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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":788},{"id":1784,"title":1614,"body":1785,"description":16332,"extension":16333,"features":16334,"hero":16334,"layout":16334,"locale":16334,"meta":16335,"navigation":16334,"path":1615,"published":16336,"seo":16337,"stem":1616,"__hash__":16338},"docs\u002Fzh\u002Fmicroeconomics\u002F11-market-design\u002Findex.md",{"type":1786,"value":1787,"toc":16273},"minimark",[1788,1793,1797,1801,1804,1820,1823,1842,1846,1854,1880,1887,1914,1924,1928,1944,1948,1952,1958,2548,2590,2623,3218,3222,3363,3817,3820,3826,3831,3842,3846,4102,4105,4506,4509,4907,5233,5934,6258,7383,7389,7393,7397,7402,7412,7417,7437,7441,7446,7449,8235,8237,9022,9027,9925,10251,10256,10747,11069,11074,11290,11691,11695,11701,11706,11783,11789,11847,12054,12086,12354,12416,12846,12909,13315,13318,13328,13333,13344,13350,13354,13436,13547,13626,13630,13634,13639,13812,13844,14118,14175,14627,14631,14636,14717,14722,14730,14734,14739,14744,14758,14763,14774,14778,14782,14788,14796,14801,14821,14825,14831,14836,14855,14860,14865,14876,14881,14892,14896,14902,14907,14927,14932,14940,14944,14948,14953,14961,14969,14977,14982,14993,14997,15003,15008,15014,15018,15029,15033,15038,15049,15054,15062,15067,15075,15079,15083,15089,15093,15101,15106,15120,15124,15129,15133,15141,15145,15227,15231,15236,15240,15248,15252,15260,15264,15270,15278,15283,15291,15297,15301,15305,15308,15311,15466,15469,15472,15538,15541,15544,15547,15550,15564,15567,15571,15577,15582,15590,15594,15599,15603,15611,15615,15623,15627,15632,15640,15646,15650,15655,15666,15671,15682,15687,15690,15693,15754,15758,15761,15815,15818,15924,15927,15931,15936,15947,15952,15963,15969,15973,15978,16000,16005,16024,16029,16043,16048,16062,16067,16072,16075,16163,16166,16184,16199,16202,16205,16211,16217,16220,16234,16237,16254,16257,16260,16263],[1789,1790,1792],"h1",{"id":1791},"第-11-讲市场设计与匹配理论","第 11 讲：市场设计与匹配理论",[1794,1795,1796],"h2",{"id":1796},"本章导学",[1798,1799,1800],"p",{},"有些重要资源不能靠“谁出价高就给谁”来分配：学校名额、住院医职位、器官移植和部分平台匹配都受到法律、伦理或制度约束。本章讨论当价格机制退居次要位置时，如何用稳定性、策略性和可操作性来评价分配规则。",[1798,1802,1803],{},"学完本章后，你应当能够：",[1805,1806,1807,1811,1814,1817],"ul",{},[1808,1809,1810],"li",{},"定义匹配、阻塞对、稳定匹配和策略不可操纵性。",[1808,1812,1813],{},"执行 Gale-Shapley 延迟接受算法，并解释学生最优或医院最优的含义。",[1808,1815,1816],{},"分析学校选择、医生匹配和肾脏交换中的机制设计取舍。",[1808,1818,1819],{},"理解市场厚度、拥堵控制和安全性为什么是市场设计的实践原则。",[1798,1821,1822],{},"常见考查会给出偏好表，要求你运行算法、判断匹配是否稳定，或比较不同提议方下的结果。答题时要一步步记录暂时接受和拒绝过程，否则很容易在算法细节上出错。",[1798,1824,1825,1826,1831,1832,1836,1837,1841],{},"本章延续",[1827,1828,1830],"a",{"href":1829},"..\u002F08-mechanism-design\u002F","第 8 章","的机制设计思想，也回应",[1827,1833,1835],{"href":1834},"..\u002F10-externalities-public-goods\u002F","第 10 章","中的非价格配置问题。学完后再进入",[1827,1838,1840],{"href":1839},"..\u002F12-review\u002F","第 12 章","，会更容易理解数字平台为什么既是市场，也是被设计出来的制度。",[1794,1843,1845],{"id":1844},"经济动机-economic-motivation","经济动机 (Economic Motivation)",[1798,1847,1848,1849,1853],{},"在许多市场中，",[1850,1851,1852],"strong",{},"价格并不是唯一的分配机制","，甚至不起主要作用：",[1805,1855,1856,1862,1868,1874],{},[1808,1857,1858,1861],{},[1850,1859,1860],{},"学校选择","：学生如何被分配到学校？（不能按价格）",[1808,1863,1864,1867],{},[1850,1865,1866],{},"医生-医院匹配","：实习医生如何匹配到医院？",[1808,1869,1870,1873],{},[1850,1871,1872],{},"器官捐赠","：肾脏捐赠者和患者如何配对？（禁止买卖）",[1808,1875,1876,1879],{},[1850,1877,1878],{},"婚姻市场","：谁和谁结婚？（文化、道德约束）",[1798,1881,1882,1883,1886],{},"这些都是",[1850,1884,1885],{},"匹配市场 (Matching Markets)"," 的例子。特点：",[1888,1889,1890,1896,1902,1908],"ol",{},[1808,1891,1892,1895],{},[1850,1893,1894],{},"双边匹配","：两组参与者相互选择",[1808,1897,1898,1901],{},[1850,1899,1900],{},"无价格或价格受限","：道德、法律、实践原因",[1808,1903,1904,1907],{},[1850,1905,1906],{},"偏好异质","：不同参与者有不同偏好",[1808,1909,1910,1913],{},[1850,1911,1912],{},"稳定性重要","：不稳定的匹配会自行瓦解",[1798,1915,1916,1919,1920,1923],{},[1850,1917,1918],{},"市场设计 (Market Design)"," 将经济理论（博弈论、机制设计）应用于解决现实世界中的匹配问题，旨在创造更",[1850,1921,1922],{},"有效、公平、简单","的市场。",[1925,1926,1927],"h3",{"id":1927},"诺贝尔奖认可",[1805,1929,1930],{},[1808,1931,1932,1935,1936],{},[1850,1933,1934],{},"2012年","：Alvin Roth 和 Lloyd Shapley\n",[1805,1937,1938,1941],{},[1808,1939,1940],{},"Shapley：稳定匹配理论（1962）",[1808,1942,1943],{},"Roth：应用于医生匹配、学校选择、器官交换",[1794,1945,1947],{"id":1946},"一稳定匹配问题-stable-matching-problem","一、稳定匹配问题 (Stable Matching Problem)",[1925,1949,1951],{"id":1950},"_11-问题设定","1.1 问题设定",[1798,1953,1954,1957],{},[1850,1955,1956],{},"稳定婚姻问题 (Stable Marriage Problem, Gale & Shapley 1962)","：",[1805,1959,1960,2275,2537,2543],{},[1808,1961,1962,2009,2010],{},[1963,1964,1967,1989],"span",{"className":1965},[1966],"katex",[1963,1968,1971],{"className":1969},[1970],"katex-mathml",[1972,1973,1975],"math",{"xmlns":1974},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[1976,1977,1978,1985],"semantics",{},[1979,1980,1981],"mrow",{},[1982,1983,1984],"mi",{},"N",[1986,1987,1984],"annotation",{"encoding":1988},"application\u002Fx-tex",[1963,1990,1994],{"className":1991,"ariaHidden":1993},[1992],"katex-html","true",[1963,1995,1998,2003],{"className":1996},[1997],"base",[1963,1999],{"className":2000,"style":2002},[2001],"strut","height:0.6833em;",[1963,2004,1984],{"className":2005,"style":2008},[2006,2007],"mord","mathnormal","margin-right:0.109em;"," 个男性：",[1963,2011,2013,2072],{"className":2012},[1966],[1963,2014,2016],{"className":2015},[1970],[1972,2017,2018],{"xmlns":1974},[1976,2019,2020,2069],{},[1979,2021,2022,2025,2029,2033,2043,2046,2053,2055,2058,2060,2066],{},[1982,2023,2024],{},"M",[2026,2027,2028],"mo",{},"=",[2026,2030,2032],{"stretchy":2031},"false","{",[2034,2035,2036,2039],"msub",{},[1982,2037,2038],{},"m",[2040,2041,2042],"mn",{},"1",[2026,2044,2045],{"separator":1993},",",[2034,2047,2048,2050],{},[1982,2049,2038],{},[2040,2051,2052],{},"2",[2026,2054,2045],{"separator":1993},[2026,2056,2057],{},"…",[2026,2059,2045],{"separator":1993},[2034,2061,2062,2064],{},[1982,2063,2038],{},[1982,2065,1984],{},[2026,2067,2068],{"stretchy":2031},"}",[1986,2070,2071],{"encoding":1988},"M = \\{m_1, m_2, \\ldots, m_N\\}",[1963,2073,2075,2096],{"className":2074,"ariaHidden":1993},[1992],[1963,2076,2078,2081,2084,2089,2093],{"className":2077},[1997],[1963,2079],{"className":2080,"style":2002},[2001],[1963,2082,2024],{"className":2083,"style":2008},[2006,2007],[1963,2085],{"className":2086,"style":2088},[2087],"mspace","margin-right:0.2778em;",[1963,2090,2028],{"className":2091},[2092],"mrel",[1963,2094],{"className":2095,"style":2088},[2087],[1963,2097,2099,2103,2107,2163,2167,2171,2211,2214,2217,2221,2224,2227,2230,2271],{"className":2098},[1997],[1963,2100],{"className":2101,"style":2102},[2001],"height:1em;vertical-align:-0.25em;",[1963,2104,2032],{"className":2105},[2106],"mopen",[1963,2108,2110,2113],{"className":2109},[2006],[1963,2111,2038],{"className":2112},[2006,2007],[1963,2114,2117],{"className":2115},[2116],"msupsub",[1963,2118,2122,2154],{"className":2119},[2120,2121],"vlist-t","vlist-t2",[1963,2123,2126,2149],{"className":2124},[2125],"vlist-r",[1963,2127,2131],{"className":2128,"style":2130},[2129],"vlist","height:0.3011em;",[1963,2132,2134,2139],{"style":2133},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[1963,2135],{"className":2136,"style":2138},[2137],"pstrut","height:2.7em;",[1963,2140,2146],{"className":2141},[2142,2143,2144,2145],"sizing","reset-size6","size3","mtight",[1963,2147,2042],{"className":2148},[2006,2145],[1963,2150,2153],{"className":2151},[2152],"vlist-s","​",[1963,2155,2157],{"className":2156},[2125],[1963,2158,2161],{"className":2159,"style":2160},[2129],"height:0.15em;",[1963,2162],{},[1963,2164,2045],{"className":2165},[2166],"mpunct",[1963,2168],{"className":2169,"style":2170},[2087],"margin-right:0.1667em;",[1963,2172,2174,2177],{"className":2173},[2006],[1963,2175,2038],{"className":2176},[2006,2007],[1963,2178,2180],{"className":2179},[2116],[1963,2181,2183,2203],{"className":2182},[2120,2121],[1963,2184,2186,2200],{"className":2185},[2125],[1963,2187,2189],{"className":2188,"style":2130},[2129],[1963,2190,2191,2194],{"style":2133},[1963,2192],{"className":2193,"style":2138},[2137],[1963,2195,2197],{"className":2196},[2142,2143,2144,2145],[1963,2198,2052],{"className":2199},[2006,2145],[1963,2201,2153],{"className":2202},[2152],[1963,2204,2206],{"className":2205},[2125],[1963,2207,2209],{"className":2208,"style":2160},[2129],[1963,2210],{},[1963,2212,2045],{"className":2213},[2166],[1963,2215],{"className":2216,"style":2170},[2087],[1963,2218,2057],{"className":2219},[2220],"minner",[1963,2222],{"className":2223,"style":2170},[2087],[1963,2225,2045],{"className":2226},[2166],[1963,2228],{"className":2229,"style":2170},[2087],[1963,2231,2233,2236],{"className":2232},[2006],[1963,2234,2038],{"className":2235},[2006,2007],[1963,2237,2239],{"className":2238},[2116],[1963,2240,2242,2263],{"className":2241},[2120,2121],[1963,2243,2245,2260],{"className":2244},[2125],[1963,2246,2249],{"className":2247,"style":2248},[2129],"height:0.3283em;",[1963,2250,2251,2254],{"style":2133},[1963,2252],{"className":2253,"style":2138},[2137],[1963,2255,2257],{"className":2256},[2142,2143,2144,2145],[1963,2258,1984],{"className":2259,"style":2008},[2006,2007,2145],[1963,2261,2153],{"className":2262},[2152],[1963,2264,2266],{"className":2265},[2125],[1963,2267,2269],{"className":2268,"style":2160},[2129],[1963,2270],{},[1963,2272,2068],{"className":2273},[2274],"mclose",[1808,2276,2277,2305,2306],{},[1963,2278,2280,2293],{"className":2279},[1966],[1963,2281,2283],{"className":2282},[1970],[1972,2284,2285],{"xmlns":1974},[1976,2286,2287,2291],{},[1979,2288,2289],{},[1982,2290,1984],{},[1986,2292,1984],{"encoding":1988},[1963,2294,2296],{"className":2295,"ariaHidden":1993},[1992],[1963,2297,2299,2302],{"className":2298},[1997],[1963,2300],{"className":2301,"style":2002},[2001],[1963,2303,1984],{"className":2304,"style":2008},[2006,2007]," 个女性：",[1963,2307,2309,2357],{"className":2308},[1966],[1963,2310,2312],{"className":2311},[1970],[1972,2313,2314],{"xmlns":1974},[1976,2315,2316,2354],{},[1979,2317,2318,2321,2323,2325,2332,2334,2340,2342,2344,2346,2352],{},[1982,2319,2320],{},"W",[2026,2322,2028],{},[2026,2324,2032],{"stretchy":2031},[2034,2326,2327,2330],{},[1982,2328,2329],{},"w",[2040,2331,2042],{},[2026,2333,2045],{"separator":1993},[2034,2335,2336,2338],{},[1982,2337,2329],{},[2040,2339,2052],{},[2026,2341,2045],{"separator":1993},[2026,2343,2057],{},[2026,2345,2045],{"separator":1993},[2034,2347,2348,2350],{},[1982,2349,2329],{},[1982,2351,1984],{},[2026,2353,2068],{"stretchy":2031},[1986,2355,2356],{"encoding":1988},"W = \\{w_1, w_2, \\ldots, w_N\\}",[1963,2358,2360,2379],{"className":2359,"ariaHidden":1993},[1992],[1963,2361,2363,2366,2370,2373,2376],{"className":2362},[1997],[1963,2364],{"className":2365,"style":2002},[2001],[1963,2367,2320],{"className":2368,"style":2369},[2006,2007],"margin-right:0.1389em;",[1963,2371],{"className":2372,"style":2088},[2087],[1963,2374,2028],{"className":2375},[2092],[1963,2377],{"className":2378,"style":2088},[2087],[1963,2380,2382,2385,2388,2430,2433,2436,2476,2479,2482,2485,2488,2491,2494,2534],{"className":2381},[1997],[1963,2383],{"className":2384,"style":2102},[2001],[1963,2386,2032],{"className":2387},[2106],[1963,2389,2391,2395],{"className":2390},[2006],[1963,2392,2329],{"className":2393,"style":2394},[2006,2007],"margin-right:0.0269em;",[1963,2396,2398],{"className":2397},[2116],[1963,2399,2401,2422],{"className":2400},[2120,2121],[1963,2402,2404,2419],{"className":2403},[2125],[1963,2405,2407],{"className":2406,"style":2130},[2129],[1963,2408,2410,2413],{"style":2409},"top:-2.55em;margin-left:-0.0269em;margin-right:0.05em;",[1963,2411],{"className":2412,"style":2138},[2137],[1963,2414,2416],{"className":2415},[2142,2143,2144,2145],[1963,2417,2042],{"className":2418},[2006,2145],[1963,2420,2153],{"className":2421},[2152],[1963,2423,2425],{"className":2424},[2125],[1963,2426,2428],{"className":2427,"style":2160},[2129],[1963,2429],{},[1963,2431,2045],{"className":2432},[2166],[1963,2434],{"className":2435,"style":2170},[2087],[1963,2437,2439,2442],{"className":2438},[2006],[1963,2440,2329],{"className":2441,"style":2394},[2006,2007],[1963,2443,2445],{"className":2444},[2116],[1963,2446,2448,2468],{"className":2447},[2120,2121],[1963,2449,2451,2465],{"className":2450},[2125],[1963,2452,2454],{"className":2453,"style":2130},[2129],[1963,2455,2456,2459],{"style":2409},[1963,2457],{"className":2458,"style":2138},[2137],[1963,2460,2462],{"className":2461},[2142,2143,2144,2145],[1963,2463,2052],{"className":2464},[2006,2145],[1963,2466,2153],{"className":2467},[2152],[1963,2469,2471],{"className":2470},[2125],[1963,2472,2474],{"className":2473,"style":2160},[2129],[1963,2475],{},[1963,2477,2045],{"className":2478},[2166],[1963,2480],{"className":2481,"style":2170},[2087],[1963,2483,2057],{"className":2484},[2220],[1963,2486],{"className":2487,"style":2170},[2087],[1963,2489,2045],{"className":2490},[2166],[1963,2492],{"className":2493,"style":2170},[2087],[1963,2495,2497,2500],{"className":2496},[2006],[1963,2498,2329],{"className":2499,"style":2394},[2006,2007],[1963,2501,2503],{"className":2502},[2116],[1963,2504,2506,2526],{"className":2505},[2120,2121],[1963,2507,2509,2523],{"className":2508},[2125],[1963,2510,2512],{"className":2511,"style":2248},[2129],[1963,2513,2514,2517],{"style":2409},[1963,2515],{"className":2516,"style":2138},[2137],[1963,2518,2520],{"className":2519},[2142,2143,2144,2145],[1963,2521,1984],{"className":2522,"style":2008},[2006,2007,2145],[1963,2524,2153],{"className":2525},[2152],[1963,2527,2529],{"className":2528},[2125],[1963,2530,2532],{"className":2531,"style":2160},[2129],[1963,2533],{},[1963,2535,2068],{"className":2536},[2274],[1808,2538,2539,2540],{},"每个男性有对所有女性的",[1850,2541,2542],{},"严格偏好排序",[1808,2544,2545,2546],{},"每个女性有对所有男性的",[1850,2547,2542],{},[1798,2549,2550,2553,2554,2557,2558,2589],{},[1850,2551,2552],{},"目标","：找到一个",[1850,2555,2556],{},"匹配"," ",[1963,2559,2561,2576],{"className":2560},[1966],[1963,2562,2564],{"className":2563},[1970],[1972,2565,2566],{"xmlns":1974},[1976,2567,2568,2573],{},[1979,2569,2570],{},[1982,2571,2572],{},"μ",[1986,2574,2575],{"encoding":1988},"\\mu",[1963,2577,2579],{"className":2578,"ariaHidden":1993},[1992],[1963,2580,2582,2586],{"className":2581},[1997],[1963,2583],{"className":2584,"style":2585},[2001],"height:0.625em;vertical-align:-0.1944em;",[1963,2587,2572],{"className":2588},[2006,2007],"，即男性和女性之间的一一对应。",[1798,2591,2592,1957],{},[1850,2593,2594,2595],{},"匹配 ",[1963,2596,2598,2611],{"className":2597},[1966],[1963,2599,2601],{"className":2600},[1970],[1972,2602,2603],{"xmlns":1974},[1976,2604,2605,2609],{},[1979,2606,2607],{},[1982,2608,2572],{},[1986,2610,2575],{"encoding":1988},[1963,2612,2614],{"className":2613,"ariaHidden":1993},[1992],[1963,2615,2617,2620],{"className":2616},[1997],[1963,2618],{"className":2619,"style":2585},[2001],[1963,2621,2572],{"className":2622},[2006,2007],[1805,2624,2625,2926,3215],{},[1808,2626,2627,2783,2784,2855,2856],{},[1963,2628,2630,2666],{"className":2629},[1966],[1963,2631,2633],{"className":2632},[1970],[1972,2634,2635],{"xmlns":1974},[1976,2636,2637,2663],{},[1979,2638,2639,2641,2644,2651,2654,2656],{},[1982,2640,2572],{},[2026,2642,2643],{"stretchy":2031},"(",[2034,2645,2646,2648],{},[1982,2647,2038],{},[1982,2649,2650],{},"i",[2026,2652,2653],{"stretchy":2031},")",[2026,2655,2028],{},[2034,2657,2658,2660],{},[1982,2659,2329],{},[1982,2661,2662],{},"j",[1986,2664,2665],{"encoding":1988},"\\mu(m_i) = w_j",[1963,2667,2669,2734],{"className":2668,"ariaHidden":1993},[1992],[1963,2670,2672,2675,2678,2681,2722,2725,2728,2731],{"className":2671},[1997],[1963,2673],{"className":2674,"style":2102},[2001],[1963,2676,2572],{"className":2677},[2006,2007],[1963,2679,2643],{"className":2680},[2106],[1963,2682,2684,2687],{"className":2683},[2006],[1963,2685,2038],{"className":2686},[2006,2007],[1963,2688,2690],{"className":2689},[2116],[1963,2691,2693,2714],{"className":2692},[2120,2121],[1963,2694,2696,2711],{"className":2695},[2125],[1963,2697,2700],{"className":2698,"style":2699},[2129],"height:0.3117em;",[1963,2701,2702,2705],{"style":2133},[1963,2703],{"className":2704,"style":2138},[2137],[1963,2706,2708],{"className":2707},[2142,2143,2144,2145],[1963,2709,2650],{"className":2710},[2006,2007,2145],[1963,2712,2153],{"className":2713},[2152],[1963,2715,2717],{"className":2716},[2125],[1963,2718,2720],{"className":2719,"style":2160},[2129],[1963,2721],{},[1963,2723,2653],{"className":2724},[2274],[1963,2726],{"className":2727,"style":2088},[2087],[1963,2729,2028],{"className":2730},[2092],[1963,2732],{"className":2733,"style":2088},[2087],[1963,2735,2737,2741],{"className":2736},[1997],[1963,2738],{"className":2739,"style":2740},[2001],"height:0.7167em;vertical-align:-0.2861em;",[1963,2742,2744,2747],{"className":2743},[2006],[1963,2745,2329],{"className":2746,"style":2394},[2006,2007],[1963,2748,2750],{"className":2749},[2116],[1963,2751,2753,2774],{"className":2752},[2120,2121],[1963,2754,2756,2771],{"className":2755},[2125],[1963,2757,2759],{"className":2758,"style":2699},[2129],[1963,2760,2761,2764],{"style":2409},[1963,2762],{"className":2763,"style":2138},[2137],[1963,2765,2767],{"className":2766},[2142,2143,2144,2145],[1963,2768,2662],{"className":2769,"style":2770},[2006,2007,2145],"margin-right:0.0572em;",[1963,2772,2153],{"className":2773},[2152],[1963,2775,2777],{"className":2776},[2125],[1963,2778,2781],{"className":2779,"style":2780},[2129],"height:0.2861em;",[1963,2782],{}," 表示 ",[1963,2785,2787,2805],{"className":2786},[1966],[1963,2788,2790],{"className":2789},[1970],[1972,2791,2792],{"xmlns":1974},[1976,2793,2794,2802],{},[1979,2795,2796],{},[2034,2797,2798,2800],{},[1982,2799,2038],{},[1982,2801,2650],{},[1986,2803,2804],{"encoding":1988},"m_i",[1963,2806,2808],{"className":2807,"ariaHidden":1993},[1992],[1963,2809,2811,2815],{"className":2810},[1997],[1963,2812],{"className":2813,"style":2814},[2001],"height:0.5806em;vertical-align:-0.15em;",[1963,2816,2818,2821],{"className":2817},[2006],[1963,2819,2038],{"className":2820},[2006,2007],[1963,2822,2824],{"className":2823},[2116],[1963,2825,2827,2847],{"className":2826},[2120,2121],[1963,2828,2830,2844],{"className":2829},[2125],[1963,2831,2833],{"className":2832,"style":2699},[2129],[1963,2834,2835,2838],{"style":2133},[1963,2836],{"className":2837,"style":2138},[2137],[1963,2839,2841],{"className":2840},[2142,2143,2144,2145],[1963,2842,2650],{"className":2843},[2006,2007,2145],[1963,2845,2153],{"className":2846},[2152],[1963,2848,2850],{"className":2849},[2125],[1963,2851,2853],{"className":2852,"style":2160},[2129],[1963,2854],{}," 匹配到 ",[1963,2857,2859,2877],{"className":2858},[1966],[1963,2860,2862],{"className":2861},[1970],[1972,2863,2864],{"xmlns":1974},[1976,2865,2866,2874],{},[1979,2867,2868],{},[2034,2869,2870,2872],{},[1982,2871,2329],{},[1982,2873,2662],{},[1986,2875,2876],{"encoding":1988},"w_j",[1963,2878,2880],{"className":2879,"ariaHidden":1993},[1992],[1963,2881,2883,2886],{"className":2882},[1997],[1963,2884],{"className":2885,"style":2740},[2001],[1963,2887,2889,2892],{"className":2888},[2006],[1963,2890,2329],{"className":2891,"style":2394},[2006,2007],[1963,2893,2895],{"className":2894},[2116],[1963,2896,2898,2918],{"className":2897},[2120,2121],[1963,2899,2901,2915],{"className":2900},[2125],[1963,2902,2904],{"className":2903,"style":2699},[2129],[1963,2905,2906,2909],{"style":2409},[1963,2907],{"className":2908,"style":2138},[2137],[1963,2910,2912],{"className":2911},[2142,2143,2144,2145],[1963,2913,2662],{"className":2914,"style":2770},[2006,2007,2145],[1963,2916,2153],{"className":2917},[2152],[1963,2919,2921],{"className":2920},[2125],[1963,2922,2924],{"className":2923,"style":2780},[2129],[1963,2925],{},[1808,2927,2928,2783,3077,2855,3146],{},[1963,2929,2931,2963],{"className":2930},[1966],[1963,2932,2934],{"className":2933},[1970],[1972,2935,2936],{"xmlns":1974},[1976,2937,2938,2960],{},[1979,2939,2940,2942,2944,2950,2952,2954],{},[1982,2941,2572],{},[2026,2943,2643],{"stretchy":2031},[2034,2945,2946,2948],{},[1982,2947,2329],{},[1982,2949,2662],{},[2026,2951,2653],{"stretchy":2031},[2026,2953,2028],{},[2034,2955,2956,2958],{},[1982,2957,2038],{},[1982,2959,2650],{},[1986,2961,2962],{"encoding":1988},"\\mu(w_j) = m_i",[1963,2964,2966,3031],{"className":2965,"ariaHidden":1993},[1992],[1963,2967,2969,2973,2976,2979,3019,3022,3025,3028],{"className":2968},[1997],[1963,2970],{"className":2971,"style":2972},[2001],"height:1.0361em;vertical-align:-0.2861em;",[1963,2974,2572],{"className":2975},[2006,2007],[1963,2977,2643],{"className":2978},[2106],[1963,2980,2982,2985],{"className":2981},[2006],[1963,2983,2329],{"className":2984,"style":2394},[2006,2007],[1963,2986,2988],{"className":2987},[2116],[1963,2989,2991,3011],{"className":2990},[2120,2121],[1963,2992,2994,3008],{"className":2993},[2125],[1963,2995,2997],{"className":2996,"style":2699},[2129],[1963,2998,2999,3002],{"style":2409},[1963,3000],{"className":3001,"style":2138},[2137],[1963,3003,3005],{"className":3004},[2142,2143,2144,2145],[1963,3006,2662],{"className":3007,"style":2770},[2006,2007,2145],[1963,3009,2153],{"className":3010},[2152],[1963,3012,3014],{"className":3013},[2125],[1963,3015,3017],{"className":3016,"style":2780},[2129],[1963,3018],{},[1963,3020,2653],{"className":3021},[2274],[1963,3023],{"className":3024,"style":2088},[2087],[1963,3026,2028],{"className":3027},[2092],[1963,3029],{"className":3030,"style":2088},[2087],[1963,3032,3034,3037],{"className":3033},[1997],[1963,3035],{"className":3036,"style":2814},[2001],[1963,3038,3040,3043],{"className":3039},[2006],[1963,3041,2038],{"className":3042},[2006,2007],[1963,3044,3046],{"className":3045},[2116],[1963,3047,3049,3069],{"className":3048},[2120,2121],[1963,3050,3052,3066],{"className":3051},[2125],[1963,3053,3055],{"className":3054,"style":2699},[2129],[1963,3056,3057,3060],{"style":2133},[1963,3058],{"className":3059,"style":2138},[2137],[1963,3061,3063],{"className":3062},[2142,2143,2144,2145],[1963,3064,2650],{"className":3065},[2006,2007,2145],[1963,3067,2153],{"className":3068},[2152],[1963,3070,3072],{"className":3071},[2125],[1963,3073,3075],{"className":3074,"style":2160},[2129],[1963,3076],{},[1963,3078,3080,3097],{"className":3079},[1966],[1963,3081,3083],{"className":3082},[1970],[1972,3084,3085],{"xmlns":1974},[1976,3086,3087,3095],{},[1979,3088,3089],{},[2034,3090,3091,3093],{},[1982,3092,2329],{},[1982,3094,2662],{},[1986,3096,2876],{"encoding":1988},[1963,3098,3100],{"className":3099,"ariaHidden":1993},[1992],[1963,3101,3103,3106],{"className":3102},[1997],[1963,3104],{"className":3105,"style":2740},[2001],[1963,3107,3109,3112],{"className":3108},[2006],[1963,3110,2329],{"className":3111,"style":2394},[2006,2007],[1963,3113,3115],{"className":3114},[2116],[1963,3116,3118,3138],{"className":3117},[2120,2121],[1963,3119,3121,3135],{"className":3120},[2125],[1963,3122,3124],{"className":3123,"style":2699},[2129],[1963,3125,3126,3129],{"style":2409},[1963,3127],{"className":3128,"style":2138},[2137],[1963,3130,3132],{"className":3131},[2142,2143,2144,2145],[1963,3133,2662],{"className":3134,"style":2770},[2006,2007,2145],[1963,3136,2153],{"className":3137},[2152],[1963,3139,3141],{"className":3140},[2125],[1963,3142,3144],{"className":3143,"style":2780},[2129],[1963,3145],{},[1963,3147,3149,3166],{"className":3148},[1966],[1963,3150,3152],{"className":3151},[1970],[1972,3153,3154],{"xmlns":1974},[1976,3155,3156,3164],{},[1979,3157,3158],{},[2034,3159,3160,3162],{},[1982,3161,2038],{},[1982,3163,2650],{},[1986,3165,2804],{"encoding":1988},[1963,3167,3169],{"className":3168,"ariaHidden":1993},[1992],[1963,3170,3172,3175],{"className":3171},[1997],[1963,3173],{"className":3174,"style":2814},[2001],[1963,3176,3178,3181],{"className":3177},[2006],[1963,3179,2038],{"className":3180},[2006,2007],[1963,3182,3184],{"className":3183},[2116],[1963,3185,3187,3207],{"className":3186},[2120,2121],[1963,3188,3190,3204],{"className":3189},[2125],[1963,3191,3193],{"className":3192,"style":2699},[2129],[1963,3194,3195,3198],{"style":2133},[1963,3196],{"className":3197,"style":2138},[2137],[1963,3199,3201],{"className":3200},[2142,2143,2144,2145],[1963,3202,2650],{"className":3203},[2006,2007,2145],[1963,3205,2153],{"className":3206},[2152],[1963,3208,3210],{"className":3209},[2125],[1963,3211,3213],{"className":3212,"style":2160},[2129],[1963,3214],{},[1808,3216,3217],{},"每个人都被匹配（一夫一妻制）",[1925,3219,3221],{"id":3220},"_12-稳定性概念","1.2 稳定性概念",[1798,3223,3224,3227,3228,3362],{},[1850,3225,3226],{},"阻塞对 (Blocking Pair)","：\n一对 ",[1963,3229,3231,3261],{"className":3230},[1966],[1963,3232,3234],{"className":3233},[1970],[1972,3235,3236],{"xmlns":1974},[1976,3237,3238,3258],{},[1979,3239,3240,3242,3248,3250,3256],{},[2026,3241,2643],{"stretchy":2031},[2034,3243,3244,3246],{},[1982,3245,2038],{},[1982,3247,2650],{},[2026,3249,2045],{"separator":1993},[2034,3251,3252,3254],{},[1982,3253,2329],{},[1982,3255,2662],{},[2026,3257,2653],{"stretchy":2031},[1986,3259,3260],{"encoding":1988},"(m_i, w_j)",[1963,3262,3264],{"className":3263,"ariaHidden":1993},[1992],[1963,3265,3267,3270,3273,3313,3316,3319,3359],{"className":3266},[1997],[1963,3268],{"className":3269,"style":2972},[2001],[1963,3271,2643],{"className":3272},[2106],[1963,3274,3276,3279],{"className":3275},[2006],[1963,3277,2038],{"className":3278},[2006,2007],[1963,3280,3282],{"className":3281},[2116],[1963,3283,3285,3305],{"className":3284},[2120,2121],[1963,3286,3288,3302],{"className":3287},[2125],[1963,3289,3291],{"className":3290,"style":2699},[2129],[1963,3292,3293,3296],{"style":2133},[1963,3294],{"className":3295,"style":2138},[2137],[1963,3297,3299],{"className":3298},[2142,2143,2144,2145],[1963,3300,2650],{"className":3301},[2006,2007,2145],[1963,3303,2153],{"className":3304},[2152],[1963,3306,3308],{"className":3307},[2125],[1963,3309,3311],{"className":3310,"style":2160},[2129],[1963,3312],{},[1963,3314,2045],{"className":3315},[2166],[1963,3317],{"className":3318,"style":2170},[2087],[1963,3320,3322,3325],{"className":3321},[2006],[1963,3323,2329],{"className":3324,"style":2394},[2006,2007],[1963,3326,3328],{"className":3327},[2116],[1963,3329,3331,3351],{"className":3330},[2120,2121],[1963,3332,3334,3348],{"className":3333},[2125],[1963,3335,3337],{"className":3336,"style":2699},[2129],[1963,3338,3339,3342],{"style":2409},[1963,3340],{"className":3341,"style":2138},[2137],[1963,3343,3345],{"className":3344},[2142,2143,2144,2145],[1963,3346,2662],{"className":3347,"style":2770},[2006,2007,2145],[1963,3349,2153],{"className":3350},[2152],[1963,3352,3354],{"className":3353},[2125],[1963,3355,3357],{"className":3356,"style":2780},[2129],[1963,3358],{},[1963,3360,2653],{"className":3361},[2274]," 是阻塞对，如果：",[1888,3364,3365,3592],{},[1808,3366,3367,3436,3437,3506,3507],{},[1963,3368,3370,3387],{"className":3369},[1966],[1963,3371,3373],{"className":3372},[1970],[1972,3374,3375],{"xmlns":1974},[1976,3376,3377,3385],{},[1979,3378,3379],{},[2034,3380,3381,3383],{},[1982,3382,2038],{},[1982,3384,2650],{},[1986,3386,2804],{"encoding":1988},[1963,3388,3390],{"className":3389,"ariaHidden":1993},[1992],[1963,3391,3393,3396],{"className":3392},[1997],[1963,3394],{"className":3395,"style":2814},[2001],[1963,3397,3399,3402],{"className":3398},[2006],[1963,3400,2038],{"className":3401},[2006,2007],[1963,3403,3405],{"className":3404},[2116],[1963,3406,3408,3428],{"className":3407},[2120,2121],[1963,3409,3411,3425],{"className":3410},[2125],[1963,3412,3414],{"className":3413,"style":2699},[2129],[1963,3415,3416,3419],{"style":2133},[1963,3417],{"className":3418,"style":2138},[2137],[1963,3420,3422],{"className":3421},[2142,2143,2144,2145],[1963,3423,2650],{"className":3424},[2006,2007,2145],[1963,3426,2153],{"className":3427},[2152],[1963,3429,3431],{"className":3430},[2125],[1963,3432,3434],{"className":3433,"style":2160},[2129],[1963,3435],{}," 