1808,14060,14061],{},"(D, R): 给定R，D是最优（2>0）；给定D，R是最优（2>0）✓",[1798,14063,14064,14065],{},"纯策略纳什均衡：",[1857,14066,14067],{},"(U, L)和(D, R)",[1798,14069,14070],{},[1857,14071,14072],{},"(2) 混合策略纳什均衡",[1798,14074,14075,14076,14104,14105,6798],{},"设参与者1选U的概率为",[1908,14077,14079,14092],{"className":14078},[1911],[1908,14080,14082],{"className":14081},[1915],[1917,14083,14084],{"xmlns":1919},[1921,14085,14086,14090],{},[1924,14087,14088],{},[1927,14089,1798],{},[1931,14091,1798],{"encoding":1933},[1908,14093,14095],{"className":14094,"ariaHidden":1938},[1937],[1908,14096,14098,14101],{"className":14097},[1942],[1908,14099],{"className":14100,"style":9508},[1946],[1908,14102,1798],{"className":14103},[1951,1952],"，参与者2选L的概率为",[1908,14106,14108,14121],{"className":14107},[1911],[1908,14109,14111],{"className":14110},[1915],[1917,14112,14113],{"xmlns":1919},[1921,14114,14115,14119],{},[1924,14116,14117],{},[1927,14118,9527],{},[1931,14120,9527],{"encoding":1933},[1908,14122,14124],{"className":14123,"ariaHidden":1938},[1937],[1908,14125,14127,14130],{"className":14126},[1942],[1908,14128],{"className":14129,"style":9508},[1946],[1908,14131,9527],{"className":14132,"style":7564},[1951,1952],[1798,14134,14135],{},"使参与者2无差异：",[1908,14137,14139],{"className":14138},[3912],[1908,14140,14142,14180],{"className":14141},[1911],[1908,14143,14145],{"className":14144},[1915],[1917,14146,14147],{"xmlns":1919,"display":3921},[1921,14148,14149,14177],{},[1924,14150,14151,14157,14159,14161,14163,14165,14171,14173,14175],{},[2137,14152,14153,14155],{},[1927,14154,2235],{},[1986,14156,1994],{},[1978,14158,2566],{"stretchy":1983},[1927,14160,14005],{},[1978,14162,2595],{"stretchy":1983},[1978,14164,1980],{},[2137,14166,14167,14169],{},[1927,14168,2235],{},[1986,14170,1994],{},[1978,14172,2566],{"stretchy":1983},[1927,14174,2274],{},[1978,14176,2595],{"stretchy":1983},[1931,14178,14179],{"encoding":1933},"u_2(L) = u_2(R)",[1908,14181,14183,14247],{"className":14182,"ariaHidden":1938},[1937],[1908,14184,14186,14189,14229,14232,14235,14238,14241,14244],{"className":14185},[1942],[1908,14187],{"className":14188,"style":2042},[1946],[1908,14190,14192,14195],{"className":14191},[1951],[1908,14193,2235],{"className":14194},[1951,1952],[1908,14196,14198],{"className":14197},[2167],[1908,14199,14201,14221],{"className":14200},[2171,2172],[1908,14202,14204,14218],{"className":14203},[2176],[1908,14205,14207],{"className":14206,"style":2362},[2180],[1908,14208,14209,14212],{"style":2308},[1908,14210],{"className":14211,"style":2189},[2188],[1908,14213,14215],{"className":14214},[2193,2194,2195,2196],[1908,14216,1994],{"className":14217},[1951,2196],[1908,14219,2204],{"className":14220},[2203],[1908,14222,14224],{"className":14223},[2176],[1908,14225,14227],{"className":14226,"style":2211},[2180],[1908,14228],{},[1908,14230,2566],{"className":14231},[2046],[1908,14233,14005],{"className":14234},[1951,1952],[1908,14236,2595],{"className":14237},[2086],[1908,14239],{"className":14240,"style":2028},[2027],[1908,14242,1980],{"className":14243},[2032],[1908,14245],{"className":14246,"style":2028},[2027],[1908,14248,14250,14253,14293,14296,14299],{"className":14249},[1942],[1908,14251],{"className":14252,"style":2042},[1946],[1908,14254,14256,14259],{"className":14255},[1951],[1908,14257,2235],{"className":14258},[1951,1952],[1908,14260,14262],{"className":14261},[2167],[1908,14263,14265,14285],{"className":14264},[2171,2172],[1908,14266,14268,14282],{"className":14267},[2176],[1908,14269,14271],{"className":14270,"style":2362},[2180],[1908,14272,14273,14276],{"style":2308},[1908,14274],{"className":14275,"style":2189},[2188],[1908,14277,14279],{"className":14278},[2193,2194,2195,2196],[1908,14280,1994],{"className":14281},[1951,2196],[1908,14283,2204],{"className":14284},[2203],[1908,14286,14288],{"className":14287},[2176],[1908,14289,14291],{"className":14290,"style":2211},[2180],[1908,14292],{},[1908,14294,2566],{"className":14295},[2046],[1908,14297,2274],{"className":14298,"style":6138},[1951,1952],[1908,14300,2595],{"className":14301},[2086],[1908,14303,14305],{"className":14304},[3912],[1908,14306,14308,14365],{"className":14307},[1911],[1908,14309,14311],{"className":14310},[1915],[1917,14312,14313],{"xmlns":1919,"display":3921},[1921,14314,14315,14363],{},[1924,14316,14317,14319,14321,14323,14325,14327,14329,14331,14333,14335,14337,14339,14341,14343,14345,14347,14349,14351,14353,14355,14357,14359,14361],{},[1986,14318,1988],{},[1978,14320,9754],{},[1927,14322,1798],{},[1978,14324,2871],{},[1986,14326,9761],{},[1978,14328,9754],{},[1978,14330,2566],{"stretchy":1983},[1986,14332,1988],{},[1978,14334,2828],{},[1927,14336,1798],{},[1978,14338,2595],{"stretchy":1983},[1978,14340,1980],{},[1986,14342,9761],{},[1978,14344,9754],{},[1927,14346,1798],{},[1978,14348,2871],{},[1986,14350,1994],{},[1978,14352,9754],{},[1978,14354,2566],{"stretchy":1983},[1986,14356,1988],{},[1978,14358,2828],{},[1927,14360,1798],{},[1978,14362,2595],{"stretchy":1983},[1931,14364,9800],{"encoding":1933},[1908,14366,14368,14386,14404,14422,14443,14464,14482,14500,14518,14539],{"className":14367,"ariaHidden":1938},[1937],[1908,14369,14371,14374,14377,14380,14383],{"className":14370},[1942],[1908,14372],{"className":14373,"style":9810},[1946],[1908,14375,1988],{"className":14376},[1951],[1908,14378],{"className":14379,"style":2388},[2027],[1908,14381,9754],{"className":14382},[2392],[1908,14384],{"className":14385,"style":2388},[2027],[1908,14387,14389,14392,14395,14398,14401],{"className":14388},[1942],[1908,14390],{"className":14391,"style":9829},[1946],[1908,14393,1798],{"className":14394},[1951,1952],[1908,14396],{"className":14397,"style":2388},[2027],[1908,14399,2871],{"className":14400},[2392],[1908,14402],{"className":14403,"style":2388},[2027],[1908,14405,14407,14410,14413,14416,14419],{"className":14406},[1942],[1908,14408],{"className":14409,"style":9810},[1946],[1908,14411,9761],{"className":14412},[1951],[1908,14414],{"className":14415,"style":2388},[2027],[1908,14417,9754],{"className":14418},[2392],[1908,14420],{"className":14421,"style":2388},[2027],[1908,14423,14425,14428,14431,14434,14437,14440],{"className":14424},[1942],[1908,14426],{"className":14427,"style":2042},[1946],[1908,14429,2566],{"className":14430},[2046],[1908,14432,1988],{"className":14433},[1951],[1908,14435],{"className":14436,"style":2388},[2027],[1908,14438,2828],{"className":14439},[2392],[1908,14441],{"className":14442,"style":2388},[2027],[1908,14444,14446,14449,14452,14455,14458,14461],{"className":14445},[1942],[1908,14447],{"className":14448,"style":2042},[1946],[1908,14450,1798],{"className":14451},[1951,1952],[1908,14453,2595],{"className":14454},[2086],[1908,14456],{"className":14457,"style":2028},[2027],[1908,14459,1980],{"className":14460},[2032],[1908,14462],{"className":14463,"style":2028},[2027],[1908,14465,14467,14470,14473,14476,14479],{"className":14466},[1942],[1908,14468],{"className":14469,"style":9810},[1946],[1908,14471,9761],{"className":14472},[1951],[1908,14474],{"className":14475,"style":2388},[2027],[1908,14477,9754],{"className":14478},[2392],[1908,14480],{"className":14481,"style":2388},[2027],[1908,14483,14485,14488,14491,14494,14497],{"className":14484},[1942],[1908,14486],{"className":14487,"style":9829},[1946],[1908,14489,1798],{"className":14490},[1951,1952],[1908,14492],{"className":14493,"style":2388},[2027],[1908,14495,2871],{"className":14496},[2392],[1908,14498],{"className":14499,"style":2388},[2027],[1908,14501,14503,14506,14509,14512,14515],{"className":14502},[1942],[1908,14504],{"className":14505,"style":9810},[1946],[1908,14507,1994],{"className":14508},[1951],[1908,14510],{"className":14511,"style":2388},[2027],[1908,14513,9754],{"className":14514},[2392],[1908,14516],{"className":14517,"style":2388},[2027],[1908,14519,14521,14524,14527,14530,14533,14536],{"className":14520},[1942],[1908,14522],{"className":14523,"style":2042},[1946],[1908,14525,2566],{"className":14526},[2046],[1908,14528,1988],{"className":14529},[1951],[1908,14531],{"className":14532,"style":2388},[2027],[1908,14534,2828],{"className":14535},[2392],[1908,14537],{"className":14538,"style":2388},[2027],[1908,14540,14542,14545,14548],{"className":14541},[1942],[1908,14543],{"className":14544,"style":2042},[1946],[1908,14546,1798],{"className":14547},[1951,1952],[1908,14549,2595],{"className":14550},[2086],[1908,14552,14554],{"className":14553},[3912],[1908,14555,14557,14584],{"className":14556},[1911],[1908,14558,14560],{"className":14559},[1915],[1917,14561,14562],{"xmlns":1919,"display":3921},[1921,14563,14564,14582],{},[1924,14565,14566,14568,14570,14572,14574,14576,14578,14580],{},[1927,14567,1798],{},[1978,14569,1980],{},[1986,14571,1994],{},[1978,14573,2566],{"stretchy":1983},[1986,14575,1988],{},[1978,14577,2828],{},[1927,14579,1798],{},[1978,14581,2595],{"stretchy":1983},[1931,14583,10022],{"encoding":1933},[1908,14585,14587,14605,14629],{"className":14586,"ariaHidden":1938},[1937],[1908,14588,14590,14593,14596,14599,14602],{"className":14589},[1942],[1908,14591],{"className":14592,"style":9508},[1946],[1908,14594,1798],{"className":14595},[1951,1952],[1908,14597],{"className":14598,"style":2028},[2027],[1908,14600,1980],{"className":14601},[2032],[1908,14603],{"className":14604,"style":2028},[2027],[1908,14606,14608,14611,14614,14617,14620,14623,14626],{"className":14607},[1942],[1908,14609],{"className":14610,"style":2042},[1946],[1908,14612,1994],{"className":14613},[1951],[1908,14615,2566],{"className":14616},[2046],[1908,14618,1988],{"className":14619},[1951],[1908,14621],{"className":14622,"style":2388},[2027],[1908,14624,2828],{"className":14625},[2392],[1908,14627],{"className":14628,"style":2388},[2027],[1908,14630,14632,14635,14638],{"className":14631},[1942],[1908,14633],{"className":14634,"style":2042},[1946],[1908,14636,1798],{"className":14637},[1951,1952],[1908,14639,2595],{"className":14640},[2086],[1908,14642,14644],{"className":14643},[3912],[1908,14645,14647,14669],{"className":14646},[1911],[1908,14648,14650],{"className":14649},[1915],[1917,14651,14652],{"xmlns":1919,"display":3921},[1921,14653,14654,14666],{},[1924,14655,14656,14658,14660],{},[1927,14657,1798],{},[1978,14659,1980],{},[10756,14661,14662,14664],{},[1986,14663,1994],{},[1986,14665,10106],{},[1931,14667,14668],{"encoding":1933},"p = \\frac{2}{3}",[1908,14670,14672,14690],{"className":14671,"ariaHidden":1938},[1937],[1908,14673,14675,14678,14681,14684,14687],{"className":14674},[1942],[1908,14676],{"className":14677,"style":9508},[1946],[1908,14679,1798],{"className":14680},[1951,1952],[1908,14682],{"className":14683,"style":2028},[2027],[1908,14685,1980],{"className":14686},[2032],[1908,14688],{"className":14689,"style":2028},[2027],[1908,14691,14693,14696],{"className":14692},[1942],[1908,14694],{"className":14695,"style":10871},[1946],[1908,14697,14699,14702,14755],{"className":14698},[1951],[1908,14700],{"className":14701},[2046,10878],[1908,14703,14705],{"className":14704},[10756],[1908,14706,14708,14747],{"className":14707},[2171,2172],[1908,14709,14711,14744],{"className":14710},[2176],[1908,14712,14714,14725,14733],{"className":14713,"style":10891},[2180],[1908,14715,14716,14719],{"style":10894},[1908,14717],{"className":14718,"style":6273},[2188],[1908,14720,14722],{"className":14721},[1951],[1908,14723,10106],{"className":14724},[1951],[1908,14726,14727,14730],{"style":10906},[1908,14728],{"className":14729,"style":6273},[2188],[1908,14731],{"className":14732,"style":10914},[10913],[1908,14734,14735,14738],{"style":10917},[1908,14736],{"className":14737,"style":6273},[2188],[1908,14739,14741],{"className":14740},[1951],[1908,14742,1994],{"className":14743},[1951],[1908,14745,2204],{"className":14746},[2203],[1908,14748,14750],{"className":14749},[2176],[1908,14751,14753],{"className":14752,"style":10936},[2180],[1908,14754],{},[1908,14756],{"className":14757},[2086,10878],[1798,14759,14760],{},"使参与者1无差异：",[1908,14762,14764],{"className":14763},[3912],[1908,14765,14767,14805],{"className":14766},[1911],[1908,14768,14770],{"className":14769},[1915],[1917,14771,14772],{"xmlns":1919,"display":3921},[1921,14773,14774,14802],{},[1924,14775,14776,14782,14784,14786,14788,14790,14796,14798,14800],{},[2137,14777,14778,14780],{},[1927,14779,2235],{},[1986,14781,1988],{},[1978,14783,2566],{"stretchy":1983},[1927,14785,14016],{},[1978,14787,2595],{"stretchy":1983},[1978,14789,1980],{},[2137,14791,14792,14794],{},[1927,14793,2235],{},[1986,14795,1988],{},[1978,14797,2566],{"stretchy":1983},[1927,14799,14028],{},[1978,14801,2595],{"stretchy":1983},[1931,14803,14804],{"encoding":1933},"u_1(U) = u_1(D)",[1908,14806,14808,14872],{"className":14807,"ariaHidden":1938},[1937],[1908,14809,14811,14814,14854,14857,14860,14863,14866,14869],{"className":14810},[1942],[1908,14812],{"className":14813,"style":2042},[1946],[1908,14815,14817,14820],{"className":14816},[1951],[1908,14818,2235],{"className":14819},[1951,1952],[1908,14821,14823],{"className":14822},[2167],[1908,14824,14826,14846],{"className":14825},[2171,2172],[1908,14827,14829,14843],{"className":14828},[2176],[1908,14830,14832],{"className":14831,"style":2362},[2180],[1908,14833,14834,14837],{"style":2308},[1908,14835],{"className":14836,"style":2189},[2188],[1908,14838,14840],{"className":14839},[2193,2194,2195,2196],[1908,14841,1988],{"className":14842},[1951,2196],[1908,14844,2204],{"className":14845},[2203],[1908,14847,14849],{"className":14848},[2176],[1908,14850,14852],{"className":14851,"style":2211},[2180],[1908,14853],{},[1908,14855,2566],{"className":14856},[2046],[1908,14858,14016],{"className":14859,"style":2023},[1951,1952],[1908,14861,2595],{"className":14862},[2086],[1908,14864],{"className":14865,"style":2028},[2027],[1908,14867,1980],{"className":14868},[2032],[1908,14870],{"className":14871,"style":2028},[2027],[1908,14873,14875,14878,14918,14921,14924],{"className":14874},[1942],[1908,14876],{"className":14877,"style":2042},[1946],[1908,14879,14881,14884],{"className":14880},[1951],[1908,14882,2235],{"className":14883},[1951,1952],[1908,14885,14887],{"className":14886},[2167],[1908,14888,14890,14910],{"className":14889},[2171,2172],[1908,14891,14893,14907],{"className":14892},[2176],[1908,14894,14896],{"className":14895,"style":2362},[2180],[1908,14897,14898,14901],{"style":2308},[1908,14899],{"className":14900,"style":2189},[2188],[1908,14902,14904],{"className":14903},[2193,2194,2195,2196],[1908,14905,1988],{"className":14906},[1951,2196],[1908,14908,2204],{"className":14909},[2203],[1908,14911,14913],{"className":14912},[2176],[1908,14914,14916],{"className":14915,"style":2211},[2180],[1908,14917],{},[1908,14919,2566],{"className":14920},[2046],[1908,14922,14028],{"className":14923,"style":9660},[1951,1952],[1908,14925,2595],{"className":14926},[2086],[1908,14928,14930],{"className":14929},[3912],[1908,14931,14933,14991],{"className":14932},[1911],[1908,14934,14936],{"className":14935},[1915],[1917,14937,14938],{"xmlns":1919,"display":3921},[1921,14939,14940,14988],{},[1924,14941,14942,14944,14946,14948,14950,14952,14954,14956,14958,14960,14962,14964,14966,14968,14970,14972,14974,14976,14978,14980,14982,14984,14986],{},[1986,14943,10106],{},[1978,14945,9754],{},[1927,14947,9527],{},[1978,14949,2871],{},[1986,14951,9761],{},[1978,14953,9754],{},[1978,14955,2566],{"stretchy":1983},[1986,14957,1988],{},[1978,14959,2828],{},[1927,14961,9527],{},[1978,14963,2595],{"stretchy":1983},[1978,14965,1980],{},[1986,14967,1988],{},[1978,14969,9754],{},[1927,14971,9527],{},[1978,14973,2871],{},[1986,14975,1994],{},[1978,14977,9754],{},[1978,14979,2566],{"stretchy":1983},[1986,14981,1988],{},[1978,14983,2828],{},[1927,14985,9527],{},[1978,14987,2595],{"stretchy":1983},[1931,14989,14990],{"encoding":1933},"3 \\cdot q + 0 \\cdot (1-q) = 1 \\cdot q + 2 \\cdot (1-q)",[1908,14992,14994,15012,15030,15048,15069,15090,15108,15126,15144,15165],{"className":14993,"ariaHidden":1938},[1937],[1908,14995,14997,15000,15003,15006,15009],{"className":14996},[1942],[1908,14998],{"className":14999,"style":9810},[1946],[1908,15001,10106],{"className":15002},[1951],[1908,15004],{"className":15005,"style":2388},[2027],[1908,15007,9754],{"className":15008},[2392],[1908,15010],{"className":15011,"style":2388},[2027],[1908,15013,15015,15018,15021,15024,15027],{"className":15014},[1942],[1908,15016],{"className":15017,"style":9829},[1946],[1908,15019,9527],{"className":15020,"style":7564},[1951,1952],[1908,15022],{"className":15023,"style":2388},[2027],[1908,15025,2871],{"className":15026},[2392],[1908,15028],{"className":15029,"style":2388},[2027],[1908,15031,15033,15036,15039,15042,15045],{"className":15032},[1942],[1908,15034],{"className":15035,"style":9810},[1946],[1908,15037,9761],{"className":15038},[1951],[1908,15040],{"className":15041,"style":2388},[2027],[1908,15043,9754],{"className":15044},[2392],[1908,15046],{"className":15047,"style":2388},[2027],[1908,15049,15051,15054,15057,15060,15063,15066],{"className":15050},[1942],[1908,15052],{"className":15053,"style":2042},[1946],[1908,15055,2566],{"className":15056},[2046],[1908,15058,1988],{"className":15059},[1951],[1908,15061],{"className":15062,"style":2388},[2027],[1908,15064,2828],{"className":15065},[2392],[1908,15067],{"className":15068,"style":2388},[2027