偏好 ",[1963,3438,3440,3457],{"className":3439},[1966],[1963,3441,3443],{"className":3442},[1970],[1972,3444,3445],{"xmlns":1974},[1976,3446,3447,3455],{},[1979,3448,3449],{},[2034,3450,3451,3453],{},[1982,3452,2329],{},[1982,3454,2662],{},[1986,3456,2876],{"encoding":1988},[1963,3458,3460],{"className":3459,"ariaHidden":1993},[1992],[1963,3461,3463,3466],{"className":3462},[1997],[1963,3464],{"className":3465,"style":2740},[2001],[1963,3467,3469,3472],{"className":3468},[2006],[1963,3470,2329],{"className":3471,"style":2394},[2006,2007],[1963,3473,3475],{"className":3474},[2116],[1963,3476,3478,3498],{"className":3477},[2120,2121],[1963,3479,3481,3495],{"className":3480},[2125],[1963,3482,3484],{"className":3483,"style":2699},[2129],[1963,3485,3486,3489],{"style":2409},[1963,3487],{"className":3488,"style":2138},[2137],[1963,3490,3492],{"className":3491},[2142,2143,2144,2145],[1963,3493,2662],{"className":3494,"style":2770},[2006,2007,2145],[1963,3496,2153],{"className":3497},[2152],[1963,3499,3501],{"className":3500},[2125],[1963,3502,3504],{"className":3503,"style":2780},[2129],[1963,3505],{}," 超过其当前配偶 ",[1963,3508,3510,3534],{"className":3509},[1966],[1963,3511,3513],{"className":3512},[1970],[1972,3514,3515],{"xmlns":1974},[1976,3516,3517,3531],{},[1979,3518,3519,3521,3523,3529],{},[1982,3520,2572],{},[2026,3522,2643],{"stretchy":2031},[2034,3524,3525,3527],{},[1982,3526,2038],{},[1982,3528,2650],{},[2026,3530,2653],{"stretchy":2031},[1986,3532,3533],{"encoding":1988},"\\mu(m_i)",[1963,3535,3537],{"className":3536,"ariaHidden":1993},[1992],[1963,3538,3540,3543,3546,3549,3589],{"className":3539},[1997],[1963,3541],{"className":3542,"style":2102},[2001],[1963,3544,2572],{"className":3545},[2006,2007],[1963,3547,2643],{"className":3548},[2106],[1963,3550,3552,3555],{"className":3551},[2006],[1963,3553,2038],{"className":3554},[2006,2007],[1963,3556,3558],{"className":3557},[2116],[1963,3559,3561,3581],{"className":3560},[2120,2121],[1963,3562,3564,3578],{"className":3563},[2125],[1963,3565,3567],{"className":3566,"style":2699},[2129],[1963,3568,3569,3572],{"style":2133},[1963,3570],{"className":3571,"style":2138},[2137],[1963,3573,3575],{"className":3574},[2142,2143,2144,2145],[1963,3576,2650],{"className":3577},[2006,2007,2145],[1963,3579,2153],{"className":3580},[2152],[1963,3582,3584],{"className":3583},[2125],[1963,3585,3587],{"className":3586,"style":2160},[2129],[1963,3588],{},[1963,3590,2653],{"className":3591},[2274],[1808,3593,3594,3436,3663,3506,3732],{},[1963,3595,3597,3614],{"className":3596},[1966],[1963,3598,3600],{"className":3599},[1970],[1972,3601,3602],{"xmlns":1974},[1976,3603,3604,3612],{},[1979,3605,3606],{},[2034,3607,3608,3610],{},[1982,3609,2329],{},[1982,3611,2662],{},[1986,3613,2876],{"encoding":1988},[1963,3615,3617],{"className":3616,"ariaHidden":1993},[1992],[1963,3618,3620,3623],{"className":3619},[1997],[1963,3621],{"className":3622,"style":2740},[2001],[1963,3624,3626,3629],{"className":3625},[2006],[1963,3627,2329],{"className":3628,"style":2394},[2006,2007],[1963,3630,3632],{"className":3631},[2116],[1963,3633,3635,3655],{"className":3634},[2120,2121],[1963,3636,3638,3652],{"className":3637},[2125],[1963,3639,3641],{"className":3640,"style":2699},[2129],[1963,3642,3643,3646],{"style":2409},[1963,3644],{"className":3645,"style":2138},[2137],[1963,3647,3649],{"className":3648},[2142,2143,2144,2145],[1963,3650,2662],{"className":3651,"style":2770},[2006,2007,2145],[1963,3653,2153],{"className":3654},[2152],[1963,3656,3658],{"className":3657},[2125],[1963,3659,3661],{"className":3660,"style":2780},[2129],[1963,3662],{},[1963,3664,3666,3683],{"className":3665},[1966],[1963,3667,3669],{"className":3668},[1970],[1972,3670,3671],{"xmlns":1974},[1976,3672,3673,3681],{},[1979,3674,3675],{},[2034,3676,3677,3679],{},[1982,3678,2038],{},[1982,3680,2650],{},[1986,3682,2804],{"encoding":1988},[1963,3684,3686],{"className":3685,"ariaHidden":1993},[1992],[1963,3687,3689,3692],{"className":3688},[1997],[1963,3690],{"className":3691,"style":2814},[2001],[1963,3693,3695,3698],{"className":3694},[2006],[1963,3696,2038],{"className":3697},[2006,2007],[1963,3699,3701],{"className":3700},[2116],[1963,3702,3704,3724],{"className":3703},[2120,2121],[1963,3705,3707,3721],{"className":3706},[2125],[1963,3708,3710],{"className":3709,"style":2699},[2129],[1963,3711,3712,3715],{"style":2133},[1963,3713],{"className":3714,"style":2138},[2137],[1963,3716,3718],{"className":3717},[2142,2143,2144,2145],[1963,3719,2650],{"className":3720},[2006,2007,2145],[1963,3722,2153],{"className":3723},[2152],[1963,3725,3727],{"className":3726},[2125],[1963,3728,3730],{"className":3729,"style":2160},[2129],[1963,3731],{},[1963,3733,3735,3759],{"className":3734},[1966],[1963,3736,3738],{"className":3737},[1970],[1972,3739,3740],{"xmlns":1974},[1976,3741,3742,3756],{},[1979,3743,3744,3746,3748,3754],{},[1982,3745,2572],{},[2026,3747,2643],{"stretchy":2031},[2034,3749,3750,3752],{},[1982,3751,2329],{},[1982,3753,2662],{},[2026,3755,2653],{"stretchy":2031},[1986,3757,3758],{"encoding":1988},"\\mu(w_j)",[1963,3760,3762],{"className":3761,"ariaHidden":1993},[1992],[1963,3763,3765,3768,3771,3774,3814],{"className":3764},[1997],[1963,3766],{"className":3767,"style":2972},[2001],[1963,3769,2572],{"className":3770},[2006,2007],[1963,3772,2643],{"className":3773},[2106],[1963,3775,3777,3780],{"className":3776},[2006],[1963,3778,2329],{"className":3779,"style":2394},[2006,2007],[1963,3781,3783],{"className":3782},[2116],[1963,3784,3786,3806],{"className":3785},[2120,2121],[1963,3787,3789,3803],{"className":3788},[2125],[1963,3790,3792],{"className":3791,"style":2699},[2129],[1963,3793,3794,3797],{"style":2409},[1963,3795],{"className":3796,"style":2138},[2137],[1963,3798,3800],{"className":3799},[2142,2143,2144,2145],[1963,3801,2662],{"className":3802,"style":2770},[2006,2007,2145],[1963,3804,2153],{"className":3805},[2152],[1963,3807,3809],{"className":3808},[2125],[1963,3810,3812],{"className":3811,"style":2780},[2129],[1963,3813],{},[1963,3815,2653],{"className":3816},[2274],[1798,3818,3819],{},"即两人都愿意抛弃当前配偶而结合。",[1798,3821,3822,3825],{},[1850,3823,3824],{},"稳定匹配 (Stable Matching)","：\n没有阻塞对的匹配。",[1798,3827,3828],{},[1850,3829,3830],{},"为什么稳定性重要？",[1805,3832,3833,3836,3839],{},[1808,3834,3835],{},"不稳定的匹配会瓦解（当事人自行重新匹配）",[1808,3837,3838],{},"实践中：医生跳槽、学生转学",[1808,3840,3841],{},"稳定匹配是\"自我实施\"的均衡",[1925,3843,3845],{"id":3844},"_13-示例","1.3 示例",[1798,3847,3848,3851,3852,3976,3977,4101],{},[1850,3849,3850],{},"偏好表","（",[1963,3853,3855,3881],{"className":3854},[1966],[1963,3856,3858],{"className":3857},[1970],[1972,3859,3860],{"xmlns":1974},[1976,3861,3862,3878],{},[1979,3863,3864,3870,3872],{},[2034,3865,3866,3868],{},[1982,3867,2038],{},[2040,3869,2042],{},[2026,3871,2045],{"separator":1993},[2034,3873,3874,3876],{},[1982,3875,2038],{},[2040,3877,2052],{},[1986,3879,3880],{"encoding":1988},"m_1, m_2",[1963,3882,3884],{"className":3883,"ariaHidden":1993},[1992],[1963,3885,3887,3890,3930,3933,3936],{"className":3886},[1997],[1963,3888],{"className":3889,"style":2585},[2001],[1963,3891,3893,3896],{"className":3892},[2006],[1963,3894,2038],{"className":3895},[2006,2007],[1963,3897,3899],{"className":3898},[2116],[1963,3900,3902,3922],{"className":3901},[2120,2121],[1963,3903,3905,3919],{"className":3904},[2125],[1963,3906,3908],{"className":3907,"style":2130},[2129],[1963,3909,3910,3913],{"style":2133},[1963,3911],{"className":3912,"style":2138},[2137],[1963,3914,3916],{"className":3915},[2142,2143,2144,2145],[1963,3917,2042],{"className":3918},[2006,2145],[1963,3920,2153],{"className":3921},[2152],[1963,3923,3925],{"className":3924},[2125],[1963,3926,3928],{"className":3927,"style":2160},[2129],[1963,3929],{},[1963,3931,2045],{"className":3932},[2166],[1963,3934],{"className":3935,"style":2170},[2087],[1963,3937,3939,3942],{"className":3938},[2006],[1963,3940,2038],{"className":3941},[2006,2007],[1963,3943,3945],{"className":3944},[2116],[1963,3946,3948,3968],{"className":3947},[2120,2121],[1963,3949,3951,3965],{"className":3950},[2125],[1963,3952,3954],{"className":3953,"style":2130},[2129],[1963,3955,3956,3959],{"style":2133},[1963,3957],{"className":3958,"style":2138},[2137],[1963,3960,3962],{"className":3961},[2142,2143,2144,2145],[1963,3963,2052],{"className":3964},[2006,2145],[1963,3966,2153],{"className":3967},[2152],[1963,3969,3971],{"className":3970},[2125],[1963,3972,3974],{"className":3973,"style":2160},[2129],[1963,3975],{}," 是男性，",[1963,3978,3980,4006],{"className":3979},[1966],[1963,3981,3983],{"className":3982},[1970],[1972,3984,3985],{"xmlns":1974},[1976,3986,3987,4003],{},[1979,3988,3989,3995,3997],{},[2034,3990,3991,3993],{},[1982,3992,2329],{},[2040,3994,2042],{},[2026,3996,2045],{"separator":1993},[2034,3998,3999,4001],{},[1982,4000,2329],{},[2040,4002,2052],{},[1986,4004,4005],{"encoding":1988},"w_1, w_2",[1963,4007,4009],{"className":4008,"ariaHidden":1993},[1992],[1963,4010,4012,4015,4055,4058,4061],{"className":4011},[1997],[1963,4013],{"className":4014,"style":2585},[2001],[1963,4016,4018,4021],{"className":4017},[2006],[1963,4019,2329],{"className":4020,"style":2394},[2006,2007],[1963,4022,4024],{"className":4023},[2116],[1963,4025,4027,4047],{"className":4026},[2120,2121],[1963,4028,4030,4044],{"className":4029},[2125],[1963,4031,4033],{"className":4032,"style":2130},[2129],[1963,4034,4035,4038],{"style":2409},[1963,4036],{"className":4037,"style":2138},[2137],[1963,4039,4041],{"className":4040},[2142,2143,2144,2145],[1963,4042,2042],{"className":4043},[2006,2145],[1963,4045,2153],{"className":4046},[2152],[1963,4048,4050],{"className":4049},[2125],[1963,4051,4053],{"className":4052,"style":2160},[2129],[1963,4054],{},[1963,4056,2045],{"className":4057},[2166],[1963,4059],{"className":4060,"style":2170},[2087],[1963,4062,4064,4067],{"className":4063},[2006],[1963,4065,2329],{"className":4066,"style":2394},[2006,2007],[1963,4068,4070],{"className":4069},[2116],[1963,4071,4073,4093],{"className":4072},[2120,2121],[1963,4074,4076,4090],{"className":4075},[2125],[1963,4077,4079],{"className":4078,"style":2130},[2129],[1963,4080,4081,4084],{"style":2409},[1963,4082],{"className":4083,"style":2138},[2137],[1963,4085,4087],{"className":4086},[2142,2143,2144,2145],[1963,4088,2052],{"className":4089},[2006,2145],[1963,4091,2153],{"className":4092},[2152],[1963,4094,4096],{"className":4095},[2125],[1963,4097,4099],{"className":4098,"style":2160},[2129],[1963,4100],{}," 是女性）：",[1798,4103,4104],{},"男性偏好（从左到右偏好递减）：",[1805,4106,4107,4308],{},[1808,4108,4109],{},[1963,4110,4112,4148],{"className":4111},[1966],[1963,4113,4115],{"className":4114},[1970],[1972,4116,4117],{"xmlns":1974},[1976,4118,4119,4145],{},[1979,4120,4121,4127,4130,4136,4139],{},[2034,4122,4123,4125],{},[1982,4124,2038],{},[2040,4126,2042],{},[2026,4128,4129],{},":",[2034,4131,4132,4134],{},[1982,4133,2329],{},[2040,4135,2042],{},[2026,4137,4138],{},"≻",[2034,4140,4141,4143],{},[1982,4142,2329],{},[2040,4144,2052],{},[1986,4146,4147],{"encoding":1988},"m_1: w_1 \\succ w_2",[1963,4149,4151,4206,4262],{"className":4150,"ariaHidden":1993},[1992],[1963,4152,4154,4157,4197,4200,4203],{"className":4153},[1997],[1963,4155],{"className":4156,"style":2814},[2001],[1963,4158,4160,4163],{"className":4159},[2006],[1963,4161,2038],{"className":4162},[2006,2007],[1963,4164,4166],{"className":4165},[2116],[1963,4167,4169,4189],{"className":4168},[2120,2121],[1963,4170,4172,4186],{"className":4171},[2125],[1963,4173,4175],{"className":4174,"style":2130},[2129],[1963,4176,4177,4180],{"style":2133},[1963,4178],{"className":4179,"style":2138},[2137],[1963,4181,4183],{"className":4182},[2142,2143,2144,2145],[1963,4184,2042],{"className":4185},[2006,2145],[1963,4187,2153],{"className":4188},[2152],[1963,4190,4192],{"className":4191},[2125],[1963,4193,4195],{"className":4194,"style":2160},[2129],[1963,4196],{},[1963,4198],{"className":4199,"style":2088},[2087],[1963,4201,4129],{"className":4202},[2092],[1963,4204],{"className":4205,"style":2088},[2087],[1963,4207,4209,4213,4253,4256,4259],{"className":4208},[1997],[1963,4210],{"className":4211,"style":4212},[2001],"height:0.6891em;vertical-align:-0.15em;",[1963,4214,4216,4219],{"className":4215},[2006],[1963,4217,2329],{"className":4218,"style":2394},[2006,2007],[1963,4220,4222],{"className":4221},[2116],[1963,4223,4225,4245],{"className":4224},[2120,2121],[1963,4226,4228,4242],{"className":4227},[2125],[1963,4229,4231],{"className":4230,"style":2130},[2129],[1963,4232,4233,4236],{"style":2409},[1963,4234],{"className":4235,"style":2138},[2137],[1963,4237,4239],{"className":4238},[2142,2143,2144,2145],[1963,4240,2042],{"className":4241},[2006,2145],[1963,4243,2153],{"className":4244},[2152],[1963,4246,4248],{"className":4247},[2125],[1963,4249,4251],{"className":4250,"style":2160},[2129],[1963,4252],{},[1963,4254],{"className":4255,"style":2088},[2087],[1963,4257,4138],{"className":4258},[2092],[1963,4260],{"className":4261,"style":2088},[2087],[1963,4263,4265,4268],{"className":4264},[1997],[1963,4266],{"className":4267,"style":2814},[2001],[1963,4269,4271,4274],{"className":4270},[2006],[1963,4272,2329],{"className":4273,"style":2394},[2006,2007],[1963,4275,4277],{"className":4276},[2116],[1963,4278,4280,4300],{"className":4279},[2120,2121],[1963,4281,4283,4297],{"className":4282},[2125],[1963,4284,4286],{"className":4285,"style":2130},[2129],[1963,4287,4288,4291],{"style":2409},[1963,4289],{"className":4290,"style":2138},[2137],[1963,4292,4294],{"className":4293},[2142,2143,2144,2145],[1963,4295,2052],{"className":4296},[2006,2145],[1963,4298,2153],{"className":4299},[2152],[1963,4301,4303],{"className":4302},[2125],[1963,4304,4306],{"className":4305,"style":2160},[2129],[1963,4307],{},[1808,4309,4310],{},[1963,4311,4313,4347],{"className":4312},[1966],[1963,4314,4316],{"className":4315},[1970],[1972,4317,4318],{"xmlns":1974},[1976,4319,4320,4344],{},[1979,4321,4322,4328,4330,4336,4338],{},[2034,4323,4324,4326],{},[1982,4325,2038],{},[2040,4327,2052],{},[2026,4329,4129],{},[2034,4331,4332,4334],{},[1982,4333,2329],{},[2040,4335,2052],{},[2026,4337,4138],{},[2034,4339,4340,4342],{},[1982,4341,2329],{},[2040,4343,2042],{},[1986,4345,4346],{"encoding":1988},"m_2: w_2 \\succ w_1",[1963,4348,4350,4405,4460],{"className":4349,"ariaHidden":1993},[1992],[1963,4351,4353,4356,4396,4399,4402],{"className":4352},[1997],[1963,4354],{"className":4355,"style":2814},[2001],[1963,4357,4359,4362],{"className":4358},[2006],[1963,4360,2038],{"className":4361},[2006,2007],[1963,4363,4365],{"className":4364},[2116],[1963,4366,4368,4388],{"className":4367},[2120,2121],[1963,4369,4371,4385],{"className":4370},[2125],[1963,4372,4374],{"className":4373,"style":2130},[2129],[1963,4375,4376,4379],{"style":2133},[1963,4377],{"className":4378,"style":2138},[2137],[1963,4380,4382],{"className":4381},[2142,2143,2144,2145],[1963,4383,2052],{"className":4384},[2006,2145],[1963,4386,2153],{"className":4387},[2152],[1963,4389,4391],{"className":4390},[2125],[1963,4392,4394],{"className":4393,"style":2160},[2129],[1963,4395],{},[1963,4397],{"className":4398,"style":2088},[2087],[1963,4400,4129],{"className":4401},[2092],[1963,4403],{"className":4404,"style":2088},[2087],[1963,4406,4408,4411,4451,4454,4457],{"className":4407},[1997],[1963,4409],{"className":4410,"style":4212},[2001],[1963,4412,4414,4417],{"className":4413},[2006],[1963,4415,2329],{"className":4416,"style":2394},[2006,2007],[1963,4418,4420],{"className":4419},[2116],[1963,4421,4423,4443],{"className":4422},[2120,2121],[1963,4424,4426,4440],{"className":4425},[2125],[1963,4427,4429],{"className":4428,"style":2130},[2129],[1963,4430,4431,4434],{"style":2409},[1963,4432],{"className":4433,"style":2138},[2137],[1963,4435,4437],{"className":4436},[2142,2143,2144,2145],[1963,4438,2052],{"className":4439},[2006,2145],[1963,4441,2153],{"className":4442},[2152],[1963,4444,4446],{"className":4445},[2125],[1963,4447,4449],{"className":4448,"style":2160},[2129],[1963,4450],{},[1963,4452],{"className":4453,"style":2088},[2087],[1963,4455,4138],{"className":4456},[2092],[1963,4458],{"className":4459,"style":2088},[2087],[1963,4461,4463,4466],{"className":4462},[1997],[1963,4464],{"className":4465,"style":2814},[2001],[1963,4467,4469,4472],{"className":4468},[2006],[1963,4470,2329],{"className":4471,"style":2394},[2006,2007],[1963,4473,4475],{"className":4474},[2116],[1963,4476,4478,4498],{"className":4477},[2120,2121],[1963,4479,4481,4495],{"className":4480},[2125],[1963,4482,4484],{"className":4483,"style":2130},[2129],[1963,4485,4486,4489],{"style":2409},[1963,4487],{"className":4488,"style":2138},[2137],[1963,4490,4492],{"className":4491},[2142,2143,2144,2145],[1963,4493,2042],{"className":4494},[2006,2145],[1963,4496,2153],{"className":4497},[2152],[1963,4499,4501],{"className":4500},[2125],[1963,4502,4504],{"className":4503,"style":2160},[2129],[1963,4505],{},[1798,4507,4508],{},"女性偏好：",[1805,4510,4511,4709],{},[1808,4512,4513],{},[1963,4514,4516,4550],{"className":4515},[1966],[1963,4517,4519],{"className":4518},[1970],[1972,4520,4521],{"xmlns":1974},[1976,4522,4523,4547],{},[1979,4524,4525,4531,4533,4539,4541],{},[2034,4526,4527,4529],{},[1982,4528,2329],{},[2040,4530,2042],{},[2026,4532,4129],{},[2034,4534,4535,4537],{},[1982,4536,2038],{},[2040,4538,2052],{},[2026,4540,4138],{},[2034,4542,4543,4545],{},[1982,4544,2038],{},[2040,4546,2042],{},[1986,4548,4549],{"encoding":1988},"w_1: m_2 \\succ 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,{},[1808,7169,7170,3436,7239,5512,7308,5583],{},[1963,7171,7173,7190],{"className":7172},[1966],[1963,7174,7176],{"className":7175},[1970],[1972,7177,7178],{"xmlns":1974},[1976,7179,7180,7188],{},[1979,7181,7182],{},[2034,7183,7184,7186],{},[1982,7185,2329],{},[2040,7187,2052],{},[1986,7189,5533],{"encoding":1988},[1963,7191,7193],{"className":7192,"ariaHidden":1993},[1992],[1963,7194,7196,7199],{"className":7195},[1997],[1963,7197],{"className":7198,"style":2814},[2001],[1963,7200,7202,7205],{"className":7201},[2006],[1963,7203,2329],{"className":7204,"style":2394},[2006,2007],[1963,7206,7208],{"className":7207},[2116],[1963,7209,7211,7231],{"className":7210},[2120,2121],[1963,7212,7214,7228],{"className":7213},[2125],[1963,7215,7217],{"className":7216,"style":2130},[2129],[1963,7218,7219,7222],{"style":2409},[1963,7220],{"className":7221,"style":2138},[2137],[1963,7223,7225],{"className":7224},[2142,2143,2144,2145],[1963,7226,2052],{"className":7227},[2006,2145],[1963,7229,2153],{"className":7230},[2152],[1963,7232,7234],{"className":7233},[2125],[1963,7235,7237],{"className":7236,"style":2160},[2129],[1963,7238],{},[1963,7240,7242,7259],{"className":7241},[1966],[1963,7243,7245],{"className":7244},[1970],[1972,7246,7247],{"xmlns":1974},[1976,7248,7249,7257],{},[1979,7250,7251],{},[2034,7252,7253,7255],{},[1982,7254,2038],{},[2040,7256,2042],{},[1986,7258,5392],{"encoding":1988},[1963,7260,7262],{"className":7261,"ariaHidden":1993},[1992],[1963,7263,7265,7268],{"className":7264},[1997],[1963,7266],{"className":7267,"style":2814},[2001],[1963,7269,7271,7274],{"className":7270},[2006],[1963,7272,2038],{"className":7273},[2006,2007],[1963,7275,7277],{"className":7276},[2116],[1963,7278,7280,7300],{"className":7279},[2120,2121],[1963,7281,7283,7297],{"className":7282},[2125],[1963,7284,7286],{"className":7285,"style":2130},[2129],[1963,7287,7288,7291],{"style":2133},[1963,7289],{"className":7290,"style":2138},[2137],[1963,7292,7294],{"className":7293},[2142,2143,2144,2145],[1963,7295,2042],{"className":7296},[2006,2145],[1963,7298,2153],{"className":7299},[2152],[1963,7301,7303],{"className":7302},[2125],[1963,7304,7306],{"className":7305,"style":2160},[2129],[1963,7307],{},[1963,7309,7311,7328],{"className":7310},[1966],[1963,7312,7314],{"className":7313},[1970],[1972,7315,7316],{"xmlns":1974},[1976,7317,7318,7326],{},[1979,7319,7320],{},[2034,7321,7322,7324],{},[1982,7323,2038],{},[2040,7325,2052],{},[1986,7327,5740],{"encoding":1988},[1963,7329,7331],{"className":7330,"ariaHidden":1993},[1992],[1963,7332,7334,7337],{"className":7333},[1997],[1963,7335],{"className":7336,"style":2814},[2001],[1963,7338,7340,7343],{"className":7339},[2006],[1963,7341,2038],{"className":7342},[2006,2007],[1963,7344,7346],{"className":7345},[2116],[1963,7347,7349,7369],{"className":7348},[2120,2121],[1963,7350,7352,7366],{"className":7351},[2125],[1963,7353,7355],{"className":7354,"style":2130},[2129],[1963,7356,7357,7360],{"style":2133},[1963,7358],{"className":7359,"style":2138},[2137],[1963,7361,7363],{"className":7362},[2142,2143,2144,2145],[1963,7364,2052],{"className":7365},[2006,2145],[1963,7367,2153],{"className":7368},[2152],[1963,7370,7372],{"className":7371},[2125],[1963,7373,7375],{"className":7374,"style":2160},[2129],[1963,7376],{},[1808,7378,6820],{},[1808,7380,5930,7381],{},[1850,7382,5933],{},[1798,7384,7385,7388],{},[1850,7386,7387],{},"结论","：两个匹配都稳定！（一般情况下可能有多个稳定匹配）",[1794,7390,7392],{"id":7391},"二gale-shapley算法-deferred-acceptance-algorithm","二、Gale-Shapley算法 (Deferred Acceptance Algorithm)",[1925,7394,7396],{"id":7395},"_21-算法描述","2.1 算法描述",[1798,7398,7399,1957],{},[1850,7400,7401],{},"男性求婚版本 (Male-Proposing DA)",[7403,7404,7409],"pre",{"className":7405,"code":7407,"language":7408},[7406],"language-text","初始化：所有人都未匹配\nwhile 存在未匹配的男性 m:\n    m 向他偏好列表中尚未拒绝他的最偏好女性 w 求婚\n    if w 当前未匹配:\n        w 暂时接受 m\n    else:\n        设当前持有者为 m'\n        if w 偏好 m over m':\n            w 拒绝 m'，暂时接受 m\n            m' 变为未匹配\n        else:\n            w 拒绝 m\n返回：最终的匹配\n","text",[7410,7411,7407],"code",{"__ignoreMap":10},[1798,7413,7414,1957],{},[1850,7415,7416],{},"关键特征",[1805,7418,7419,7425,7431],{},[1808,7420,7421,7424],{},[1850,7422,7423],{},"延迟接受","：女性暂时接受，但可能后续拒绝",[1808,7426,7427,7430],{},[1850,7428,7429],{},"单调性","：女性的匹配对象只会越来越好",[1808,7432,7433,7436],{},[1850,7434,7435],{},"男性降级","：被拒绝的男性向次优选择求婚",[1925,7438,7440],{"id":7439},"_22-算法执行示例","2.2 算法执行示例",[1798,7442,7443,1957],{},[1850,7444,7445],{},"3男3女的例子",[1798,7447,7448],{},"男性偏好：",[1805,7450,7451,7713,7974],{},[1808,7452,7453],{},[1963,7454,7456,7499],{"className":7455},[1966],[1963,7457,7459],{"className":7458},[1970],[1972,7460,7461],{"xmlns":1974},[1976,7462,7463,7496],{},[1979,7464,7465,7471,7473,7479,7481,7487,7489],{},[2034,7466,7467,7469],{},[1982,7468,2038],{},[2040,7470,2042],{},[2026,7472,4129],{},[2034,7474,7475,7477],{},[1982,7476,2329],{},[2040,7478,2052],{},[2026,7480,4138],{},[2034,7482,7483,7485],{},[1982,7484,2329],{},[2040,7486,2042],{},[2026,7488,4138],{},[2034,7490,7491,7493],{},[1982,7492,2329],{},[2040,7494,7495],{},"3",[1986,7497,7498],{"encoding":1988},"m_1: w_2 \\succ w_1 \\succ w_3",[1963,7500,7502,7557,7612,7667],{"className":7501,"ariaHidden":1993},[1992],[1963,7503,7505,7508,7548,7551,7554],{"className":7504},[1997],[1963,7506],{"className":7507,"style":2814},[2001],[1963,7509,7511,7514],{"className":7510},[2006],[1963,7512,2038],{"className":7513},[2006,2007],[1963,7515,7517],{"className":7516},[2116],[1963,7518,7520,7540],{"className":7519},[2120,2121],[1963,7521,7523,7537],{"className":7522},[2125],[1963,7524,7526],{"className":7525,"style":2130},[2129],[1963,7527,7528,7531],{"style":2133},[1963,7529],{"className":7530,"style":2138},[2137],[1963,7532,7534],{"className":7533},[2142,2143,2144,2145],[1963,7535,2042],{"className":7536},[2006,2145],[1963,7538,2153],{"className":7539},[2152],[1963,7541,7543],{"className":7542},[2125],[1963,7544,7546],{"className":7545,"style":2160},[2129],[1963,7547],{},[1963,7549],{"className":7550,"style":2088},[2087],[1963,7552,4129],{"className":7553},[2092],[1963,7555],{"className":7556,"style":2088},[2087],[1963,7558,7560,7563,7603,7606,7609],{"className":7559},[1997],[1963,7561],{"className":7562,"style":4212},[2001],[1963,7564,7566,7569],{"className":7565},[2006],[1963,7567,2329],{"className":7568,"style":2394},[2006,2007],[1963,7570,7572],{"className":7571},[2116],[1963,7573,7575,7595],{"className":7574},[2120,2121],[1963,7576,7578,7592],{"className":7577},[2125],[1963,7579,7581],{"className":7580,"style":2130},[2129],[1963,7582,7583,7586],{"style":2409},[1963,7584],{"className":7585,"style":2138},[2137],[1963,7587,7589],{"className":7588},[2142,2143,2144,2145],[1963,7590,2052],{"className":7591},[2006,2145],[1963,7593,2153],{"className":7594},[2152],[1963,7596,7598],{"className":7597},[2125],[1963,7599,7601],{"className":7600,"style":2160},[2129],[1963,7602],{},[1963,7604],{"className":7605,"style":2088},[2087],[1963,7607,4138],{"className":7608},[2092],[1963,7610],{"className":7611,"style":2088},[2087],[1963,7613,7615,7618,7658,7661,7664],{"className":7614},[1997],[1963,7616],{"className":7617,"style":4212},[2001],[1963,7619,7621,7624],{"className":7620},[2006],[1963,7622,2329],{"className":7623,"style":2394},[2006,2007],[1963,7625,7627],{"className":7626},[2116],[1963,7628,7630,7650],{"className":7629},[2120,2121],[1963,7631,7633,7647],{"className":7632},[2125],[1963,7634,7636],{"className":7635,"style":2130},[2129],[1963,7637,7638,7641],{"style":2409},[1963,7639],{"className":7640,"style":2138},[2137],[1963,7642,7644],{"className":7643},[2142,2143,2144,2145],[1963,7645,2042],{"className":7646},[2006,2145],[1963,7648,2153],{"className":7649},[2152],[1963,7651,7653],{"className":7652},[2125],[1963,7654,7656],{"className":7655,"style":2160},[2129],[1963,7657],{},[1963,7659],{"className":7660,"style":2088},[2087],[1963,7662,4138],{"className":7663},[2092],[1963,7665],{"className":7666,"style":2088},[2087],[1963,7668,7670,7673],{"className":7669},[1997],[1963,7671],{"className":7672,"style":2814},[2001],[1963,7674,7676,7679],{"className":7675},[2006],[1963,7677,2329],{"className":7678,"style":2394},[2006,2007],[1963,7680,7682],{"className":7681},[2116],[1963,7683,7685,7705],{"className":7684},[2120,2121],[1963,7686,7688,7702],{"className":7687},[2125],[1963,7689,7691],{"className":7690,"style":2130},[2129],[1963,7692,7693,7696],{"style":2409},[1963,7694],{"className":7695,"style":2138},[2137],[1963,7697,7699],{"className":7698},[2142,2143,2144,2145],[1963,7700,7495],{"className":7701},[2006,2145],[1963,7703,2153],{"className":7704},[2152],[1963,7706,7708],{"className":7707},[2125],[1963,7709,7711],{"className":7710,"style":2160},[2129],[1963,7712],{},[1808,7714,7715],{},[1963,7716,7718,7760],{"className":7717},[1966],[1963,7719,7721],{"className":7720},[1970],[1972,7722,7723],{"xmlns":1974},[1976,7724,7725,7757],{},[1979,7726,7727,7733,7735,7741,7743,7749,7751],{},[2034,7728,7729,7731],{},[1982,7730,2038],{},[2040,7732,2052],{},[2026,7734,4129],{},[2034,7736,7737,7739],{},[1982,7738,2329],{},[2040,7740,2042],{},[2026,7742,4138],{},[2034,7744,7745,7747],{},[1982,7746,2329],{},[2040,7748,2052],{},[2026,7750,4138],{},[2034,7752,7753,7755],{},[1982,7754,2329],{},[2040,7756,7495],{},[1986,7758,7759],{"encoding":1988},"m_2: w_1 \\succ w_2 \\succ 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接受（当前最优）",[1808,9236,9237,1957,9370,9439],{},[1963,9238,9240,9266],{"className":9239},[1966],[1963,9241,9243],{"className":9242},[1970],[1972,9244,9245],{"xmlns":1974},[1976,9246,9247,9263],{},[1979,9248,9249,9255,9257],{},[2034,9250,9251,9253],{},[1982,9252,2038],{},[2040,9254,2052],{},[2026,9256,9051],{},[2034,9258,9259,9261],{},[1982,9260,2329],{},[2040,9262,2042],{},[1986,9264,9265],{"encoding":1988},"m_2 \\to