],[1908,15070,15072,15075,15078,15081,15084,15087],{"className":15071},[1942],[1908,15073],{"className":15074,"style":2042},[1946],[1908,15076,9527],{"className":15077,"style":7564},[1951,1952],[1908,15079,2595],{"className":15080},[2086],[1908,15082],{"className":15083,"style":2028},[2027],[1908,15085,1980],{"className":15086},[2032],[1908,15088],{"className":15089,"style":2028},[2027],[1908,15091,15093,15096,15099,15102,15105],{"className":15092},[1942],[1908,15094],{"className":15095,"style":9810},[1946],[1908,15097,1988],{"className":15098},[1951],[1908,15100],{"className":15101,"style":2388},[2027],[1908,15103,9754],{"className":15104},[2392],[1908,15106],{"className":15107,"style":2388},[2027],[1908,15109,15111,15114,15117,15120,15123],{"className":15110},[1942],[1908,15112],{"className":15113,"style":9829},[1946],[1908,15115,9527],{"className":15116,"style":7564},[1951,1952],[1908,15118],{"className":15119,"style":2388},[2027],[1908,15121,2871],{"className":15122},[2392],[1908,15124],{"className":15125,"style":2388},[2027],[1908,15127,15129,15132,15135,15138,15141],{"className":15128},[1942],[1908,15130],{"className":15131,"style":9810},[1946],[1908,15133,1994],{"className":15134},[1951],[1908,15136],{"className":15137,"style":2388},[2027],[1908,15139,9754],{"className":15140},[2392],[1908,15142],{"className":15143,"style":2388},[2027],[1908,15145,15147,15150,15153,15156,15159,15162],{"className":15146},[1942],[1908,15148],{"className":15149,"style":2042},[1946],[1908,15151,2566],{"className":15152},[2046],[1908,15154,1988],{"className":15155},[1951],[1908,15157],{"className":15158,"style":2388},[2027],[1908,15160,2828],{"className":15161},[2392],[1908,15163],{"className":15164,"style":2388},[2027],[1908,15166,15168,15171,15174],{"className":15167},[1942],[1908,15169],{"className":15170,"style":2042},[1946],[1908,15172,9527],{"className":15173,"style":7564},[1951,1952],[1908,15175,2595],{"className":15176},[2086],[1908,15178,15180],{"className":15179},[3912],[1908,15181,15183,15213],{"className":15182},[1911],[1908,15184,15186],{"className":15185},[1915],[1917,15187,15188],{"xmlns":1919,"display":3921},[1921,15189,15190,15210],{},[1924,15191,15192,15194,15196,15198,15200,15202,15204,15206,15208],{},[1986,15193,10106],{},[1927,15195,9527],{},[1978,15197,1980],{},[1927,15199,9527],{},[1978,15201,2871],{},[1986,15203,1994],{},[1978,15205,2828],{},[1986,15207,1994],{},[1927,15209,9527],{},[1931,15211,15212],{"encoding":1933},"3q = q + 2 - 2q",[1908,15214,15216,15237,15255,15273],{"className":15215,"ariaHidden":1938},[1937],[1908,15217,15219,15222,15225,15228,15231,15234],{"className":15218},[1942],[1908,15220],{"className":15221,"style":10614},[1946],[1908,15223,10106],{"className":15224},[1951],[1908,15226,9527],{"className":15227,"style":7564},[1951,1952],[1908,15229],{"className":15230,"style":2028},[2027],[1908,15232,1980],{"className":15233},[2032],[1908,15235],{"className":15236,"style":2028},[2027],[1908,15238,15240,15243,15246,15249,15252],{"className":15239},[1942],[1908,15241],{"className":15242,"style":9829},[1946],[1908,15244,9527],{"className":15245,"style":7564},[1951,1952],[1908,15247],{"className":15248,"style":2388},[2027],[1908,15250,2871],{"className":15251},[2392],[1908,15253],{"className":15254,"style":2388},[2027],[1908,15256,15258,15261,15264,15267,15270],{"className":15257},[1942],[1908,15259],{"className":15260,"style":10636},[1946],[1908,15262,1994],{"className":15263},[1951],[1908,15265],{"className":15266,"style":2388},[2027],[1908,15268,2828],{"className":15269},[2392],[1908,15271],{"className":15272,"style":2388},[2027],[1908,15274,15276,15279,15282],{"className":15275},[1942],[1908,15277],{"className":15278,"style":10614},[1946],[1908,15280,1994],{"className":15281},[1951],[1908,15283,9527],{"className":15284,"style":7564},[1951,1952],[1908,15286,15288],{"className":15287},[3912],[1908,15289,15291,15311],{"className":15290},[1911],[1908,15292,15294],{"className":15293},[1915],[1917,15295,15296],{"xmlns":1919,"display":3921},[1921,15297,15298,15308],{},[1924,15299,15300,15302,15304,15306],{},[1986,15301,10776],{},[1927,15303,9527],{},[1978,15305,1980],{},[1986,15307,1994],{},[1931,15309,15310],{"encoding":1933},"4q = 2",[1908,15312,15314,15335],{"className":15313,"ariaHidden":1938},[1937],[1908,15315,15317,15320,15323,15326,15329,15332],{"className":15316},[1942],[1908,15318],{"className":15319,"style":10614},[1946],[1908,15321,10776],{"className":15322},[1951],[1908,15324,9527],{"className":15325,"style":7564},[1951,1952],[1908,15327],{"className":15328,"style":2028},[2027],[1908,15330,1980],{"className":15331},[2032],[1908,15333],{"className":15334,"style":2028},[2027],[1908,15336,15338,15341],{"className":15337},[1942],[1908,15339],{"className":15340,"style":9810},[1946],[1908,15342,1994],{"className":15343},[1951],[1908,15345,15347],{"className":15346},[3912],[1908,15348,15350,15372],{"className":15349},[1911],[1908,15351,15353],{"className":15352},[1915],[1917,15354,15355],{"xmlns":1919,"display":3921},[1921,15356,15357,15369],{},[1924,15358,15359,15361,15363],{},[1927,15360,9527],{},[1978,15362,1980],{},[10756,15364,15365,15367],{},[1986,15366,1988],{},[1986,15368,1994],{},[1931,15370,15371],{"encoding":1933},"q = \\frac{1}{2}",[1908,15373,15375,15393],{"className":15374,"ariaHidden":1938},[1937],[1908,15376,15378,15381,15384,15387,15390],{"className":15377},[1942],[1908,15379],{"className":15380,"style":9508},[1946],[1908,15382,9527],{"className":15383,"style":7564},[1951,1952],[1908,15385],{"className":15386,"style":2028},[2027],[1908,15388,1980],{"className":15389},[2032],[1908,15391],{"className":15392,"style":2028},[2027],[1908,15394,15396,15399],{"className":15395},[1942],[1908,15397],{"className":15398,"style":10871},[1946],[1908,15400,15402,15405,15458],{"className":15401},[1951],[1908,15403],{"className":15404},[2046,10878],[1908,15406,15408],{"className":15407},[10756],[1908,15409,15411,15450],{"className":15410},[2171,2172],[1908,15412,15414,15447],{"className":15413},[2176],[1908,15415,15417,15428,15436],{"className":15416,"style":10891},[2180],[1908,15418,15419,15422],{"style":10894},[1908,15420],{"className":15421,"style":6273},[2188],[1908,15423,15425],{"className":15424},[1951],[1908,15426,1994],{"className":15427},[1951],[1908,15429,15430,15433],{"style":10906},[1908,15431],{"className":15432,"style":6273},[2188],[1908,15434],{"className":15435,"style":10914},[10913],[1908,15437,15438,15441],{"style":10917},[1908,15439],{"className":15440,"style":6273},[2188],[1908,15442,15444],{"className":15443},[1951],[1908,15445,1988],{"className":15446},[1951],[1908,15448,2204],{"className":15449},[2203],[1908,15451,15453],{"className":15452},[2176],[1908,15454,15456],{"className":15455,"style":10936},[2180],[1908,15457],{},[1908,15459],{"className":15460},[2086,10878],[1798,15462,15463,1961,15465],{},[1857,15464,10721],{},[1908,15466,15468,15510],{"className":15467},[1911],[1908,15469,15471],{"className":15470},[1915],[1917,15472,15473],{"xmlns":1919},[1921,15474,15475,15507],{},[1924,15476,15477,15483,15485,15487,15489,15491,15493,15499,15501,15503,15505],{},[5080,15478,15479,15481],{},[1927,15480,1798],{},[1978,15482,3548],{},[1978,15484,1980],{},[1986,15486,1994],{},[1927,15488,10103],{"mathvariant":3638},[1986,15490,10106],{},[1978,15492,1991],{"separator":1938},[5080,15494,15495,15497],{},[1927,15496,9527],{},[1978,15498,3548],{},[1978,15500,1980],{},[1986,15502,1988],{},[1927,15504,10103],{"mathvariant":3638},[1986,15506,1994],{},[1931,15508,15509],{"encoding":1933},"p^* = 2\u002F3, q^* = 1\u002F2",[1908,15511,15513,15558,15611],{"className":15512,"ariaHidden":1938},[1937],[1908,15514,15516,15520,15549,15552,15555],{"className":15515},[1942],[1908,15517],{"className":15518,"style":15519},[1946],"height:0.8831em;vertical-align:-0.1944em;",[1908,15521,15523,15526],{"className":15522},[1951],[1908,15524,1798],{"className":15525},[1951,1952],[1908,15527,15529],{"className":15528},[2167],[1908,15530,15532],{"className":15531},[2171],[1908,15533,15535],{"className":15534},[2176],[1908,15536,15538],{"className":15537,"style":3580},[2180],[1908,15539,15540,15543],{"style":3595},[1908,15541],{"className":15542,"style":2189},[2188],[1908,15544,15546],{"className":15545},[2193,2194,2195,2196],[1908,15547,3548],{"className":15548},[2392,2196],[1908,15550],{"className":15551,"style":2028},[2027],[1908,15553,1980],{"className":15554},[2032],[1908,15556],{"className":15557,"style":2028},[2027],[1908,15559,15561,15564,15567,15570,15573,15602,15605,15608],{"className":15560},[1942],[1908,15562],{"className":15563,"style":2042},[1946],[1908,15565,10140],{"className":15566},[1951],[1908,15568,1991],{"className":15569},[2053],[1908,15571],{"className":15572,"style":2057},[2027],[1908,15574,15576,15579],{"className":15575},[1951],[1908,15577,9527],{"className":15578,"style":7564},[1951,1952],[1908,15580,15582],{"className":15581},[2167],[1908,15583,15585],{"className":15584},[2171],[1908,15586,15588],{"className":15587},[2176],[1908,15589,15591],{"className":15590,"style":3580},[2180],[1908,15592,15593,15596],{"style":3595},[1908,15594],{"className":15595,"style":2189},[2188],[1908,15597,15599],{"className":15598},[2193,2194,2195,2196],[1908,15600,3548],{"className":15601},[2392,2196],[1908,15603],{"className":15604,"style":2028},[2027],[1908,15606,1980],{"className":15607},[2032],[1908,15609],{"className":15610,"style":2028},[2027],[1908,15612,15614,15617],{"className":15613},[1942],[1908,15615],{"className":15616,"style":2042},[1946],[1908,15618,15620],{"className":15619},[1951],"1\u002F2",[1798,15622,15623],{},"期望支付：",[1908,15625,15627],{"className":15626},[3912],[1908,15628,15630,15708],{"className":15629},[1911],[1908,15631,15633],{"className":15632},[1915],[1917,15634,15635],{"xmlns":1919,"display":3921},[1921,15636,15637,15705],{},[1924,15638,15639,15645,15647,15649,15651,15657,15659,15665,15667,15669,15671,15677,15679,15685,15687,15689,15691,15697,15699],{},[2137,15640,15641,15643],{},[1927,15642,2235],{},[1986,15644,1988],{},[1978,15646,1980],{},[1986,15648,10106],{},[1978,15650,2248],{},[10756,15652,15653,15655],{},[1986,15654,1988],{},[1986,15656,1994],{},[1978,15658,2248],{},[10756,15660,15661,15663],{},[1986,15662,1994],{},[1986,15664,10106],{},[1978,15666,2871],{},[1986,15668,1994],{},[1978,15670,2248],{},[10756,15672,15673,15675],{},[1986,15674,1988],{},[1986,15676,1994],{},[1978,15678,2248],{},[10756,15680,15681,15683],{},[1986,15682,1988],{},[1986,15684,10106],{},[1978,15686,1980],{},[1986,15688,1988],{},[1978,15690,2871],{},[10756,15692,15693,15695],{},[1986,15694,1988],{},[1986,15696,10106],{},[1978,15698,1980],{},[10756,15700,15701,15703],{},[1986,15702,10776],{},[1986,15704,10106],{},[1931,15706,15707],{"encoding":1933},"u_1 = 3 \\times \\frac{1}{2} \\times \\frac{2}{3} + 2 \\times \\frac{1}{2} \\times \\frac{1}{3} = 1 + \\frac{1}{3} = \\frac{4}{3}",[1908,15709,15711,15766,15784,15861,15938,15956,16033,16110,16128,16205],{"className":15710,"ariaHidden":1938},[1937],[1908,15712,15714,15717,15757,15760,15763],{"className":15713},[1942],[1908,15715],{"className":15716,"style":2287},[1946],[1908,15718,15720,15723],{"className":15719},[1951],[1908,15721,2235],{"className":15722},[1951,1952],[1908,15724,15726],{"className":15725},[2167],[1908,15727,15729,15749],{"className":15728},[2171,2172],[1908,15730,15732,15746],{"className":15731},[2176],[1908,15733,15735],{"className":15734,"style":2362},[2180],[1908,15736,15737,15740],{"style":2308},[1908,15738],{"className":15739,"style":2189},[2188],[1908,15741,15743],{"className":15742},[2193,2194,2195,2196],[1908,15744,1988],{"className":15745},[1951,2196],[1908,15747,2204],{"className":15748},[2203],[1908,15750,15752],{"className":15751},[2176],[1908,15753,15755],{"className":15754,"style":2211},[2180],[1908,15756],{},[1908,15758],{"className":15759,"style":2028},[2027],[1908,15761,1980],{"className":15762},[2032],[1908,15764],{"className":15765,"style":2028},[2027],[1908,15767,15769,15772,15775,15778,15781],{"className":15768},[1942],[1908,15770],{"className":15771,"style":10636},[1946],[1908,15773,10106],{"className":15774},[1951],[1908,15776],{"className":15777,"style":2388},[2027],[1908,15779,2248],{"className":15780},[2392],[1908,15782],{"className":15783,"style":2388},[2027],[1908,15785,15787,15790,15852,15855,15858],{"className":15786},[1942],[1908,15788],{"className":15789,"style":10871},[1946],[1908,15791,15793,15796,15849],{"className":15792},[1951],[1908,15794],{"className":15795},[2046,10878],[1908,15797,15799],{"className":15798},[10756],[1908,15800,15802,15841],{"className":15801},[2171,2172],[1908,15803,15805,15838],{"className":15804},[2176],[1908,15806,15808,15819,15827],{"className":15807,"style":10891},[2180],[1908,15809,15810,15813],{"style":10894},[1908,15811],{"className":15812,"style":6273},[2188],[1908,15814,15816],{"className":15815},[1951],[1908,15817,1994],{"className":15818},[1951],[1908,15820,15821,15824],{"style":10906},[1908,15822],{"className":15823,"style":6273},[2188],[1908,15825],{"className":15826,"style":10914},[10913],[1908,15828,15829,15832],{"style":10917},[1908,15830],{"className":15831,"style":6273},[2188],[1908,15833,15835],{"className":15834},[1951],[1908,15836,1988],{"className":15837},[1951],[1908,15839,2204],{"className":15840},[2203],[1908,15842,15844],{"className":15843},[2176],[1908,15845,15847],{"className":15846,"style":10936},[2180],[1908,15848],{},[1908,15850],{"className":15851},[2086,10878],[1908,15853],{"className":15854,"style":2388},[2027],[1908,15856,2248],{"className":15857},[2392],[1908,15859],{"className":15860,"style":2388},[2027],[1908,15862,15864,15867,15929,15932,15935],{"className":15863},[1942],[1908,15865],{"className":15866,"style":10871},[1946],[1908,15868,15870,15873,15926],{"className":15869},[1951],[1908,15871],{"className":15872},[2046,10878],[1908,15874,15876],{"className":15875},[10756],[1908,15877,15879,15918],{"className":15878},[2171,2172],[1908,15880,15882,15915],{"className":15881},[2176],[1908,15883,15885,15896,15904],{"className":15884,"style":10891},[2180],[1908,15886,15887,15890],{"style":10894},[1908,15888],{"className":15889,"style":6273},[2188],[1908,15891,15893],{"className":15892},[1951],[1908,15894,10106],{"className":15895},[1951],[1908,15897,15898,15901],{"style":10906},[1908,15899],{"className":15900,"style":6273},[2188],[1908,15902],{"className":15903,"style":10914},[10913],[1908,15905,15906,15909],{"style":10917},[1908,15907],{"className":15908,"style":6273},[2188],[1908,15910,15912],{"className":15911},[1951],[1908,15913,1994],{"className":15914},[1951],[1908,15916,2204],{"className":15917},[2203],[1908,15919,15921],{"className":15920},[2176],[1908,15922,15924],{"className":15923,"style":10936},[2180],[1908,15925],{},[1908,15927],{"className":15928},[2086,10878],[1908,15930],{"className":15931,"style":2388},[2027],[1908,15933,2871],{"className":15934},[2392],[1908,15936],{"className":15937,"style":2388},[2027],[1908,15939,15941,15944,15947,15950,15953],{"className":15940},[1942],[1908,15942],{"className":15943,"style":10636},[1946],[1908,15945,1994],{"className":15946},[1951],[1908,15948],{"className":15949,"style":2388},[2027],[1908,15951,2248],{"className":15952},[2392],[1908,15954],{"className":15955,"style":2388},[2027],[1908,15957,15959,15962,16024,16027,16030],{"className":15958},[1942],[1908,15960],{"className":15961,"style":10871},[1946],[1908,15963,15965,15968,16021],{"className":15964},[1951],[1908,15966],{"className":15967},[2046,10878],[1908,15969,15971],{"className":15970},[10756],[1908,15972,15974,16013],{"className":15973},[2171,2172],[1908,15975,15977,16010],{"className":15976},[2176],[1908,15978,15980,15991,15999],{"className":15979,"style":10891},[2180],[1908,15981,15982,15985],{"style":10894},[1908,15983],{"className":15984,"style":6273},[2188],[1908,15986,15988],{"className":15987},[1951],[1908,15989,1994],{"className":15990},[1951],[1908,15992,15993,15996],{"style":10906},[1908,15994],{"className":15995,"style":6273},[2188],[1908,15997],{"className":15998,"style":10914},[10913],[1908,16000,16001,16004],{"style":10917},[1908,16002],{"className":16003,"style":6273},[2188],[1908,16005,16007],{"className":16006},[1951],[1908,16008,1988],{"className":16009},[1951],[1908,16011,2204],{"className":16012},[2203],[1908,16014,16016],{"className":16015},[2176],[1908,16017,16019],{"className":16018,"style":10936},[2180],[1908,16020],{},[1908,16022],{"className":16023},[2086,10878],[1908,16025],{"className":16026,"style":2388},[2027],[1908,16028,2248],{"className":16029},[2392],[1908,16031],{"className":16032,"style":2388},[2027],[1908,16034,16036,16039,16101,16104,16107],{"className":16035},[1942],[1908,16037],{"className":16038,"style":10871},[1946],[1908,16040,16042,16045,16098],{"className":16041},[1951],[1908,16043],{"className":16044},[2046,10878],[1908,16046,16048],{"className":16047},[10756],[1908,16049,16051,16090],{"className":16050},[2171,2172],[1908,16052,16054,16087],{"className":16053},[2176],[1908,16055,16057,16068,16076],{"className":16056,"style":10891},[2180],[1908,16058,16059,16062],{"style":10894},[1908,16060],{"className":16061,"style":6273},[2188],[1908,16063,16065],{"className":16064},[1951],[1908,16066,10106],{"className":16067},[1951],[1908,16069,16