w_1",[1963,9267,9269,9324],{"className":9268,"ariaHidden":1993},[1992],[1963,9270,9272,9275,9315,9318,9321],{"className":9271},[1997],[1963,9273],{"className":9274,"style":2814},[2001],[1963,9276,9278,9281],{"className":9277},[2006],[1963,9279,2038],{"className":9280},[2006,2007],[1963,9282,9284],{"className":9283},[2116],[1963,9285,9287,9307],{"className":9286},[2120,2121],[1963,9288,9290,9304],{"className":9289},[2125],[1963,9291,9293],{"className":9292,"style":2130},[2129],[1963,9294,9295,9298],{"style":2133},[1963,9296],{"className":9297,"style":2138},[2137],[1963,9299,9301],{"className":9300},[2142,2143,2144,2145],[1963,9302,2052],{"className":9303},[2006,2145],[1963,9305,2153],{"className":9306},[2152],[1963,9308,9310],{"className":9309},[2125],[1963,9311,9313],{"className":9312,"style":2160},[2129],[1963,9314],{},[1963,9316],{"className":9317,"style":2088},[2087],[1963,9319,9051],{"className":9320},[2092],[1963,9322],{"className":9323,"style":2088},[2087],[1963,9325,9327,9330],{"className":9326},[1997],[1963,9328],{"className":9329,"style":2814},[2001],[1963,9331,9333,9336],{"className":9332},[2006],[1963,9334,2329],{"className":9335,"style":2394},[2006,2007],[1963,9337,9339],{"className":9338},[2116],[1963,9340,9342,9362],{"className":9341},[2120,2121],[1963,9343,9345,9359],{"className":9344},[2125],[1963,9346,9348],{"className":9347,"style":2130},[2129],[1963,9349,9350,9353],{"style":2409},[1963,9351],{"className":9352,"style":2138},[2137],[1963,9354,9356],{"className":9355},[2142,2143,2144,2145],[1963,9357,2042],{"className":9358},[2006,2145],[1963,9360,2153],{"className":9361},[2152],[1963,9363,9365],{"className":9364},[2125],[1963,9366,9368],{"className":9367,"style":2160},[2129],[1963,9369],{},[1963,9371,9373,9390],{"className":9372},[1966],[1963,9374,9376],{"className":9375},[1970],[1972,9377,9378],{"xmlns":1974},[1976,9379,9380,9388],{},[1979,9381,9382],{},[2034,9383,9384,9386],{},[1982,9385,2329],{},[2040,9387,2042],{},[1986,9389,5462],{"encoding":1988},[1963,9391,9393],{"className":9392,"ariaHidden":1993},[1992],[1963,9394,9396,9399],{"className":9395},[1997],[1963,9397],{"className":9398,"style":2814},[2001],[1963,9400,9402,9405],{"className":9401},[2006],[1963,9403,2329],{"className":9404,"style":2394},[2006,2007],[1963,9406,9408],{"className":9407},[2116],[1963,9409,9411,9431],{"className":9410},[2120,2121],[1963,9412,9414,9428],{"className":9413},[2125],[1963,9415,9417],{"className":9416,"style":2130},[2129],[1963,9418,9419,9422],{"style":2409},[1963,9420],{"className":9421,"style":2138},[2137],[1963,9423,9425],{"className":9424},[2142,2143,2144,2145],[1963,9426,2042],{"className":9427},[2006,2145],[1963,9429,2153],{"className":9430},[2152],[1963,9432,9434],{"className":9433},[2125],[1963,9435,9437],{"className":9436,"style":2160},[2129],[1963,9438],{}," 接受",[1808,9441,9442,1957,9575,9644,9645,9714,9715,9785,9786,9855,9856],{},[1963,9443,9445,9471],{"className":9444},[1966],[1963,9446,9448],{"className":9447},[1970],[1972,9449,9450],{"xmlns":1974},[1976,9451,9452,9468],{},[1979,9453,9454,9460,9462],{},[2034,9455,9456,9458],{},[1982,9457,2038],{},[2040,9459,7495],{},[2026,9461,9051],{},[2034,9463,9464,9466],{},[1982,9465,2329],{},[2040,9467,2042],{},[1986,9469,9470],{"encoding":1988},"m_3 \\to w_1",[1963,9472,9474,9529],{"className":9473,"ariaHidden":1993},[1992],[1963,9475,9477,9480,9520,9523,9526],{"className":9476},[1997],[1963,9478],{"className":9479,"style":2814},[2001],[1963,9481,9483,9486],{"className":9482},[2006],[1963,9484,2038],{"className":9485},[2006,2007],[1963,9487,9489],{"className":9488},[2116],[1963,9490,9492,9512],{"className":9491},[2120,2121],[1963,9493,9495,9509],{"className":9494},[2125],[1963,9496,9498],{"className":9497,"style":2130},[2129],[1963,9499,9500,9503],{"style":2133},[1963,9501],{"className":9502,"style":2138},[2137],[1963,9504,9506],{"className":9505},[2142,2143,2144,2145],[1963,9507,7495],{"className":9508},[2006,2145],[1963,9510,2153],{"className":9511},[2152],[1963,9513,9515],{"className":9514},[2125],[1963,9516,9518],{"className":9517,"style":2160},[2129],[1963,9519],{},[1963,9521],{"className":9522,"style":2088},[2087],[1963,9524,9051],{"className":9525},[2092],[1963,9527],{"className":9528,"style":2088},[2087],[1963,9530,9532,9535],{"className":9531},[1997],[1963,9533],{"className":9534,"style":2814},[2001],[1963,9536,9538,9541],{"className":9537},[2006],[1963,9539,2329],{"className":9540,"style":2394},[2006,2007],[1963,9542,9544],{"className":9543},[2116],[1963,9545,9547,9567],{"className":9546},[2120,2121],[1963,9548,9550,9564],{"className":9549},[2125],[1963,9551,9553],{"className":9552,"style":2130},[2129],[1963,9554,9555,9558],{"style":2409},[1963,9556],{"className":9557,"style":2138},[2137],[1963,9559,9561],{"className":9560},[2142,2143,2144,2145],[1963,9562,2042],{"className":9563},[2006,2145],[1963,9565,2153],{"className":9566},[2152],[1963,9568,9570],{"className":9569},[2125],[1963,9571,9573],{"className":9572,"style":2160},[2129],[1963,9574],{},[1963,9576,9578,9595],{"className":9577},[1966],[1963,9579,9581],{"className":9580},[1970],[1972,9582,9583],{"xmlns":1974},[1976,9584,9585,9593],{},[1979,9586,9587],{},[2034,9588,9589,9591],{},[1982,9590,2329],{},[2040,9592,2042],{},[1986,9594,5462],{"encoding":1988},[1963,9596,9598],{"className":9597,"ariaHidden":1993},[1992],[1963,9599,9601,9604],{"className":9600},[1997],[1963,9602],{"className":9603,"style":2814},[2001],[1963,9605,9607,9610],{"className":9606},[2006],[1963,9608,2329],{"className":9609,"style":2394},[2006,2007],[1963,9611,9613],{"className":9612},[2116],[1963,9614,9616,9636],{"className":9615},[2120,2121],[1963,9617,9619,9633],{"className":9618},[2125],[1963,9620,9622],{"className":9621,"style":2130},[2129],[1963,9623,9624,9627],{"style":2409},[1963,9625],{"className":9626,"style":2138},[2137],[1963,9628,9630],{"className":9629},[2142,2143,2144,2145],[1963,9631,2042],{"className":9632},[2006,2145],[1963,9634,2153],{"className":9635},[2152],[1963,9637,9639],{"className":9638},[2125],[1963,9640,9642],{"className":9641,"style":2160},[2129],[1963,9643],{}," 比较 ",[1963,9646,9648,9665],{"className":9647},[1966],[1963,9649,9651],{"className":9650},[1970],[1972,9652,9653],{"xmlns":1974},[1976,9654,9655,9663],{},[1979,9656,9657],{},[2034,9658,9659,9661],{},[1982,9660,2038],{},[2040,9662,2052],{},[1986,9664,5740],{"encoding":1988},[1963,9666,9668],{"className":9667,"ariaHidden":1993},[1992],[1963,9669,9671,9674],{"className":9670},[1997],[1963,9672],{"className":9673,"style":2814},[2001],[1963,9675,9677,9680],{"className":9676},[2006],[1963,9678,2038],{"className":9679},[2006,2007],[1963,9681,9683],{"className":9682},[2116],[1963,9684,9686,9706],{"className":9685},[2120,2121],[1963,9687,9689,9703],{"className":9688},[2125],[1963,9690,9692],{"className":9691,"style":2130},[2129],[1963,9693,9694,9697],{"style":2133},[1963,9695],{"className":9696,"style":2138},[2137],[1963,9698,9700],{"className":9699},[2142,2143,2144,2145],[1963,9701,2052],{"className":9702},[2006,2145],[1963,9704,2153],{"className":9705},[2152],[1963,9707,9709],{"className":9708},[2125],[1963,9710,9712],{"className":9711,"style":2160},[2129],[1963,9713],{}," vs. ",[1963,9716,9718,9736],{"className":9717},[1966],[1963,9719,9721],{"className":9720},[1970],[1972,9722,9723],{"xmlns":1974},[1976,9724,9725,9733],{},[1979,9726,9727],{},[2034,9728,9729,9731],{},[1982,9730,2038],{},[2040,9732,7495],{},[1986,9734,9735],{"encoding":1988},"m_3",[1963,9737,9739],{"className":9738,"ariaHidden":1993},[1992],[1963,9740,9742,9745],{"className":9741},[1997],[1963,9743],{"className":9744,"style":2814},[2001],[1963,9746,9748,9751],{"className":9747},[2006],[1963,9749,2038],{"className":9750},[2006,2007],[1963,9752,9754],{"className":9753},[2116],[1963,9755,9757,9777],{"className":9756},[2120,2121],[1963,9758,9760,9774],{"className":9759},[2125],[1963,9761,9763],{"className":9762,"style":2130},[2129],[1963,9764,9765,9768],{"style":2133},[1963,9766],{"className":9767,"style":2138},[2137],[1963,9769,9771],{"className":9770},[2142,2143,2144,2145],[1963,9772,7495],{"className":9773},[2006,2145],[1963,9775,2153],{"className":9776},[2152],[1963,9778,9780],{"className":9779},[2125],[1963,9781,9783],{"className":9782,"style":2160},[2129],[1963,9784],{},"，偏好 ",[1963,9787,9789,9806],{"className":9788},[1966],[1963,9790,9792],{"className":9791},[1970],[1972,9793,9794],{"xmlns":1974},[1976,9795,9796,9804],{},[1979,9797,9798],{},[2034,9799,9800,9802],{},[1982,9801,2038],{},[2040,9803,2052],{},[1986,9805,5740],{"encoding":1988},[1963,9807,9809],{"className":9808,"ariaHidden":1993},[1992],[1963,9810,9812,9815],{"className":9811},[1997],[1963,9813],{"className":9814,"style":2814},[2001],[1963,9816,9818,9821],{"className":9817},[2006],[1963,9819,2038],{"className":9820},[2006,2007],[1963,9822,9824],{"className":9823},[2116],[1963,9825,9827,9847],{"className":9826},[2120,2121],[1963,9828,9830,9844],{"className":9829},[2125],[1963,9831,9833],{"className":9832,"style":2130},[2129],[1963,9834,9835,9838],{"style":2133},[1963,9836],{"className":9837,"style":2138},[2137],[1963,9839,9841],{"className":9840},[2142,2143,2144,2145],[1963,9842,2052],{"className":9843},[2006,2145],[1963,9845,2153],{"className":9846},[2152],[1963,9848,9850],{"className":9849},[2125],[1963,9851,9853],{"className":9852,"style":2160},[2129],[1963,9854],{},"，拒绝 ",[1963,9857,9859,9876],{"className":9858},[1966],[1963,9860,9862],{"className":9861},[1970],[1972,9863,9864],{"xmlns":1974},[1976,9865,9866,9874],{},[1979,9867,9868],{},[2034,9869,9870,9872],{},[1982,9871,2038],{},[2040,9873,7495],{},[1986,9875,9735],{"encoding":1988},[1963,9877,9879],{"className":9878,"ariaHidden":1993},[1992],[1963,9880,9882,9885],{"className":9881},[1997],[1963,9883],{"className":9884,"style":2814},[2001],[1963,9886,9888,9891],{"className":9887},[2006],[1963,9889,2038],{"className":9890},[2006,2007],[1963,9892,9894],{"className":9893},[2116],[1963,9895,9897,9917],{"className":9896},[2120,2121],[1963,9898,9900,9914],{"className":9899},[2125],[1963,9901,9903],{"className":9902,"style":2130},[2129],[1963,9904,9905,9908],{"style":2133},[1963,9906],{"className":9907,"style":2138},[2137],[1963,9909,9911],{"className":9910},[2142,2143,2144,2145],[1963,9912,7495],{"className":9913},[2006,2145],[1963,9915,2153],{"className":9916},[2152],[1963,9918,9920],{"className":9919},[2125],[1963,9921,9923],{"className":9922,"style":2160},[2129],[1963,9924],{},[1798,9926,9927,9928,10180,10181,10250],{},"当前匹配：",[1963,9929,9931,9981],{"className":9930},[1966],[1963,9932,9934],{"className":9933},[1970],[1972,9935,9936],{"xmlns":1974},[1976,9937,9938,9978],{},[1979,9939,9940,9942,9948,9950,9956,9958,9960,9962,9968,9970,9976],{},[2026,9941,2643],{"stretchy":2031},[2034,9943,9944,9946],{},[1982,9945,2038],{},[2040,9947,2042],{},[2026,9949,2045],{"separator":1993},[2034,9951,9952,9954],{},[1982,9953,2329],{},[2040,9955,2052],{},[2026,9957,2653],{"stretchy":2031},[2026,9959,2045],{"separator":1993},[2026,9961,2643],{"stretchy":2031},[2034,9963,9964,9966],{},[1982,9965,2038],{},[2040,9967,2052],{},[2026,9969,2045],{"separator":1993},[2034,9971,9972,9974],{},[1982,9973,2329],{},[2040,9975,2042],{},[2026,9977,2653],{"stretchy":2031},[1986,9979,9980],{"encoding":1988},"(m_1, w_2), (m_2, w_1)",[1963,9982,9984],{"className":9983,"ariaHidden":1993},[1992],[1963,9985,9987,9990,9993,10033,10036,10039,10079,10082,10085,10088,10091,10131,10134,10137,10177],{"className":9986},[1997],[1963,9988],{"className":9989,"style":2102},[2001],[1963,9991,2643],{"className":9992},[2106],[1963,9994,9996,9999],{"className":9995},[2006],[1963,9997,2038],{"className":9998},[2006,2007],[1963,10000,10002],{"className":10001},[2116],[1963,10003,10005,10025],{"className":10004},[2120,2121],[1963,10006,10008,10022],{"className":10007},[2125],[1963,10009,10011],{"className":10010,"style":2130},[2129],[1963,10012,10013,10016],{"style":2133},[1963,10014],{"className":10015,"style":2138},[2137],[1963,10017,10019],{"className":10018},[2142,2143,2144,2145],[1963,10020,2042],{"className":10021},[2006,2145],[1963,10023,2153],{"className":10024},[2152],[1963,10026,10028],{"className":10027},[2125],[1963,10029,10031],{"className":10030,"style":2160},[2129],[1963,10032],{},[1963,10034,2045],{"className":10035},[2166],[1963,10037],{"className":10038,"style":2170},[2087],[1963,10040,10042,10045],{"className":10041},[2006],[1963,10043,2329],{"className":10044,"style":2394},[2006,2007],[1963,10046,10048],{"className":10047},[2116],[1963,10049,10051,10071],{"className":10050},[2120,2121],[1963,10052,10054,10068],{"className":10053},[2125],[1963,10055,10057],{"className":10056,"style":2130},[2129],[1963,10058,10059,10062],{"style":2409},[1963,10060],{"className":10061,"style":2138},[2137],[1963,10063,10065],{"className":10064},[2142,2143,2144,2145],[1963,10066,2052],{"className":10067},[2006,2145],[1963,10069,2153],{"className":10070},[2152],[1963,10072,10074],{"className":10073},[2125],[1963,10075,10077],{"className":10076,"style":2160},[2129],[1963,10078],{},[1963,10080,2653],{"className":10081},[2274],[1963,10083,2045],{"className":10084},[2166],[1963,10086],{"className":10087,"style":2170},[2087],[1963,10089,2643],{"className":10090},[2106],[1963,10092,10094,10097],{"className":10093},[2006],[1963,10095,2038],{"className":10096},[2006,2007],[1963,10098,10100],{"className":10099},[2116],[1963,10101,10103,10123],{"className":10102},[2120,2121],[1963,10104,10106,10120],{"className":10105},[2125],[1963,10107,10109],{"className":10108,"style":2130},[2129],[1963,10110,10111,10114],{"style":2133},[1963,10112],{"className":10113,"style":2138},[2137],[1963,10115,10117],{"className":10116},[2142,2143,2144,2145],[1963,10118,2052],{"className":10119},[2006,2145],[1963,10121,2153],{"className":10122},[2152],[1963,10124,10126],{"className":10125},[2125],[1963,10127,10129],{"className":10128,"style":2160},[2129],[1963,10130],{},[1963,10132,2045],{"className":10133},[2166],[1963,10135],{"className":10136,"style":2170},[2087],[1963,10138,10140,10143],{"className":10139},[2006],[1963,10141,2329],{"className":10142,"style":2394},[2006,2007],[1963,10144,10146],{"className":10145},[2116],[1963,10147,10149,10169],{"className":10148},[2120,2121],[1963,10150,10152,10166],{"className":10151},[2125],[1963,10153,10155],{"className":10154,"style":2130},[2129],[1963,10156,10157,10160],{"style":2409},[1963,10158],{"className":10159,"style":2138},[2137],[1963,10161,10163],{"className":10162},[2142,2143,2144,2145],[1963,10164,2042],{"className":10165},[2006,2145],[1963,10167,2153],{"className":10168},[2152],[1963,10170,10172],{"className":10171},[2125],[1963,10173,10175],{"className":10174,"style":2160},[2129],[1963,10176],{},[1963,10178,2653],{"className":10179},[2274],"，",[1963,10182,10184,10201],{"className":10183},[1966],[1963,10185,10187],{"className":10186},[1970],[1972,10188,10189],{"xmlns":1974},[1976,10190,10191,10199],{},[1979,10192,10193],{},[2034,10194,10195,10197],{},[1982,10196,2038],{},[2040,10198,7495],{},[1986,10200,9735],{"encoding":1988},[1963,10202,10204],{"className":10203,"ariaHidden":1993},[1992],[1963,10205,10207,10210],{"className":10206},[1997],[1963,10208],{"className":10209,"style":2814},[2001],[1963,10211,10213,10216],{"className":10212},[2006],[1963,10214,2038],{"className":10215},[2006,2007],[1963,10217,10219],{"className":10218},[2116],[1963,10220,10222,10242],{"className":10221},[2120,2121],[1963,10223,10225,10239],{"className":10224},[2125],[1963,10226,10228],{"className":10227,"style":2130},[2129],[1963,10229,10230,10233],{"style":2133},[1963,10231],{"className":10232,"style":2138},[2137],[1963,10234,10236],{"className":10235},[2142,2143,2144,2145],[1963,10237,7495],{"className":10238},[2006,2145],[1963,10240,2153],{"className":10241},[2152],[1963,10243,10245],{"className":10244},[2125],[1963,10246,10248],{"className":10247,"style":2160},[2129],[1963,10249],{}," 未匹配",[1798,10252,10253,1957],{},[1850,10254,10255],{},"第2轮",[1805,10257,10258,10400],{},[1808,10259,10260,10329,10330,10399],{},[1963,10261,10263,10280],{"className":10262},[1966],[1963,10264,10266],{"className":10265},[1970],[1972,10267,10268],{"xmlns":1974},[1976,10269,10270,10278],{},[1979,10271,10272],{},[2034,10273,10274,10276],{},[1982,10275,2038],{},[2040,10277,7495],{},[1986,10279,9735],{"encoding":1988},[1963,10281,10283],{"className":10282,"ariaHidden":1993},[1992],[1963,10284,10286,10289],{"className":10285},[1997],[1963,10287],{"className":10288,"style":2814},[2001],[1963,10290,10292,10295],{"className":10291},[2006],[1963,10293,2038],{"className":10294},[2006,2007],[1963,10296,10298],{"className":10297},[2116],[1963,10299,10301,10321],{"className":10300},[2120,2121],[1963,10302,10304,10318],{"className":10303},[2125],[1963,10305,10307],{"className":10306,"style":2130},[2129],[1963,10308,10309,10312],{"style":2133},[1963,10310],{"className":10311,"style":2138},[2137],[1963,10313,10315],{"className":10314},[2142,2143,2144,2145],[1963,10316,7495],{"className":10317},[2006,2145],[1963,10319,2153],{"className":10320},[2152],[1963,10322,10324],{"className":10323},[2125],[1963,10325,10327],{"className":10326,"style":2160},[2129],[1963,10328],{}," 向次优 ",[1963,10331,10333,10350],{"className":10332},[1966],[1963,10334,10336],{"className":10335},[1970],[1972,10337,10338],{"xmlns":1974},[1976,10339,10340,10348],{},[1979,10341,10342],{},[2034,10343,10344,10346],{},[1982,10345,2329],{},[2040,10347,2052],{},[1986,10349,5533],{"encoding":1988},[1963,10351,10353],{"className":10352,"ariaHidden":1993},[1992],[1963,10354,10356,10359],{"className":10355},[1997],[1963,10357],{"className":10358,"style":2814},[2001],[1963,10360,10362,10365],{"className":10361},[2006],[1963,10363,2329],{"className":10364,"style":2394},[2006,2007],[1963,10366,10368],{"className":10367},[2116],[1963,10369,10371,10391],{"className":10370},[2120,2121],[1963,10372,10374,10388],{"className":10373},[2125],[1963,10375,10377],{"className":10376,"style":2130},[2129],[1963,10378,10379,10382],{"style":2409},[1963,10380],{"className":10381,"style":2138},[2137],[1963,10383,10385],{"className":10384},[2142,2143,2144,2145],[1963,10386,2052],{"className":10387},[2006,2145],[1963,10389,2153],{"className":10390},[2152],[1963,10392,10394],{"className":10393},[2125],[1963,10395,10397],{"className":10396,"style":2160},[2129],[1963,10398],{}," 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向再次优 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接受（当前未匹配）",[1798,11291,11292,1957,11295],{},[1850,11293,11294],{},"最终匹配",[1963,11296,11298,11376],{"className":11297},[1966],[1963,11299,11301],{"className":11300},[1970],[1972,11302,11303],{"xmlns":1974},[1976,11304,11305,11373],{},[1979,11306,11307,11309,11311,11313,11315,11321,11323,11329,11331,11333,11335,11341,11343,11349,11351,11353,11355,11361,11363,11369,11371],{},[1982,11308,2572],{},[2026,11310,2028],{},[2026,11312,2032],{"stretchy":2031},[2026,11314,2643],{"stretchy":2031},[2034,11316,11317,11319],{},[1982,11318,2038],{},[2040,11320,2042],{},[2026,11322,2045],{"separator":1993},[2034,11324,11325,11327],{},[1982,11326,2329],{},[2040,11328,2052],{},[2026,11330,2653],{"stretchy":2031},[2026,11332,2045],{"separator":1993},[2026,11334,2643],{"stretchy":2031},[2034,11336,11337,11339],{},[1982,11338,2038],{},[2040,11340,2052],{},[2026,11342,2045],{"separator":1993},[2034,11344,11345,11347],{},[1982,11346,2329],{},[2040,11348,2042],{},[2026,11350,2653],{"stretchy":2031},[2026,11352,2045],{"separator":1993},[2026,11354,2643],{"stretchy":2031},[2034,11356,11357,11359],{},[1982,11358,2038],{},[2040,11360,7495],{},[2026,11362,2045],{"separator":1993},[2034,11364,11365,11367],{},[1982,11366,2329],{},[2040,11368,7495],{},[2026,11370,2653],{"stretchy":2031},[2026,11372,2068],{"stretchy":2031},[1986,11374,11375],{"encoding":1988},"\\mu = \\{(m_1, w_2), (m_2, w_1), (m_3, w_3)\\}",[1963,11377,11379,11397],{"className":11378,"ariaHidden":1993},[1992],[1963,11380,11382,11385,11388,11391,11394],{"className":11381},[1997],[1963,11383],{"className":11384,"style":2585},[2001],[1963,11386,2572],{"className":11387},[2006,2007],[1963,11389],{"className":11390,"style":2088},[2087],[1963,11392,2028],{"className":11393},[2092],[1963,11395],{"className":11396,"style":2088},[2087],[1963,11398,11400,11403,11406,11446,11449,11452,11492,11495,11498,11501,11504,11544,11547,11550,11590,11593,11596,11599,11602,11642,11645,11648,11688],{"className":11399},[1997],[1963,11401],{"className":11402,"style":2102},[2001],[1963,11404,5044],{"className":11405},[2106],[1963,11407,11409,11412],{"className":11408},[2006],[1963,11410,2038],{"className":11411},[2006,2007],[1963,11413,11415],{"className":11414},[2116],[1963,11416,11418,11438],{"className":11417},[2120,2121],[1963,11419,11421,11435],{"className":11420},[2125],[1963,11422,11424],{"className":11423,"style":2130},[2129],[1963,11425,11426,11429],{"style":2133},[1963,11427],{"className":11428,"style":2138},[2137],[1963,11430,11432],{"className":11431},[2142,2143,2144,2145],[1963,11433,2042],{"className":11434},[2006,2145],[1963,11436,2153],{"className":11437},[2152],[1963,11439,11441],{"className":11440},[2125],[1963,11442,11444],{"className":11443,"style":2160},[2129],[1963,11445],{},[1963,11447,2045],{"className":11448},[2166],[1963,11450],{"className":11451,"style":2170},[2087],[1963,11453,11455,11458],{"className":11454},[2006],[1963,11456,2329],{"className":11457,"style":2394},[2006,2007],[1963,11459,11461],{"className":11460},[2116],[1963,11462,11464,11484],{"className":11463},[2120,2121],[1963,11465,11467,11481],{"className":11466},[2125],[1963,11468,11470],{"className":11469,"style":2130},[2129],[1963,11471,11472,11475],{"style":2409},[1963,11473],{"className":11474,"style":2138},[2137],[1963,11476,11478],{"className":11477},[2142,2143,2144,2145],[1963,11479,2052],{"className":11480},[2006,2145],[1963,11482,2153],{"className":11483},[2152],[1963,11485,11487],{"className":11486},[2125],[1963,11488,11490],{"className":11489,"style":2160},[2129],[1963,11491],{},[1963,11493,2653],{"className":11494},[2274],[1963,11496,2045],{"className":11497},[2166],[1963,11499],{"className":11500,"style":2170},[2087],[1963,11502,2643],{"className":11503},[2106],[1963,11505,11507,11510],{"className":11506},[2006],[1963,11508,2038],{"className":11509},[2006,2007],[1963,11511,11513],{"className":11512},[2116],[1963,11514,11516,11536],{"className":11515},[2120,2121],[1963,11517,11519,11533],{"className":11518},[2125],[1963,11520,11522],{"className":11521,"style":2130},[2129],[1963,11523,11524,11527],{"style":2133},[1963,11525],{"className":11526,"style":2138},[2137],[1963,11528,11530],{"className":11529},[2142,2143,2144,2145],[1963,11531,2052],{"className":11532},[2006,2145],[1963,11534,2153],{"className":11535},[2152],[1963,11537,11539],{"className":11538},[2125],[1963,11540,11542],{"className":11541,"style":2160},[2129],[1963,11543],{},[1963,11545,2045],{"className":11546},[2166],[1963,11548],{"className":11549,"style":2170},[2087],[1963,11551,11553,11556],{"className":11552},[2006],[1963,11554,2329],{"className":11555,"style":2394},[2006,2007],[1963,11557,11559],{"className":11558},[2116],[1963,11560,11562,11582],{"className":11561},[2120,2121],[1963,11563,11565,11579],{"className":11564},[2125],[1963,11566,11568],{"className":11567,"style":2130},[2129],[1963,11569,11570,11573],{"style":2409},[1963,11571],{"className":11572,"style":2138},[2137],[1963,11574,11576],{"className":11575},[2142,2143,2144,2145],[1963,11577,2042],{"className":11578},[2006,2145],[1963,11580,2153],{"className":11581},[2152],[1963,11583,11585],{"className":11584},[2125],[1963,11586,11588],{"className":11587,"style":2160},[2129],[1963,11589],{},[1963,11591,2653],{"className":11592},[2274],[1963,11594,2045],{"className":11595},[2166],[1963,11597],{"className":11598,"style":2170},[2087],[1963,11600,2643],{"className":11601},[2106],[1963,11603,11605,11608],{"className":11604},[2006],[1963,11606,2038],{"className":11607},[2006,2007],[1963,11609,11611],{"className":11610},[2116],[1963,11612,11614,11634],{"className":11613},[2120,2121],[1963,11615,11617,11631],{"className":11616},[2125],[1963,11618,11620],{"className":11619,"style":2130},[2129],[1963,11621,11622,11625],{"style":2133},[1963,11623],{"className":11624,"style":2138},[2137],[1963,11626,11628],{"className":11627},[2142,2143,2144,2145],[1963,11629,7495],{"className":11630},[2006,2145],[1963,11632,2153],{"className":11633},[2152],[1963,11635,11637],{"className":11636},[2125],[1963,11638,11640],{"className":11639,"style":2160},[2129],[1963,11641],{},[1963,11643,2045],{"className":11644},[2166],[1963,11646],{"className":11647,"style":2170},[2087],[1963,11649,11651,11654],{"className":11650},[2006],[1963,11652,2329],{"className":11653,"style":2394},[2006,2007],[1963,11655,11657],{"className":11656},[2116],[1963,11658,11660,11680],{"className":11659},[2120,2121],[1963,11661,11663,11677],{"className":11662},[2125],[1963,11664,11666],{"className":11665,"style":2130},[2129],[1963,11667,11668,11671],{"style":2409},[1963,11669],{"className":11670,"style":2138},[2137],[1963,11672,11674],{"className":11673},[2142,2143,2144,2145],[1963,11675,7495],{"className":11676},[2006,2145],[1963,11678,2153],{"className":11679},[2152],[1963,11681,11683],{"className":11682},[2125],[1963,11684,11686],{"className":11685,"style":2160},[2129],[1963,11687],{},[1963,11689,5232],{"className":11690},[2274],[1925,11692,11694],{"id":11693},"_23-算法的性质","2.3 算法的性质",[1798,11696,11697,11700],{},[1850,11698,11699],{},"定理1（终止性）","：算法在有限步内终止。",[1798,11702,11703,1957],{},[1850,11704,11705],{},"证明",[1805,11707,11708,11711,11714,11780],{},[1808,11709,11710],{},"每轮至少有一个新的拒绝",[1808,11712,11713],{},"每个男性最多被每个女性拒绝一次",[1808,11715,11716,11717,11779],{},"最多 ",[1963,11718,11720,11739],{"className":11719},[1966],[1963,11721,11723],{"className":11722},[1970],[1972,11724,11725],{"xmlns":1974},[1976,11726,11727,11736],{},[1979,11728,11729],{},[11730,11731,11732,11734],"msup",{},[1982,11733,1984],{},[2040,11735,2052],{},[1986,11737,11738],{"encoding":1988},"N^2",[1963,11740,11742],{"className":11741,"ariaHidden":1993},[1992],[1963,11743,11745,11749],{"className":11744},[1997],[1963,11746],{"className":11747,"style":11748},[2001],"height:0.8141em;",[1963,11750,11752,11755],{"className":11751},[2006],[1963,11753,1984],{"className":11754,"style":2008},[2006,2007],[1963,11756,11758],{"className":11757},[2116],[1963,11759,11761],{"className":11760},[2120],[1963,11762,11764],{"className":11763},[2125],[1963,11765,11767],{"className":11766,"style":11748},[2129],[1963,11768,11770,11773],{"style":11769},"top:-3.063em;margin-right:0.05em;",[1963,11771],{"className":11772,"style":2138},[2137],[1963,11774,11776],{"className":11775},[2142,2143,2144,2145],[1963,11777,2052],{"className":11778},[2006,2145]," 次拒绝",[1808,11781,11782],{},"因此算法必然终止",[1798,11784,11785,11788],{},[1850,11786,11787],{},"定理2（稳定性）","：算法产生的匹配是稳定的。",[1798,11790,11791,11793,11794,11846],{},[1850,11792,11705],{},"（反证法）：\n假设存在阻塞对 ",[1963,11795,11797,11819],{"className":11796},[1966],[1963,11798,11800],{"className":11799},[1970],[1972,11801,11802],{"xmlns":1974},[1976,11803,11804,11816],{},[1979,11805,11806,11808,11810,11812,11814],{},[2026,11807,2643],{"stretchy":2031},[1982,11809,2038],{},[2026,11811,2045],{"separator":1993},[1982,11813,2329],{},[2026,11815,2653],{"stretchy":2031},[1986,11817,11818],{"encoding":1988},"(m, w)",[1963,11820,11822],{"className":11821,"ariaHidden":1993},[1992],[1963,11823,11825,11828,11831,11834,11837,11840,11843],{"className":11824},[1997],[1963,11826],{"className":11827,"style":2102},[2001],[1963,11829,2643],{"className":11830},[2106],[1963,11832,2038],{"className":11833},[2006,2007],[1963,11835,2045],{"className":11836},[2166],[1963,11838],{"className":11839,"style":2170},[2087],[1963,11841,2329],{"className":11842,"style":2394},[2006,2007],[1963,11844,2653],{"className":11845},[2274],"，即：",[1888,11848,11849,11952],{},[1808,11850,11851,3436,11880,5512,11908],{},[1963,11852,11854,11867],{"className":11853},[1966],[1963,11855,11857],{"className":11856},[1970],[1972,11858,11859],{"xmlns":1974},[1976,11860,11861,11865],{},[1979,11862,11863],{},[1982,11864,2038],{},[1986,11866,2038],{"encoding":1988},[1963,11868,11870],{"className":11869,"ariaHidden":1993},[1992],[1963,11871,11873,11877],{"className":11872},[1997],[1963,11874],{"className":11875,"style":11876},[2001],"height:0.4306em;",[1963,11878,2038],{"className":11879},[2006,2007],[1963,11881,11883,11896],{"className":11882},[1966],[1963,11884,11886],{"className":11885},[1970],[1972,11887,11888],{"xmlns":1974},[1976,11889,11890,11894],{},[1979,11891,11892],{},[1982,11893,2329],{},[1986,11895,2329],{"encoding":1988},[1963,11897,11899],{"className":11898,"ariaHidden":1993},[1992],[1963,11900,11902,11905],{"className":11901},[1997],[1963,11903],{"className":11904,"style":11876},[2001],[1963,11906,2329],{"className":11907,"style":2394},[2006,2007],[1963,11909,11911,11931],{"className":11910},[1966],[1963,11912,11914],{"className":11913},[1970],[1972,11915,11916],{"xmlns":1974},[1976,11917,11918,11928],{},[1979,11919,11920,11922,11924,11926],{},[1982,11921,2572],{},[2026,11923,2643],{"stretchy":2031},[1982,11925,2038],{},[2026,11927,2653],{"stretchy":2031},[1986,11929,11930],{"encoding":1988},"\\mu(m)",[1963,11932,11934],{"className":11933,"ariaHidden":1993},[1992],[1963,11935,11937,11940,11943,11946,11949],{"className":11936},[1997],[1963,11938],{"className":11939,"style":2102},[2001],[1963,11941,2572],{"className":11942},[2006,2007],[1963,11944,2643],{"className":11945},[2106],[1963,11947,2038],{"className":11948},[2006,2007],[1963,11950,2653],{"className":11951},[2274],[1808,11953,11954,3436,11982,5512,12010],{},[1963,11955,11957,11970],{"className":11956},[1966],[1963,11958,11960],{"className":11959},[1970],[1972,11961,11962],{"xmlns":1974},[1976,11963,11964,11968],{},[1979,11965,11966],{},[1982,11967,2329],{},[1986,11969,2329],{"encoding":1988},[1963,11971,11973],{"className":11972,"ariaHidden":1993},[1992],[1963,11974,11976,11979],{"className":11975},[1997],[1963,11977],{"className":11978,"style":11876},[2001],[1963,11980,2329],{"className":11981,"style":2394},[2006,2007],[1963,11983,11985,11998],{"className":11984},[1966],[1963,11986,11988],{"className":11987},[1970],[1972,11989,11990],{"xmlns":1974},[1976,11991,11992,11996],{},[1979,11993,11994],{},[1982,11995,2038],{},[1986,11997,2038],{"encoding":1988},[1963,11999,12001],{"className":12000,"ariaHidden":1993},[1992],[1963,12002,12004,12007],{"className":12003},[1997],[1963,12005],{"className":12006,"style":11876},[2001],[1963,12008,2038],{"className":12009},[2006,2007],[1963,12011,12013,12033],{"className":12012},[1966],[1963,12014,12016],{"className":12015},[1970],[1972,12017,12018],{"xmlns":1974},[1976,12019,12020,12030],{},[1979,12021,12022,12024,12026,12028],{},[1982,12023,2572],{},[2026,12025,2643],{"stretchy":2031},[1982,12027,2329],{},[2026,12029,2653],{"stretchy":2031},[1986,12031,12032],{"encoding":1988},"\\mu(w)",[1963,12034,12036],{"className":12035,"ariaHidden":1993},[1992],[1963,12037,12039,12042,12045,12048,12051],{"className":12038},[1997],[1963,12040],{"className":12041,"style":2102},[2001],[1963,12043,2572],{"className":12044},[2006,2007],[1963,12046,2643],{"className":12047},[2106],[1963,12049,2329],{"className":12050,"style":2394},[2006,2007],[1963,12052,2653],{"className":12053},[2274],[1798,12055,12056,12057,12085],{},"由于算法中 ",[1963,12058,12060,12073],{"className":12059},[1966],[1963,12061,12063],{"className":12062},[1970],[1972,12064,12065],{"xmlns":1974},[1976,12066,12067,12071],{},[1979,12068,12069],{},[1982,12070,2038],{},[1986,12072,2038],{"encoding":1988},[1963,12074,12076],{"className":12075,"ariaHidden":1993},[1992],[1963,12077,12079,12082],{"className":12078},[1997],[1963,12080],{"className":12081,"style":11876},[2001],[1963,12083,2038],{"className":12084},[2006,2007]," 按偏好顺序求婚：",[1805,12087,12088,12293],{},[1808,12089,12090,12091,3436,12119,5512,12147,12190,12191,12219,12220,12263,12264,12292],{},"如果 ",[1963,12092,12094,12107],{"className":12093},[1966],[1963,12095,12097],{"className":12096},[1970],[1972,12098,12099],{"xmlns":1974},[1976,12100,12101,12105],{},[1979,12102,12103],{},[1982,12104,2038],{},[1986,12106,2038],{"encoding":1988},[1963,12108,12110],{"className":12109,"ariaHidden":1993},[1992],[1963,12111,12113,12116],{"className":12112},[1997],[1963,12114],{"className":12115,"style":11876},[2001],[1963,12117,2038],{"className":12118},[2006,2007],[1963,12120,12122,12135],{"className":12121},[1966],[1963,12123,12125],{"className":12124},[1970],[1972,12126,12127],{"xmlns":1974},[1976,12128,12129,12133],{},[1979,12130,12131],{},[1982,12132,2329],{},[1986,12134,2329],{"encoding":1988},[1963,12136,12138],{"className":12137,"ariaHidden":1993},[1992],[1963,12139,12141,12144],{"className":12140},[1997],[1963,12142],{"className":12143,"style":11876},[2001],[1963,12145,2329],{"className":12146,"style":2394},[2006,2007],[1963,12148,12150,12169],{"className":12149},[1966],[1963,12151,12153],{"className":12152},[1970],[1972,12154,12155],{"xmlns":1974},[1976,12156,12157,12167],{},[1979,12158,12159,12161,12163,12165],{},[1982,12160,2572],{},[2026,12162,2643],{"stretchy":2031},[1982,12164,2038],{},[2026,12166,2653],{"stretchy":2031},[1986,12168,11930],{"encoding":1988},[1963,12170,12172],{"className":12171,"ariaHidden":1993},[1992],[1963,12173,12175,12178,12181,12184,12187],{"className":12174},[1997],[1963,12176],{"className":12177,"style":2102},[2001],[1963,12179,2572],{"className":12180},[2006,2007],[1963,12182,2643],{"className":12183},[2106],[1963,12185,2038],{"className":12186},[2006,2007],[1963,12188,2653],{"className":12189},[2274],"，则 ",[1963,12192,12194,12207],{"className":12193},[1966],[1963,12195,12197],{"className":12196},[1970],[1972,12198,12199],{"xmlns":1974},[1976,12200,12201,12205],{},[1979,12202,12203],{},[1982,12204,2038],{},[1986,12206,2038],{"encoding":1988},[1963,12208,12210],{"className":12209,"ariaHidden":1993},[1992],[1963,12211,12213,12216],{"className":12212},[1997],[1963,12214],{"className":12215,"style":11876},[2001],[1963,12217,2038],{"className":12218},[2006,2007]," 一定在求婚 ",[1963,12221,12223,12242],{"className":12222},[1966],[1963,12224,12226],{"className":12225},[1970],[1972,12227,12228],{"xmlns":1974},[1976,12229,12230,12240],{},[1979,12231,12232,12234,12236,12238],{},[1982,12233,2572],{},[2026,12235,2643],{"stretchy":2031},[1982,12237,2038],{},[2026,12239,2653],{"stretchy":2031},[1986,12241,11930],{"encoding":1988},[1963,12243,12245],{"className":12244,"ariaHidden":1993},[1992],[1963,12246,12248,12251,12254,12257,12260],{"className":12247},[1997],[1963,12249],{"className":12250,"style":2102},[2001],[1963,12252,2572],{"className":12253},[2006,2007],[1963,12255,2643],{"className":12256},[2106],[1963,12258,2038],{"className":12259},[2006,2007],[1963,12261,2653],{"className":12262},[2274]," 之前向 ",[1963,12265,12267,12280],{"className":12266},[1966],[1963,12268,12270],{"className":12269},[1970],[1972,12271,12272],{"xmlns":1974},[1976,12273,12274,12278],{},[1979,12275,12276],{},[1982,12277,2329],{},[1986,12279,2329],{"encoding":1988},[1963,12281,12283],{"className":12282,"ariaHidden":1993},[1992],[1963,12284,12286,12289],{"className":12285},[1997],[1963,12287],{"className":12288,"style":11876},[2001],[1963,12290,2329],{"className":12291,"style":2394},[2006,2007]," 求过婚",[1808,12294,12295,12296,12324,12325,12353],{},"那么为什么 ",[1963,12297,12299,12312],{"className":12298},[1966],[1963,12300,12302],{"className":12301},[1970],[1972,12303,12304],{"xmlns":1974},[1976,12305,12306,12310],{},[1979,12307,12308],{},[1982,12309,2038],{},[1986,12311,2038],{"encoding":1988},[1963,12313,12315],{"className":12314,"ariaHidden":1993},[1992],[1963,12316,12318,12321],{"className":12317},[1997],[1963,12319],{"className":12320,"style":11876},[2001],[1963,12322,2038],{"className":12323},[2006,2007]," 最终没有和 ",[1963,12326,12328,12341],{"className":12327},[1966],[1963,12329,12331],{"className":12330},[1970],[1972,12332,12333],{"xmlns":1974},[1976,12334,12335,12339],{},[1979,12336,12337],{},[1982,12338,2329],{},[1986,12340,2329],{"encoding":1988},[1963,12342,12344],{"className":12343,"ariaHidden":1993},[1992],[1963,12345,12347,12350],{"className":12346},[1997],[1963,12348],{"className":12349,"style":11876},[2001],[1963,12351,2329],{"className":12352,"style":2394},[2006,2007]," 匹配？",[1798,12355,12356,1957,12359,12387,12388],{},[1850,12357,12358],{},"情况1",[1963,12360,12362,12375],{"className":12361},[1966],[1963,12363,12365],{"className":12364},[1970],[1972,12366,12367],{"xmlns":1974},[1976,12368,12369,12373],{},[1979,12370,12371],{},[1982,12372,2329],{},[1986,12374,2329],{"encoding":1988},[1963,12376,12378],{"className":12377,"ariaHidden":1993},[1992],[1963,12379,12381,12384],{"className":12380},[1997],[1963,12382],{"className":12383,"style":11876},[2001],[1963,12385,2329],{"className":12386,"style":2394},[2006,2007]," 当时拒绝了 ",[1963,12389,12391,12404],{"className":12390},[1966],[1963,12392,12394],{"className":12393},[1970],[1972,12395,12396],{"xmlns":1974},[1976,12397,12398,12402],{},[1979,12399,12400],{},[1982,12401,2038],{},[1986,12403,2038],{"encoding":1988},[1963,12405,12407],{"className":12406,"ariaHidden":1993},[1992],[1963,12408,12410,12413],{"className":12409},[1997],[1963,12411],{"className":12412,"style":11876},[2001],[1963,12414,2038],{"className":12415},[2006,2007],[1805,12417,12418,12634,12743],{},[1808,12419,12420,12421,12449,12450,3851,12516,3436,12544,5512,12605,12633],{},"说明 ",[1963,12422,12424,12437],{"className":12423},[1966],[1963,12425,12427],{"className":12426},[1970],[1972,12428,12429],{"xmlns":1974},[1976,12430,12431,12435],{},[1979,12432,12433],{},[1982,12434,2329],{},[1986,12436,2329],{"encoding":1988},[1963,12438,12440],{"className":12439,"ariaHidden":1993},[1992],[1963,12441,12443,12446],{"className":12442},[1997],[1963,12444],{"className":12445,"style":11876},[2001],[1963,12447,2329],{"className":12448,"style":2394},[2006,2007]," 当时已有更好的持有者 ",[1963,12451,12453,12474],{"className":12452},[1966],[1963,12454,12456],{"className":12455},[1970],[1972,12457,12458],{"xmlns":1974},[1976,12459,12460,12471],{},[1979,12461,12462],{},[11730,12463,12464,12466],{},[1982,12465,2038],{},[2026,12467,12470],{"mathvariant":12468,"lspace":12469,"rspace":12469},"normal","0em","′",[1986,12472,12473],{"encoding":1988},"m'",[1963,12475,12477],{"className":12476,"ariaHidden":1993},[1992],[1963,12478,12480,12484],{"className":12479},[1997],[1963,12481],{"className":12482,"style":12483},[2001],"height:0.7519em;",[1963,12485,12487,12490],{"className":12486},[2006],[1963,12488,2038],{"className":12489},[2006,2007],[1963,12491,12493],{"className":12492},[2116],[1963,12494,12496],{"className":12495},[2120],[1963,12497,12499],{"className":12498},[2125],[1963,12500,12502],{"className":12501,"style":12483},[2129],[1963,12503,12504,12507],{"style":11769},[1963,12505],{"className":12506,"style":2138},[2137],[1963,12508,12510],{"className":12509},[2142,2143,2144,2145],[1963,12511,12513],{"className":12512},[2006,2145],[1963,12514,12470],{"className":12515},[2006,2145],[1963,12517,12519,12532],{"className":12518},[1966],[1963,12520,12522],{"className":12521},[1970],[1972,12523,12524],{"xmlns":1974},[1976,12525,12526,12530],{},[1979,12527,12528],{},[1982,12529,2329],{},[1986,12531,2329],{"encoding":1988},[1963,12533,12535],{"className":12534,"ariaHidden":1993},[1992],[1963,12536,12538,12541],{"className":12537},[1997],[1963,12539],{"className":12540,"style":11876},[2001],[1963,12542,2329],{"className":12543,"style":2394},[2006,2007],[1963,12545,12547,12564],{"className":12546},[1966],[1963,12548,12550],{"className":12549},[1970],[1972,12551,12552],{"xmlns":1974},[1976,12553,12554,12562],{},[1979,12555,12556],{},[11730,12557,12558,12560],{},[1982,12559,2038],{},[2026,12561,12470],{"mathvariant":12468,"lspace":12469,"rspace":12469},[1986,12563,12473],{"encoding":1988},[1963,12565,12567],{"className":12566,"ariaHidden":1993},[1992],[1963,12568,12570,12573],{"className":12569},[1997],[1963,12571],{"className":12572,"style":12483},[2001],[1963,12574,12576,12579],{"className":12575},[2006],[1963,12577,2038],{"className":12578},[2006,2007],[1963,12580,12582],{"className":12581},[2116],[1963,12583,12585],{"className":12584},[2120],[1963,12586,12588],{"className":12587},[2125],[1963,12589,12591],{"className":12590,"style":12483},[2129],[1963,12592,12593,12596],{"style":11769},[1963,12594],{"className":12595,"style":2138},[2137],[1963,12597,12599],{"className":12598},[2142,2143,2144,2145],[1963,12600,12602],{"className":12601},[2006,2145],[1963,12603,12470],{"className":12604},[2006,2145],[1963,12606,12608,12621],{"className":12607},[1966],[1963,12609,12611],{"className":12610},[1970],[1972,12612,12613],{"xmlns":1974},[1976,12614,12615,12619],{},[1979,12616,12617],{},[1982,12618,2038],{},[1986,12620,2038],{"encoding":1988},[1963,12622,12624],{"className":12623,"ariaHidden":1993},[1992],[1963,12625,12627,12630],{"className":12626},[1997],[1963,12628],{"className":12629,"style":11876},[2001],[1963,12631,2038],{"className":12632},[2006,2007],"）",[1808,12635,12636,12637,12680,12681,12742],{},"由于女性的持有者只会越来越好，",[1963,12638,12640,12659],{"className":12639},[1966],[1963,12641,12643],{"className":12642},[1970],[1972,12644,12645],{"xmlns":1974},[1976,12646,12647,12657],{},[1979,12648,12649,12651,12653,12655],{},[1982,12650,2572],{},[2026,12652,2643],{"stretchy":2031},[1982,12654,2329],{},[2026,12656,2653],{"stretchy":2031},[1986,12658,12032],{"encoding":1988},[1963,12660,12662],{"className":12661,"ariaHidden":1993},[1992],[1963,12663,12665,12668,12671,12674,12677],{"className":12664},[1997],[1963,12666],{"className":12667,"style":2102},[2001],[1963,12669,2572],{"className":12670},[2006,2007],[1963,12672,2643],{"className":12673},[2106],[1963,12675,2329],{"className":12676,"style":2394},[2006,2007],[1963,12678,2653],{"className":12679},[2274]," 