070,16073],{"style":10906},[1908,16071],{"className":16072,"style":6273},[2188],[1908,16074],{"className":16075,"style":10914},[10913],[1908,16077,16078,16081],{"style":10917},[1908,16079],{"className":16080,"style":6273},[2188],[1908,16082,16084],{"className":16083},[1951],[1908,16085,1988],{"className":16086},[1951],[1908,16088,2204],{"className":16089},[2203],[1908,16091,16093],{"className":16092},[2176],[1908,16094,16096],{"className":16095,"style":10936},[2180],[1908,16097],{},[1908,16099],{"className":16100},[2086,10878],[1908,16102],{"className":16103,"style":2028},[2027],[1908,16105,1980],{"className":16106},[2032],[1908,16108],{"className":16109,"style":2028},[2027],[1908,16111,16113,16116,16119,16122,16125],{"className":16112},[1942],[1908,16114],{"className":16115,"style":10636},[1946],[1908,16117,1988],{"className":16118},[1951],[1908,16120],{"className":16121,"style":2388},[2027],[1908,16123,2871],{"className":16124},[2392],[1908,16126],{"className":16127,"style":2388},[2027],[1908,16129,16131,16134,16196,16199,16202],{"className":16130},[1942],[1908,16132],{"className":16133,"style":10871},[1946],[1908,16135,16137,16140,16193],{"className":16136},[1951],[1908,16138],{"className":16139},[2046,10878],[1908,16141,16143],{"className":16142},[10756],[1908,16144,16146,16185],{"className":16145},[2171,2172],[1908,16147,16149,16182],{"className":16148},[2176],[1908,16150,16152,16163,16171],{"className":16151,"style":10891},[2180],[1908,16153,16154,16157],{"style":10894},[1908,16155],{"className":16156,"style":6273},[2188],[1908,16158,16160],{"className":16159},[1951],[1908,16161,10106],{"className":16162},[1951],[1908,16164,16165,16168],{"style":10906},[1908,16166],{"className":16167,"style":6273},[2188],[1908,16169],{"className":16170,"style":10914},[10913],[1908,16172,16173,16176],{"style":10917},[1908,16174],{"className":16175,"style":6273},[2188],[1908,16177,16179],{"className":16178},[1951],[1908,16180,1988],{"className":16181},[1951],[1908,16183,2204],{"className":16184},[2203],[1908,16186,16188],{"className":16187},[2176],[1908,16189,16191],{"className":16190,"style":10936},[2180],[1908,16192],{},[1908,16194],{"className":16195},[2086,10878],[1908,16197],{"className":16198,"style":2028},[2027],[1908,16200,1980],{"className":16201},[2032],[1908,16203],{"className":16204,"style":2028},[2027],[1908,16206,16208,16211],{"className":16207},[1942],[1908,16209],{"className":16210,"style":10871},[1946],[1908,16212,16214,16217,16270],{"className":16213},[1951],[1908,16215],{"className":16216},[2046,10878],[1908,16218,16220],{"className":16219},[10756],[1908,16221,16223,16262],{"className":16222},[2171,2172],[1908,16224,16226,16259],{"className":16225},[2176],[1908,16227,16229,16240,16248],{"className":16228,"style":10891},[2180],[1908,16230,16231,16234],{"style":10894},[1908,16232],{"className":16233,"style":6273},[2188],[1908,16235,16237],{"className":16236},[1951],[1908,16238,10106],{"className":16239},[1951],[1908,16241,16242,16245],{"style":10906},[1908,16243],{"className":16244,"style":6273},[2188],[1908,16246],{"className":16247,"style":10914},[10913],[1908,16249,16250,16253],{"style":10917},[1908,16251],{"className":16252,"style":6273},[2188],[1908,16254,16256],{"className":16255},[1951],[1908,16257,10776],{"className":16258},[1951],[1908,16260,2204],{"className":16261},[2203],[1908,16263,16265],{"className":16264},[2176],[1908,16266,16268],{"className":16267,"style":10936},[2180],[1908,16269],{},[1908,16271],{"className":16272},[2086,10878],[1908,16274,16276],{"className":16275},[3912],[1908,16277,16279,16361],{"className":16278},[1911],[1908,16280,16282],{"className":16281},[1915],[1917,16283,16284],{"xmlns":1919,"display":3921},[1921,16285,16286,16358],{},[1924,16287,16288,16294,16296,16298,16300,16306,16308,16314,16316,16318,16320,16326,16328,16334,16336,16342,16344,16350,16352],{},[2137,16289,16290,16292],{},[1927,16291,2235],{},[1986,16293,1994],{},[1978,16295,1980],{},[1986,16297,1988],{},[1978,16299,2248],{},[10756,16301,16302,16304],{},[1986,16303,1988],{},[1986,16305,1994],{},[1978,16307,2248],{},[10756,16309,16310,16312],{},[1986,16311,1994],{},[1986,16313,10106],{},[1978,16315,2871],{},[1986,16317,1994],{},[1978,16319,2248],{},[10756,16321,16322,16324],{},[1986,16323,1988],{},[1986,16325,1994],{},[1978,16327,2248],{},[10756,16329,16330,16332],{},[1986,16331,1988],{},[1986,16333,10106],{},[1978,16335,1980],{},[10756,16337,16338,16340],{},[1986,16339,1988],{},[1986,16341,10106],{},[1978,16343,2871],{},[10756,16345,16346,16348],{},[1986,16347,1988],{},[1986,16349,10106],{},[1978,16351,1980],{},[10756,16353,16354,16356],{},[1986,16355,1994],{},[1986,16357,10106],{},[1931,16359,16360],{"encoding":1933},"u_2 = 1 \\times \\frac{1}{2} \\times \\frac{2}{3} + 2 \\times \\frac{1}{2} \\times \\frac{1}{3} = \\frac{1}{3} + \\frac{1}{3} = \\frac{2}{3}",[1908,16362,16364,16419,16437,16514,16591,16609,16686,16763,16840,16917],{"className":16363,"ariaHidden":1938},[1937],[1908,16365,16367,16370,16410,16413,16416],{"className":16366},[1942],[1908,16368],{"className":16369,"style":2287},[1946],[1908,16371,16373,16376],{"className":16372},[1951],[1908,16374,2235],{"className":16375},[1951,1952],[1908,16377,16379],{"className":16378},[2167],[1908,16380,16382,16402],{"className":16381},[2171,2172],[1908,16383,16385,16399],{"className":16384},[2176],[1908,16386,16388],{"className":16387,"style":2362},[2180],[1908,16389,16390,16393],{"style":2308},[1908,16391],{"className":16392,"style":2189},[2188],[1908,16394,16396],{"className":16395},[2193,2194,2195,2196],[1908,16397,1994],{"className":16398},[1951,2196],[1908,16400,2204],{"className":16401},[2203],[1908,16403,16405],{"className":16404},[2176],[1908,16406,16408],{"className":16407,"style":2211},[2180],[1908,16409],{},[1908,16411],{"className":16412,"style":2028},[2027],[1908,16414,1980],{"className":16415},[2032],[1908,16417],{"className":16418,"style":2028},[2027],[1908,16420,16422,16425,16428,16431,16434],{"className":16421},[1942],[1908,16423],{"className":16424,"style":10636},[1946],[1908,16426,1988],{"className":16427},[1951],[1908,16429],{"className":16430,"style":2388},[2027],[1908,16432,2248],{"className":16433},[2392],[1908,16435],{"className":16436,"style":2388},[2027],[1908,16438,16440,16443,16505,16508,16511],{"className":16439},[1942],[1908,16441],{"className":16442,"style":10871},[1946],[1908,16444,16446,16449,16502],{"className":16445},[1951],[1908,16447],{"className":16448},[2046,10878],[1908,16450,16452],{"className":16451},[10756],[1908,16453,16455,16494],{"className":16454},[2171,2172],[1908,16456,16458,16491],{"className":16457},[2176],[1908,16459,16461,16472,16480],{"className":16460,"style":10891},[2180],[1908,16462,16463,16466],{"style":10894},[1908,16464],{"className":16465,"style":6273},[2188],[1908,16467,16469],{"className":16468},[1951],[1908,16470,1994],{"className":16471},[1951],[1908,16473,16474,16477],{"style":10906},[1908,16475],{"className":16476,"style":6273},[2188],[1908,16478],{"className":16479,"style":10914},[10913],[1908,16481,16482,16485],{"style":10917},[1908,16483],{"className":16484,"style":6273},[2188],[1908,16486,16488],{"className":16487},[1951],[1908,16489,1988],{"className":16490},[1951],[1908,16492,2204],{"className":16493},[2203],[1908,16495,16497],{"className":16496},[2176],[1908,16498,16500],{"className":16499,"style":10936},[2180],[1908,16501],{},[1908,16503],{"className":16504},[2086,10878],[1908,16506],{"className":16507,"style":2388},[2027],[1908,16509,2248],{"className":16510},[2392],[1908,16512],{"className":16513,"style":2388},[2027],[1908,16515,16517,16520,16582,16585,16588],{"className":16516},[1942],[1908,16518],{"className":16519,"style":10871},[1946],[1908,16521,16523,16526,16579],{"className":16522},[1951],[1908,16524],{"className":16525},[2046,10878],[1908,16527,16529],{"className":16528},[10756],[1908,16530,16532,16571],{"className":16531},[2171,2172],[1908,16533,16535,16568],{"className":16534},[2176],[1908,16536,16538,16549,16557],{"className":16537,"style":10891},[2180],[1908,16539,16540,16543],{"style":10894},[1908,16541],{"className":16542,"style":6273},[2188],[1908,16544,16546],{"className":16545},[1951],[1908,16547,10106],{"className":16548},[1951],[1908,16550,16551,16554],{"style":10906},[1908,16552],{"className":16553,"style":6273},[2188],[1908,16555],{"className":16556,"style":10914},[10913],[1908,16558,16559,16562],{"style":10917},[1908,16560],{"className":16561,"style":6273},[2188],[1908,16563,16565],{"className":16564},[1951],[1908,16566,1994],{"className":16567},[1951],[1908,16569,2204],{"className":16570},[2203],[1908,16572,16574],{"className":16573},[2176],[1908,16575,16577],{"className":16576,"style":10936},[2180],[1908,16578],{},[1908,16580],{"className":16581},[2086,10878],[1908,16583],{"className":16584,"style":2388},[2027],[1908,16586,2871],{"className":16587},[2392],[1908,16589],{"className":16590,"style":2388},[2027],[1908,16592,16594,16597,16600,16603,16606],{"className":16593},[1942],[1908,16595],{"className":16596,"style":10636},[1946],[1908,16598,1994],{"className":16599},[1951],[1908,16601],{"className":16602,"style":2388},[2027],[1908,16604,2248],{"className":16605},[2392],[1908,16607],{"className":16608,"style":2388},[2027],[1908,16610,16612,16615,16677,16680,16683],{"className":16611},[1942],[1908,16613],{"className":16614,"style":10871},[1946],[1908,16616,16618,16621,16674],{"className":16617},[1951],[1908,16619],{"className":16620},[2046,10878],[1908,16622,16624],{"className":16623},[10756],[1908,16625,16627,16666],{"className":16626},[2171,2172],[1908,16628,16630,16663],{"className":16629},[2176],[1908,16631,16633,16644,16652],{"className":16632,"style":10891},[2180],[1908,16634,16635,16638],{"style":10894},[1908,16636],{"className":16637,"style":6273},[2188],[1908,16639,16641],{"className":16640},[1951],[1908,16642,1994],{"className":16643},[1951],[1908,16645,16646,16649],{"style":10906},[1908,16647],{"className":16648,"style":6273},[2188],[1908,16650],{"className":16651,"style":10914},[10913],[1908,16653,16654,16657],{"style":10917},[1908,16655],{"className":16656,"style":6273},[2188],[1908,16658,16660],{"className":16659},[1951],[1908,16661,1988],{"className":16662},[1951],[1908,16664,2204],{"className":16665},[2203],[1908,16667,16669],{"className":16668},[2176],[1908,16670,16672],{"className":16671,"style":10936},[2180],[1908,16673],{},[1908,16675],{"className":16676},[2086,10878],[1908,16678],{"className":16679,"style":2388},[2027],[1908,16681,2248],{"className":16682},[2392],[1908,16684],{"className":16685,"style":2388},[2027],[1908,16687,16689,16692,16754,16757,16760],{"className":16688},[1942],[1908,16690],{"className":16691,"style":10871},[1946],[1908,16693,16695,16698,16751],{"className":16694},[1951],[1908,16696],{"className":16697},[2046,10878],[1908,16699,16701],{"className":16700},[10756],[1908,16702,16704,16743],{"className":16703},[2171,2172],[1908,16705,16707,16740],{"className":16706},[2176],[1908,16708,16710,16721,16729],{"className":16709,"style":10891},[2180],[1908,16711,16712,16715],{"style":10894},[1908,16713],{"className":16714,"style":6273},[2188],[1908,16716,16718],{"className":16717},[1951],[1908,16719,10106],{"className":16720},[1951],[1908,16722,16723,16726],{"style":10906},[1908,16724],{"className":16725,"style":6273},[2188],[1908,16727],{"className":16728,"style":10914},[10913],[1908,16730,16731,16734],{"style":10917},[1908,16732],{"className":16733,"style":6273},[2188],[1908,16735,16737],{"className":16736},[1951],[1908,16738,1988],{"className":16739},[1951],[1908,16741,2204],{"className":16742},[2203],[1908,16744,16746],{"className":16745},[2176],[1908,16747,16749],{"className":16748,"style":10936},[2180],[1908,16750],{},[1908,16752],{"className":16753},[2086,10878],[1908,16755],{"className":16756,"style":2028},[2027],[1908,16758,1980],{"className":16759},[2032],[1908,16761],{"className":16762,"style":2028},[2027],[1908,16764,16766,16769,16831,16834,16837],{"className":16765},[1942],[1908,16767],{"className":16768,"style":10871},[1946],[1908,16770,16772,16775,16828],{"className":16771},[1951],[1908,16773],{"className":16774},[2046,10878],[1908,16776,16778],{"className":16777},[10756],[1908,16779,16781,16820],{"className":16780},[2171,2172],[1908,16782,16784,16817],{"className":16783},[2176],[1908,16785,16787,16798,16806],{"className":16786,"style":10891},[2180],[1908,16788,16789,16792],{"style":10894},[1908,16790],{"className":16791,"style":6273},[2188],[1908,16793,16795],{"className":16794},[1951],[1908,16796,10106],{"className":16797},[1951],[1908,16799,16800,16803],{"style":10906},[1908,16801],{"className":16802,"style":6273},[2188],[1908,16804],{"className":16805,"style":10914},[10913],[1908,16807,16808,16811],{"style":10917},[1908,16809],{"className":16810,"style":6273},[2188],[1908,16812,16814],{"className":16813},[1951],[1908,16815,1988],{"className":16816},[1951],[1908,16818,2204],{"className":16819},[2203],[1908,16821,16823],{"className":16822},[2176],[1908,16824,16826],{"className":16825,"style":10936},[2180],[1908,16827],{},[1908,16829],{"className":16830},[2086,10878],[1908,16832],{"className":16833,"style":2388},[2027],[1908,16835,2871],{"className":16836},[2392],[1908,16838],{"className":16839,"style":2388},[2027],[1908,16841,16843,16846,16908,16911,16914],{"className":16842},[1942],[1908,16844],{"className":16845,"style":10871},[1946],[1908,16847,16849,16852,16905],{"className":16848},[1951],[1908,16850],{"className":16851},[2046,10878],[1908,16853,16855],{"className":16854},[10756],[1908,16856,16858,16897],{"className":16857},[2171,2172],[1908,16859,16861,16894],{"className":16860},[2176],[1908,16862,16864,16875,16883],{"className":16863,"style":10891},[2180],[1908,16865,16866,16869],{"style":10894},[1908,16867],{"className":16868,"style":6273},[2188],[1908,16870,16872],{"className":16871},[1951],[1908,16873,10106],{"className":16874},[1951],[1908,16876,16877,16880],{"style":10906},[1908,16878],{"className":16879,"style":6273},[2188],[1908,16881],{"className":16882,"style":10914},[10913],[1908,16884,16885,16888],{"style":10917},[1908,16886],{"className":16887,"style":6273},[2188],[1908,16889,16891],{"className":16890},[1951],[1908,16892,1988],{"className":16893},[1951],[1908,16895,2204],{"className":16896},[2203],[1908,16898,16900],{"className":16899},[2176],[1908,16901,16903],{"className":16902,"style":10936},[2180],[1908,16904],{},[1908,16906],{"className":16907},[2086,10878],[1908,16909],{"className":16910,"style":2028},[2027],[1908,16912,1980],{"className":16913},[2032],[1908,16915],{"className":16916,"style":2028},[2027],[1908,16918,16920,16923],{"className":16919},[1942],[1908,16921],{"className":16922,"style":10871},[1946],[1908,16924,16926,16929,16982],{"className":16925},[1951],[1908,16927],{"className":16928},[2046,10878],[1908,16930,16932],{"className":16931},[10756],[1908,16933,16935,16974],{"className":16934},[2171,2172],[1908,16936,16938,16971],{"className":16937},[2176],[1908,16939,16941,16952,16960],{"className":16940,"style":10891},[2180],[1908,16942,16943,16946],{"style":10894},[1908,16944],{"className":16945,"style":6273},[2188],[1908,16947,16949],{"className":16948},[1951],[1908,16950,10106],{"className":16951},[1951],[1908,16953,16954,16957],{"style":10906},[1908,16955],{"className":16956,"style":6273},[2188],[1908,16958],{"className":16959,"style":10914},[10913],[1908,16961,16962,16965],{"style":10917},[1908,16963],{"className":16964,"style":6273},[2188],[1908,16966,16968],{"className":16967},[1951],[1908,16969,1994],{"className":16970},[1951],[1908,16972,2204],{"className":16973},[2203],[1908,16975,16977],{"className":16976},[2176],[1908,16978,16980],{"className":16979,"style":10936},[2180],[1908,16981],{},[1908,16983],{"className":16984},[2086,10878],[1897,16986,16988],{"id":16987},"例题2-逆向归纳求解动态博弈","例题2: 逆向归纳求解动态博弈",[1798,16990,16991,16993],{},[1857,16992,13993],{},": 公司1（先行者）和公司2（跟随者）依次决定进入市场与否。进入成本为2，市场利润取决于进入者数量：",[1805,16995,16996,16999],{},[1808,16997,16998],{},"1家公司进入：获利6",[1808,17000,17001],{},"2家公司进入：各获利3",[1798,17003,17004],{},"求SPNE。",[1798,17006,17007,1860],{},[1857,17008,14039],{},[1798,17010,17011],{},"画出博弈树：",[11662,17013,17016],{"className":17014,"code":17015,"language":9638},[11665],"         公司1\n        \u002F      \\\n      进入      不进入\n      \u002F          \\\n   公司2         (0, 0)\n   \u002F    \\\n 进入   不进入\n  \u002F      \\\n(1,1)   (4,0)\n",[11668,17017,17015],{"__ignoreMap":10},[1798,17019,17020],{},"支付计算：",[1805,17022,17023,17029,17032,17035],{},[1808,17024,17025,17026],{},"都进入：(6-2, 6-2) = (4, 4)  ",[1908,17027,17028],{},"等等，题目说各获利3",[1808,17030,17031],{},"正确的：都进入(3-2, 3-2) = (1, 1)",[1808,17033,17034],{},"只1进入：(6-2, 0) = (4, 0)",[1808,17036,17037],{},"都不进入：(0, 0)",[1798,17039,17040,1860],{},[1857,17041,11674],{},[1805,17043,17044,17050],{},[1808,17045,17046,17047],{},"公司2的决策节点：比较进入(1)和不进入(0)，选择",[1857,17048,17049],{},"进入",[1808,17051,17052,17053],{},"回到公司1：预期公司2进入，比较进入得1和不进入得0，选择",[1857,17054,17049],{},[1798,17056,17057,17060],{},[1857,17058,17059],{},"SPNE",": (进入, 进入)",[1798,17062,17063,17066],{},[1857,17064,17065],{},"先行者优势？"," 在这个例子中不存在——先动者并未获得优势。",[1890,17068],{},[1794,17070,17072],{"id":17071},"_7-应用案例","7. 应用案例",[1897,17074,17076],{"id":17075},"_71-价格竞争中的伯特兰悖论","7.1 价格竞争中的伯特兰悖论",[1798,17078,17079],{},"两家公司同时定价，消费者总是选择低价者。如果价格相同，平分市场。",[1798,17081,17082],{},"这是一个博弈！纳什均衡是什么？",[1798,17084,17085,17088,17089,17148],{},[1857,17086,17087],{},"答案",": 两家公司都定价等于边际成本",[1908,17090,17092,17114],{"className":17091},[1911],[1908,17093,17095],{"className":17094},[1915],[1917,17096,17097],{"xmlns":1919},[1921,17098,17099,17111],{},[1924,17100,17101,17103,17105,17108],{},[1927,17102,1798],{},[1978,17104,1980],{},[1927,17106,17107],{},"M",[1927,17109,17110],{},"C",[1931,17112,17113],{"encoding":1933},"p = MC",[1908,17115,17117,17135],{"className":17116,"ariaHidden":1938},[1937],[1908,17118,17120,17123,17126,17129,17132],{"className":17119},[1942],[1908,17121],{"className":17122,"style":9508},[1946],[1908,17124,1798],{"className":17125},[1951,1952],[1908,17127],{"className":17128,"style":2028},[2027],[1908,17130,1980],{"className":17131},[2032],[1908,17133],{"className":17134,"style":2028},[2027],[1908,17136,17138,17141,17144],{"className":17137},[1942],[1908,17139],{"className":17140,"style":2019},[1946],[1908,17142,17107],{"className":17143,"style":2023},[1951,1952],[1908,17145,17110],{"className":17146,"style":17147},[1951,1952],"margin-right:0.0715em;","（零利润）。",[1798,17150,17151,17154,17155,17212,17213,17268],{},[1857,17152,17153],{},"推理",": 如果",[1908,17156,17158,17178],{"className":17157},[1911],[1908,17159,17161],{"className":17160},[1915],[1917,17162,17163],{"xmlns":1919},[1921,17164,17165,17175],{},[1924,17166,17167,17169,17171,17173],{},[1927,17168,1798],{},[1978,17170,3958],{},[1927,17172,17107],{},[1927,17174,17110],{},[1931,17176,17177],{"encoding":1933},"p > MC",[1908,17179,17181,17200],{"className":17180,"ariaHidden":1938},[1937],[1908,17182,17184,17188,17191,17194,17197],{"className":17183},[1942],[1908,17185],{"className":17186,"style":17187},[1946],"height:0.7335em;vertical-align:-0.1944em;",[1908,17189,1798],{"className":17190},[1951,1952],[1908,17192],{"className":17193,"style":2028},[2027],[1908,17195,3958],{"className":17196},[2032],[1908,17198],{"className":17199,"style":2028},[2027],[1908,17201,17203,17206,17209],{"className":17202},[1942],[1908,17204],{"className":17205,"style":2019},[1946],[1908,17207,17107],{"className":17208,"style":2023},[1951,1952],[1908,17210,17110],{"className":17211,"style":17147},[1951,1952],"，对手有动机微降价抢走全部市场。只有",[1908,17214,17216,17235],{"className":17215},[1911],[1908,17217,17219],{"className":17218},[1915],[1917,17220,17221],{"xmlns":1919},[1921,17222,17223,17233],{},[1924,17224,17225,17227,17229,17231],{},[1927,17226,1798],{},[1978,17228,1980],{},[1927,17230,17107],{},[1927,17232,17110],{},[1931,17234,17113],{"encoding":1933},[1908,17236,17238,17256],{"className":17237,"ariaHidden":1938},[1937],[1908,17239,17241,17244,17247,17250,17253],{"className":17240},[1942],[1908,17242],{"className":17243,"style":9508},[1946],[1908,17245,1798],{"className":17246},[1951,1952],[1908,17248],{"className":17249,"style":2028},[2027],[1908,17251,1980],{"className":17252},[2032],[1908,17254],{"className":17255,"style":2028},[2027],[1908,17257,17259,17262,17265],{"className":17258},[1942],[1908,17260],{"className":17261,"style":2019},[1946],[1908,17263,17107],{"className":17264,"style":2023},[1951,1952],[1908,17266,17110],{"className":17267,"style":17147},[1951,1952],"时，降价会亏损，没有偏离动机。",[1798,17270,17271,17272,17275],{},"这是",[1857,17273,17274],{},"伯特兰悖论","：仅两家公司的市场，却达到完全竞争结果！",[1897,17277,17279],{"id":17278},"_72-公共物品自愿供给","7.2 公共物品自愿供给",[1798,17281,17282,17310,17311,17340,17341,17393],{},[1908,17283,17285,17298],{"className":17284},[1911],[1908,17286,17288],{"className":17287},[1915],[1917,17289,17290],{"xmlns":1919},[1921,17291,17292,17296],{},[1924,17293,17294],{},[1927,17295,1929],{},[1931,17297,1929],{"encoding":1933},[1908,17299,17301],{"className":17300,"ariaHidden":1938},[1937],[1908,17302,17304,17307],{"className":17303},[1942],[1908,17305],{"className":17306,"style":1947},[1946],[1908,17308,1929],{"className":17309},[1951,1952],"个人决定是否贡献成本",[1908,17312,17314,17328],{"className":17313},[1911],[1908,17315,17317],{"className":17316},[1915],[1917,17318,17319],{"xmlns":1919},[1921,17320,17321,17326],{},[1924,17322,17323],{},[1927,17324,17325],{},"c",[1931,17327,17325],{"encoding":1933},[1908,17329,17331],{"className":17330,"ariaHidden":1938},[1937],[1908,17332,17334,17337],{"className":17333},[1942],[1908,17335],{"className":17336,"style":1947},[1946],[1908,17338,17325],{"className":17339},[1951,1952],"来提供公共物品（价值",[1908,17342,17344,17363],{"className":17343},[1911],[1908,17345,17347],{"className":17346},[1915],[1917,17348,17349],{"xmlns":1919},[1921,17350,17351,17360],{},[1924,17352,17353,17356,17358],{},[1927,17354,17355],{},"v",[1978,17357,3958],{},[1927,17359,17325],{},[1931,17361,17362],{"encoding":1933},"v > c",[1908,17364,17366,17384],{"className":17365,"ariaHidden":1938},[1937],[1908,17367,17369,17372,17375,17378,17381],{"className":17368},[1942],[1908,17370],{"className":17371,"style":4354},[1946],[1908,17373,17355],{"className":17374,"style":7564},[1951,1952],[1908,17376],{"className":17377,"style":2028},[2027],[1908,17379,3958],{"className":17380},[2032],[1908,17382],{"className":17383,"style":2028},[2027],[1908,17385,17387,17390],{"className":17386},[1942],[1908,17388],{"className":17389,"style":1947},[1946],[1908,17391,17325],{"className":17392},[1951,1952],"给每个人）。公共物品只需一人贡献即可提供。",[1798,17395,17396],{},"这是一个对称博弈。分析对称纳什均衡：",[1798,17398,17399,17400,17428],{},"设其他人贡献的概率为",[1908,17401,17403,17416],{"className":17402},[1911],[1908,17404,17406],{"className":17405},[1915],[1917,17407,17408],{"xmlns":1919},[1921,17409,17410,17414],{},[1924,17411,17412],{},[1927,17413,1798],{},[1931,17415,1798],{"encoding":1933},[1908,17417,17419],{"className":17418,"ariaHidden":1938},[1937],[1908,17420,17422,17425],{"className":17421},[1942],[1908,17423],{"className":17424,"style":9508},[1946],[1908,17426,1798],{"className":17427},[1951,1952],"，某人选择贡献与否无差异需要：",[1908,17430,17432],{"className":17431},[3912],[1908,17433,17435,17485],{"className":17434},[1911],[1908,17436,17438],{"className":17437},[1915],[1917,17439,17440],{"xmlns":1919,"display":3921},[1921,17441,17442,17482],{},[1924,17443,17444,17446,17448,17450,17452,17454,17456,17458,17460,17462,17464,17466,17468,17480],{},[1927,17445,17355],{},[1978,17447,2828],{},[1927,17449,17325],{},[1978,17451,1980],{},[1927,17453,17355],{},[1978,17455,2566],{"stretchy":1983},[1986,17457,1988],{},[1978,17459,2828],{},[1978,17461,2566],{"stretchy":1983},[1986,17463,1988],{},[1978,17465,2828],{},[1927,17467,1798],{},[5080,17469,17470,17472],{},[1978,17471,2595],{"stretchy":1983},[1924,17473,17474,17476,17478],{},[1927,17475,1929],{},[1978,17477,2828],{},[1986,17479,1988],{},[1978,17481,2595],{"stretchy":1983},[1931,17483,17484],{"encoding":1933},"v - c = v(1 - (1-p)^{n-1})",[1908,17486,17488,17506,17524,17548,17569],{"className":17487,"ariaHidden":1938},[1937],[1908,17489,17491,17494,17497,17500,17503],{"className":17490},[1942],[1908,17492],{"className":17493,"style":2457},[1946],[1908,17495,17355],{"className":17496,"style":7564},[1951,1952],[1908,17498],{"className":17499,"style":2388},[2027],[1908,17501,2828],{"className":17502},[2392],[1908,17504],{"className":17505,"style":2388},[2027],[1908,17507,17509,17512,17515,17518,17521],{"className":17508},[1942],[1908,17510],{"className":17511,"style":1947},[1946],[1908,17513,17325],{"className":17514},[1951,1952],[1908,17516],{"className":17517,"style":2028},[2027],[1908,17519,1980],{"className":17520},[2032],[1908,17522],{"className":17523,"style":2028},[2027],[1908,17525,17527,17530,17533,17536,17539,17542,17545],{"className":17526},[1942],[1908,17528],{"className":17529,"style":2042},[1946],[1908,17531,17355],{"className":17532,"style":7564},[1951,1952],[1908,17534,2566],{"className":17535},[2046],[1908,17537,1988],{"className":17538},[1951],[1908,17540],{"className":17541,"style":2388},[2027],[1908,17543,2828],{"className":17544},[2392],[1908,17546],{"className":17547,"style":2388},[2027],[1908,17549,17551,17554,17557,17560,17563,17566],{"className":17550},[1942],[1908,17552],{"className":17553,"style":2042},[1946],[1908,17555,2566],{"className":17556},[2046],[1908,17558,1988],{"className":17559},[1951],[1908,17561],{"className":17562,"style":2388},[2027],[1908,17564,2828],{"className":17565},[2392],[1908,17567],{"className":17568,"style":2388},[2027],[1908,17570,17572,17576,17579,17618],{"className":17571},[1942],[1908,17573],{"className":17574,"style":17575},[1946],"height:1.1141em;vertical-align:-0.25em;",[1908,17577,1798],{"className":17578},[1951,1952],[1908,17580,17582,17585],{"className":17581},[2086],[1908,17583,2595],{"className":17584},[2086],[1908,17586,17588],{"className":17587},[2167],[1908,17589,17591],{"className":17590},[2171],[1908,17592,17594],{"className":17593},[2176],[1908,17595,17598],{"className":17596,"style":17597},[2180],"height:0.8641em;",[1908,17599,17600,17603],{"style":4077},[1908,17601],{"className":17602,"style":2189},[2188],[1908,17604,17606],{"className":17605},[2193,2194,2195,2196],[1908,17607,17609,17612,17615],{"className":17608},[1951,2196],[1908,17610,1929],{"className":17611},[1951,1952,2196],[1908,17613,2828],{"className":17614},[2392,2196],[1908,17616,1988],{"className":17617},[1951,2196],[1908,17619,2595],{"className":17620},[2086],[1798,17622,17623,17624,17652,17653,17681,17682,17733],{},"解得",[1908,17625,17627,17640],{"className":17626},[1911],[1908,17628,17630],{"className":17629},[1915],[1917,17631,17632],{"xmlns":1919},[1921,17633,17634,17638],{},[1924,17635,17636],{},[1927,17637,1798],{},[1931,17639,1798],{"encoding":1933},[1908,17641,17643],{"className":17642,"ariaHidden":1938},[1937],[1908,17644,17646,17649],{"className":17645},[1942],[1908,17647],{"className":17648,"style":9508},[1946],[1908,17650,1798],{"className":17651},[1951,1952],"。当",[1908,17654,17656,17669],{"className":17655},[1911],[1908,17657,17659],{"className":17658},[1915],[1917,17660,17661],{"xmlns":1919},[1921,17662,17663,17667],{},[1924,17664,17665],{},[1927,17666,1929],{},[1931,17668,1929],{"encoding":1933},[1908,17670,17672],{"className":17671,"ariaHidden":1938},[1937],[1908,17673,17675,17678],{"className":17674},[1942],[1908,17676],{"className":17677,"style":1947},[1946],[1908,17679,1929],{"className":17680},[1951,1952],"很大时，",[1908,17683,17685,17703],{"className":17684},[1911],[1908,17686,17688],{"className":17687},[1915],[1917,17689,17690],{"xmlns":1919},[1921,17691,17692,17700],{},[1924,17693,17694,17696,17698],{},[1927,17695,1798],{},[1978,17697,2270],{},[1986,17699,9761],{},[1931,17701,17702],{"encoding":1933},"p \\to 0",[1908,17704,17706,17724],{"className":17705,"ariaHidden":1938},[1937],[1908,17707,17709,17712,17715,17718,17721],{"className":17708},[1942],[1908,17710],{"className":17711,"style":9508},[1946],[1908,17713,1798],{"className":17714},[1951,1952],[1908,17716],{"className":17717,"style":2028},[2027],[1908,17719,2270],{"className":17720},[2032],[1908,17722],{"className":17723,"style":2028},[2027],[1908,17725,17727,17730],{"className":17726},[1942],[1908,17728],{"className":17729,"style":9810},[1946],[1908,17731,9761],{"className":17732},[1951],"——搭便车问题！",[1897,17735,17737],{"id":17736},"_73-拍卖中的策略","7.3 拍卖中的策略",[1798,17739,17740],{},"在二价密封拍卖中，诚实出价是占优策略（无论其他人出多少，说真话总是最优的）。",[1798,17742,17743],{},"这是博弈论在机制设计中的应用——下一章的主题。",[1890,17745],{},[1794,17747,17749],{"id":17748},"_8-文献与拓展","8. 文献与拓展",[1798,17751,17752,1860],{},[1857,17753,17754],{},"经典著作",[1805,17756,17757,17764,17767,17770],{},[1808,17758,17759,17760],{},"von Neumann & Morgenstern (1944). ",[17761,17762,17763],"em",{},"Theory of Games and Economic Behavior",[1808,17765,17766],{},"Nash, J. (1950). \"Equilibrium Points in N-Person Games\"",[1808,17768,17769],{},"Nash, J. (1951). \"Non-Cooperative Games\"",[1808,17771,17772],{},"Selten, R. (1975). \"Reexamination of the Perfectness Concept for Equilibrium Points\"",[1798,17774,17775,1860],{},[1857,17776,17777],{},"现代教材",[1805,17779,17780,17786,17792,17795],{},[1808,17781,17782,17783],{},"Gibbons, R. (1992). ",[17761,17784,17785],{},"Game Theory for Applied Economists",[1808,17787,17788,17789],{},"Osborne, M. & Rubinstein, A. (1994). ",[17761,17790,17791],{},"A Course in Game Theory",[1808,17793,17794],{},"Mas-Colell et al. (1995), Chapter 7-9",[1808,17796,17797,17798],{},"Fudenberg & Tirole (1991). ",[17761,17799,17800],{},"Game Theory",[1890,17802],{},[1794,17804,17806],{"id":17805},"_9-本章小结","9. 本章小结",[3421,17808,17809,17821],{},[3424,17810,17811],{},[3427,17812,17813,17816,17819],{},[3430,17814,17815],{},"核心概念",[3430,17817,17818],{},"关键结果",[3430,17820,12364],{},[3439,17822,17823,17835,17847,17859,17871],{},[3427,17824,17825,17830,17833],{},[3444,17826,17827],{},[1857,17828,17829],{},"占优策略",[3444,17831,17832],{},"无论对手如何，总是最优",[3444,17834,12978],{},[3427,17836,17837,17841,17844],{},[3444,17838,17839],{},[1857,17840,6865],{},[3444,17842,17843],{},"无人愿单方面偏离",[3444,17845,17846],{},"预测博弈结果",[3427,17848,17849,17853,17856],{},[3444,17850,17851],{},[1857,17852,7506],{},[3444,17854,17855],{},"概率化选择",[3444,17857,17858],{},"无纯策略均衡时",[3427,17860,17861,17865,17868],{},[3444,17862,17863],{},[1857,17864,17059],{},[3444,17866,17867],{},"排除不可信威胁",[3444,17869,17870],{},"动态博弈分析",[3427,17872,17873,17878,17881],{},[3444,17874,17875],{},[1857,17876,17877],{},"民间定理",[3444,17879,17880],{},"重复博弈支撑合作",[3444,17882,17883],{},"隐性合谋",[1798,17885,17886,17888,17889,17892,17893,17895,17896,17898,17899,17901],{},[1857,17887,11693],{},":\n✅ 策略互动中，理性选择取决于对对方行为的预期",[17890,17891],"br",{},"\n✅ 纳什均衡提供了预测博弈结果的稳定概念",[17890,17894],{},"\n✅ 个体理性可能导致集体非理性（囚徒困境）",[17890,17897],{},"\n✅ 重复互动和声誉可以支撑合作行为",[17890,17900],{},"\n✅ 行动顺序和承诺能力影响博弈结果",[1794,17903,17904],{"id":17904},"自学检查",[1798,17906,17907,17910],{},[1857,17908,17909],{},"核心直觉回看","：博弈论研究“我的最优选择取决于你怎么选”的情境。纳什均衡不是说所有人都满意，而是说在给定别人策略时，没有人愿意单方面改变自己的策略。",[1798,17912,17913,17916],{},[1857,17914,17915],{},"关键模型提醒","：静态博弈先找最优反应，再找交点；混合策略均衡让对手在其纯策略之间无差异；动态博弈用逆向归纳排除不可信威胁。",[1897,17918,17919],{"id":17919},"常见误区",[1805,17921,17922,17925,17928,17931],{},[1808,17923,17924],{},"混淆占优策略均衡和纳什均衡。有占优策略一定是纳什均衡，但纳什均衡不一定来自占优策略。",[1808,17926,17927],{},"认为纳什均衡就是社会最优。囚徒困境正说明个体理性可能导致集体低效。",[1808,17929,17930],{},"求混合策略时让自己无差异，而不是让对手无差异。",[1808,17932,17933],{},"在动态博弈中接受空洞威胁，没有检查子博弈精炼性。",[1897,17935,17936],{"id":17936},"自测题",[1875,17938,17939,17942,17945,17948,17951],{},[1808,17940,17941],{},"用支付矩阵解释囚徒困境中为什么背叛是占优策略。",[1808,17943,17944],{},"一个博弈可能有多个纳什均衡吗？这会给预测带来什么问题？",[1808,17946,17947],{},"求混合策略均衡时，为什么要令对手的期望支付相等？",[1808,17949,17950],{},"逆向归纳法如何排除“不可信威胁”？",[1808,17952,17953],{},"无限重复博弈中，折现因子为什么影响合作能否维持？",[1897,17955,17956],{"id":17956},"下一步学习提示",[1798,17958,17959],{},"下一章的寡头模型就是博弈论的直接应用。复习时请特别熟悉“最优反应函数”的写法，因为古诺、伯特兰和斯塔克尔伯格都要从这里出发。",[1798,17961,17962,17965,17966,17969],{},[1857,17963,17964],{},"下一章预告",": 博弈论为我们提供了分析策略互动的工具。下一章我们将应用这些工具分析",[1857,17967,17968],{},"寡头市场","——少数几家公司竞争的市场结构。我们将看到古诺、伯特兰和斯塔克尔伯格如何用博弈论建模不同的竞争方式，以及这些模型对福利和政策的含义。",{"title":10,"searchDepth":17971,"depth":17971,"links":17972},2,[17973,17974,17975,17981,17988,17995,18001,18008,18012,18017,18018,18019],{"id":1796,"depth":17971,"text":1796},{"id":1849,"depth":17971,"text":1850},{"id":1894,"depth":17971,"text":1895,"children":17976},[17977,17979,17980],{"id":1899,"depth":17978,"text":1900},3,{"id":3413,"depth":17978,"text":3414},{"id":3489,"depth":17978,"text":3490},{"id":3515,"depth":17971,"text":3516,"children":17982},[17983,17984,17985,17986,17987],{"id":3519,"depth":17978,"text":3520},{"id":5060,"depth":17978,"text":5061},{"id":5969,"depth":17978,"text":5970},{"id":6875,"depth":17978,"text":6876},{"id":6989,"depth":17978,"text":6990},{"id":7490,"depth":17971,"text":7491,"children":17989},[17990,17991,17992,17993,17994],{"id":7494,"depth":17978,"text":7495},{"id":8055,"depth":17978,"text":8056},{"id":8702,"depth":17978,"text":8703},{"id":9427,"depth":17978,"text":9428},{"id":11457,"depth":17978,"text":11458},{"id":11571,"depth":17971,"text":11572,"children":17996},[17997,17998,17999,18000],{"id":11575,"depth":17978,"text":11576},{"id":11626,"depth":17978,"text":11627},{"id":11697,"depth":17978,"text":11698},{"id":11736,"depth":17978,"text":11737},{"id":11804,"depth":17971,"text":11805,"children":18002},[18003,18004,18005,18006,18007],{"id":11808,"depth":17978,"text":11809},{"id":12368,"depth":17978,"text":12369},{"id":12829,"depth":17978,"text":12830},{"id":12865,"depth":17978,"text":12866},{"id":12972,"depth":17978,"text":12973},{"id":13983,"depth":17971,"text":13984,"children":18009},[18010,18011],{"id":13987,"depth":17978,"text":13988},{"id":16987,"depth":17978,"text":16988},{"id":17071,"depth":17971,"text":17072,"children":18013},[18014,18015,18016],{"id":17075,"depth":17978,"text":17076},{"id":17278,"depth":17978,"text":17279},{"id":17736,"depth":17978,"text":17737},{"id":17748,"depth":17971,"text":17749},{"id":17805,"depth":17971,"text":17806},{"id":17904,"depth":17971,"text":17904,"children":18020},[18021,18022,18023],{"id":17919,"depth":17978,"text":17919},{"id":17936,"depth":17978,"text":17936},{"id":17956,"depth":17978,"text":17956},"纳什均衡、混合策略、子博弈精炼均衡、重复博弈","md",null,{},true,{"title":1578,"description":18024},"GHsuRDYJKfKsRWOSDaGXi6o8gaDhTSBn7F2sR6ff3f0",[18032,18034],{"title":1572,"path":1573,"stem":1574,"description":18033,"children":-1},"埃奇沃斯盒子分析、帕累托效率、福利经济学基本定理",{"title":1584,"path":1585,"stem":1586,"description":18035,"children":-1},"古诺、伯特兰、斯塔克尔伯格模型、卡特尔稳定性、进入阻止",1785754754318]