至少和 ",[1963,12682,12684,12701],{"className":12683},[1966],[1963,12685,12687],{"className":12686},[1970],[1972,12688,12689],{"xmlns":1974},[1976,12690,12691,12699],{},[1979,12692,12693],{},[11730,12694,12695,12697],{},[1982,12696,2038],{},[2026,12698,12470],{"mathvariant":12468,"lspace":12469,"rspace":12469},[1986,12700,12473],{"encoding":1988},[1963,12702,12704],{"className":12703,"ariaHidden":1993},[1992],[1963,12705,12707,12710],{"className":12706},[1997],[1963,12708],{"className":12709,"style":12483},[2001],[1963,12711,12713,12716],{"className":12712},[2006],[1963,12714,2038],{"className":12715},[2006,2007],[1963,12717,12719],{"className":12718},[2116],[1963,12720,12722],{"className":12721},[2120],[1963,12723,12725],{"className":12724},[2125],[1963,12726,12728],{"className":12727,"style":12483},[2129],[1963,12729,12730,12733],{"style":11769},[1963,12731],{"className":12732,"style":2138},[2137],[1963,12734,12736],{"className":12735},[2142,2143,2144,2145],[1963,12737,12739],{"className":12738},[2006,2145],[1963,12740,12470],{"className":12741},[2006,2145]," 一样好",[1808,12744,12745,12746,3436,12774,5512,12817,12845],{},"因此 ",[1963,12747,12749,12762],{"className":12748},[1966],[1963,12750,12752],{"className":12751},[1970],[1972,12753,12754],{"xmlns":1974},[1976,12755,12756,12760],{},[1979,12757,12758],{},[1982,12759,2329],{},[1986,12761,2329],{"encoding":1988},[1963,12763,12765],{"className":12764,"ariaHidden":1993},[1992],[1963,12766,12768,12771],{"className":12767},[1997],[1963,12769],{"className":12770,"style":11876},[2001],[1963,12772,2329],{"className":12773,"style":2394},[2006,2007],[1963,12775,12777,12796],{"className":12776},[1966],[1963,12778,12780],{"className":12779},[1970],[1972,12781,12782],{"xmlns":1974},[1976,12783,12784,12794],{},[1979,12785,12786,12788,12790,12792],{},[1982,12787,2572],{},[2026,12789,2643],{"stretchy":2031},[1982,12791,2329],{},[2026,12793,2653],{"stretchy":2031},[1986,12795,12032],{"encoding":1988},[1963,12797,12799],{"className":12798,"ariaHidden":1993},[1992],[1963,12800,12802,12805,12808,12811,12814],{"className":12801},[1997],[1963,12803],{"className":12804,"style":2102},[2001],[1963,12806,2572],{"className":12807},[2006,2007],[1963,12809,2643],{"className":12810},[2106],[1963,12812,2329],{"className":12813,"style":2394},[2006,2007],[1963,12815,2653],{"className":12816},[2274],[1963,12818,12820,12833],{"className":12819},[1966],[1963,12821,12823],{"className":12822},[1970],[1972,12824,12825],{"xmlns":1974},[1976,12826,12827,12831],{},[1979,12828,12829],{},[1982,12830,2038],{},[1986,12832,2038],{"encoding":1988},[1963,12834,12836],{"className":12835,"ariaHidden":1993},[1992],[1963,12837,12839,12842],{"className":12838},[1997],[1963,12840],{"className":12841,"style":11876},[2001],[1963,12843,2038],{"className":12844},[2006,2007],"，矛盾！",[1798,12847,12848,1957,12851,12879,12880,12908],{},[1850,12849,12850],{},"情况2",[1963,12852,12854,12867],{"className":12853},[1966],[1963,12855,12857],{"className":12856},[1970],[1972,12858,12859],{"xmlns":1974},[1976,12860,12861,12865],{},[1979,12862,12863],{},[1982,12864,2329],{},[1986,12866,2329],{"encoding":1988},[1963,12868,12870],{"className":12869,"ariaHidden":1993},[1992],[1963,12871,12873,12876],{"className":12872},[1997],[1963,12874],{"className":12875,"style":11876},[2001],[1963,12877,2329],{"className":12878,"style":2394},[2006,2007]," 当时接受了 ",[1963,12881,12883,12896],{"className":12882},[1966],[1963,12884,12886],{"className":12885},[1970],[1972,12887,12888],{"xmlns":1974},[1976,12889,12890,12894],{},[1979,12891,12892],{},[1982,12893,2038],{},[1986,12895,2038],{"encoding":1988},[1963,12897,12899],{"className":12898,"ariaHidden":1993},[1992],[1963,12900,12902,12905],{"className":12901},[1997],[1963,12903],{"className":12904,"style":11876},[2001],[1963,12906,2038],{"className":12907},[2006,2007]," 但后来换人",[1805,12910,12911,13103,13214],{},[1808,12912,12913,12914,12981,12982,3436,13010,5512,13075,12633],{},"说明后来有更好的 ",[1963,12915,12917,12939],{"className":12916},[1966],[1963,12918,12920],{"className":12919},[1970],[1972,12921,12922],{"xmlns":1974},[1976,12923,12924,12936],{},[1979,12925,12926],{},[11730,12927,12928,12930],{},[1982,12929,2038],{},[1979,12931,12932,12934],{},[2026,12933,12470],{"mathvariant":12468},[2026,12935,12470],{"mathvariant":12468},[1986,12937,12938],{"encoding":1988},"m''",[1963,12940,12942],{"className":12941,"ariaHidden":1993},[1992],[1963,12943,12945,12948],{"className":12944},[1997],[1963,12946],{"className":12947,"style":12483},[2001],[1963,12949,12951,12954],{"className":12950},[2006],[1963,12952,2038],{"className":12953},[2006,2007],[1963,12955,12957],{"className":12956},[2116],[1963,12958,12960],{"className":12959},[2120],[1963,12961,12963],{"className":12962},[2125],[1963,12964,12966],{"className":12965,"style":12483},[2129],[1963,12967,12968,12971],{"style":11769},[1963,12969],{"className":12970,"style":2138},[2137],[1963,12972,12974],{"className":12973},[2142,2143,2144,2145],[1963,12975,12977],{"className":12976},[2006,2145],[1963,12978,12980],{"className":12979},[2006,2145],"′′"," 求婚（",[1963,12983,12985,12998],{"className":12984},[1966],[1963,12986,12988],{"className":12987},[1970],[1972,12989,12990],{"xmlns":1974},[1976,12991,12992,12996],{},[1979,12993,12994],{},[1982,12995,2329],{},[1986,12997,2329],{"encoding":1988},[1963,12999,13001],{"className":13000,"ariaHidden":1993},[1992],[1963,13002,13004,13007],{"className":13003},[1997],[1963,13005],{"className":13006,"style":11876},[2001],[1963,13008,2329],{"className":13009,"style":2394},[2006,2007],[1963,13011,13013,13034],{"className":13012},[1966],[1963,13014,13016],{"className":13015},[1970],[1972,13017,13018],{"xmlns":1974},[1976,13019,13020,13032],{},[1979,13021,13022],{},[11730,13023,13024,13026],{},[1982,13025,2038],{},[1979,13027,13028,13030],{},[2026,13029,12470],{"mathvariant":12468},[2026,13031,12470],{"mathvariant":12468},[1986,13033,12938],{"encoding":1988},[1963,13035,13037],{"className":13036,"ariaHidden":1993},[1992],[1963,13038,13040,13043],{"className":13039},[1997],[1963,13041],{"className":13042,"style":12483},[2001],[1963,13044,13046,13049],{"className":13045},[2006],[1963,13047,2038],{"className":13048},[2006,2007],[1963,13050,13052],{"className":13051},[2116],[1963,13053,13055],{"className":13054},[2120],[1963,13056,13058],{"className":13057},[2125],[1963,13059,13061],{"className":13060,"style":12483},[2129],[1963,13062,13063,13066],{"style":11769},[1963,13064],{"className":13065,"style":2138},[2137],[1963,13067,13069],{"className":13068},[2142,2143,2144,2145],[1963,13070,13072],{"className":13071},[2006,2145],[1963,13073,12980],{"className":13074},[2006,2145],[1963,13076,13078,13091],{"className":13077},[1966],[1963,13079,13081],{"className":13080},[1970],[1972,13082,13083],{"xmlns":1974},[1976,13084,13085,13089],{},[1979,13086,13087],{},[1982,13088,2038],{},[1986,13090,2038],{"encoding":1988},[1963,13092,13094],{"className":13093,"ariaHidden":1993},[1992],[1963,13095,13097,13100],{"className":13096},[1997],[1963,13098],{"className":13099,"style":11876},[2001],[1963,13101,2038],{"className":13102},[2006,2007],[1808,13104,13105,13106,12680,13149,12742],{},"同样，",[1963,13107,13109,13128],{"className":13108},[1966],[1963,13110,13112],{"className":13111},[1970],[1972,13113,13114],{"xmlns":1974},[1976,13115,13116,13126],{},[1979,13117,13118,13120,13122,13124],{},[1982,13119,2572],{},[2026,13121,2643],{"stretchy":2031},[1982,13123,2329],{},[2026,13125,2653],{"stretchy":2031},[1986,13127,12032],{"encoding":1988},[1963,13129,13131],{"className":13130,"ariaHidden":1993},[1992],[1963,13132,13134,13137,13140,13143,13146],{"className":13133},[1997],[1963,13135],{"className":13136,"style":2102},[2001],[1963,13138,2572],{"className":13139},[2006,2007],[1963,13141,2643],{"className":13142},[2106],[1963,13144,2329],{"className":13145,"style":2394},[2006,2007],[1963,13147,2653],{"className":13148},[2274],[1963,13150,13152,13173],{"className":13151},[1966],[1963,13153,13155],{"className":13154},[1970],[1972,13156,13157],{"xmlns":1974},[1976,13158,13159,13171],{},[1979,13160,13161],{},[11730,13162,13163,13165],{},[1982,13164,2038],{},[1979,13166,13167,13169],{},[2026,13168,12470],{"mathvariant":12468},[2026,13170,12470],{"mathvariant":12468},[1986,13172,12938],{"encoding":1988},[1963,13174,13176],{"className":13175,"ariaHidden":1993},[1992],[1963,13177,13179,13182],{"className":13178},[1997],[1963,13180],{"className":13181,"style":12483},[2001],[1963,13183,13185,13188],{"className":13184},[2006],[1963,13186,2038],{"className":13187},[2006,2007],[1963,13189,13191],{"className":13190},[2116],[1963,13192,13194],{"className":13193},[2120],[1963,13195,13197],{"className":13196},[2125],[1963,13198,13200],{"className":13199,"style":12483},[2129],[1963,13201,13202,13205],{"style":11769},[1963,13203],{"className":13204,"style":2138},[2137],[1963,13206,13208],{"className":13207},[2142,2143,2144,2145],[1963,13209,13211],{"className":13210},[2006,2145],[1963,13212,12980],{"className":13213},[2006,2145],[1808,13215,12745,13216,3436,13244,5512,13287,12845],{},[1963,13217,13219,13232],{"className":13218},[1966],[1963,13220,13222],{"className":13221},[1970],[1972,13223,13224],{"xmlns":1974},[1976,13225,13226,13230],{},[1979,13227,13228],{},[1982,13229,2329],{},[1986,13231,2329],{"encoding":1988},[1963,13233,13235],{"className":13234,"ariaHidden":1993},[1992],[1963,13236,13238,13241],{"className":13237},[1997],[1963,13239],{"className":13240,"style":11876},[2001],[1963,13242,2329],{"className":13243,"style":2394},[2006,2007],[1963,13245,13247,13266],{"className":13246},[1966],[1963,13248,13250],{"className":13249},[1970],[1972,13251,13252],{"xmlns":1974},[1976,13253,13254,13264],{},[1979,13255,13256,13258,13260,13262],{},[1982,13257,2572],{},[2026,13259,2643],{"stretchy":2031},[1982,13261,2329],{},[2026,13263,2653],{"stretchy":2031},[1986,13265,12032],{"encoding":1988},[1963,13267,13269],{"className":13268,"ariaHidden":1993},[1992],[1963,13270,13272,13275,13278,13281,13284],{"className":13271},[1997],[1963,13273],{"className":13274,"style":2102},[2001],[1963,13276,2572],{"className":13277},[2006,2007],[1963,13279,2643],{"className":13280},[2106],[1963,13282,2329],{"className":13283,"style":2394},[2006,2007],[1963,13285,2653],{"className":13286},[2274],[1963,13288,13290,13303],{"className":13289},[1966],[1963,13291,13293],{"className":13292},[1970],[1972,13294,13295],{"xmlns":1974},[1976,13296,13297,13301],{},[1979,13298,13299],{},[1982,13300,2038],{},[1986,13302,2038],{"encoding":1988},[1963,13304,13306],{"className":13305,"ariaHidden":1993},[1992],[1963,13307,13309,13312],{"className":13308},[1997],[1963,13310],{"className":13311,"style":11876},[2001],[1963,13313,2038],{"className":13314},[2006,2007],[1798,13316,13317],{},"结论：不存在阻塞对，匹配稳定。",[1798,13319,13320,13323,13324,13327],{},[1850,13321,13322],{},"定理3（男性最优）","：男性求婚版本产生的稳定匹配是所有稳定匹配中对",[1850,13325,13326],{},"所有男性","最优的。",[1798,13329,13330,1957],{},[1850,13331,13332],{},"证明思路",[1805,13334,13335,13338,13341],{},[1808,13336,13337],{},"定义\"可行\"女性：在某个稳定匹配中能匹配到该男性的女性",[1808,13339,13340],{},"算法保证每个男性得到他的最优可行女性",[1808,13342,13343],{},"反过来，女性得到她的最差可行男性（女性悲观）",[1798,13345,13346,13349],{},[1850,13347,13348],{},"对称性","：女性求婚版本产生对所有女性最优的稳定匹配。",[1925,13351,13353],{"id":13352},"_24-复杂度","2.4 复杂度",[1798,13355,13356,1957,13359],{},[1850,13357,13358],{},"时间复杂度",[1963,13360,13362,13387],{"className":13361},[1966],[1963,13363,13365],{"className":13364},[1970],[1972,13366,13367],{"xmlns":1974},[1976,13368,13369,13384],{},[1979,13370,13371,13374,13376,13382],{},[1982,13372,13373],{},"O",[2026,13375,2643],{"stretchy":2031},[11730,13377,13378,13380],{},[1982,13379,1984],{},[2040,13381,2052],{},[2026,13383,2653],{"stretchy":2031},[1986,13385,13386],{"encoding":1988},"O(N^2)",[1963,13388,13390],{"className":13389,"ariaHidden":1993},[1992],[1963,13391,13393,13397,13401,13404,13433],{"className":13392},[1997],[1963,13394],{"className":13395,"style":13396},[2001],"height:1.0641em;vertical-align:-0.25em;",[1963,13398,13373],{"className":13399,"style":13400},[2006,2007],"margin-right:0.0278em;",[1963,13402,2643],{"className":13403},[2106],[1963,13405,13407,13410],{"className":13406},[2006],[1963,13408,1984],{"className":13409,"style":2008},[2006,2007],[1963,13411,13413],{"className":13412},[2116],[1963,13414,13416],{"className":13415},[2120],[1963,13417,13419],{"className":13418},[2125],[1963,13420,13422],{"className":13421,"style":11748},[2129],[1963,13423,13424,13427],{"style":11769},[1963,13425],{"className":13426,"style":2138},[2137],[1963,13428,13430],{"className":13429},[2142,2143,2144,2145],[1963,13431,2052],{"className":13432},[2006,2145],[1963,13434,2653],{"className":13435},[2274],[1805,13437,13438,13499],{},[1808,13439,11716,13440,13498],{},[1963,13441,13443,13460],{"className":13442},[1966],[1963,13444,13446],{"className":13445},[1970],[1972,13447,13448],{"xmlns":1974},[1976,13449,13450,13458],{},[1979,13451,13452],{},[11730,13453,13454,13456],{},[1982,13455,1984],{},[2040,13457,2052],{},[1986,13459,11738],{"encoding":1988},[1963,13461,13463],{"className":13462,"ariaHidden":1993},[1992],[1963,13464,13466,13469],{"className":13465},[1997],[1963,13467],{"className":13468,"style":11748},[2001],[1963,13470,13472,13475],{"className":13471},[2006],[1963,13473,1984],{"className":13474,"style":2008},[2006,2007],[1963,13476,13478],{"className":13477},[2116],[1963,13479,13481],{"className":13480},[2120],[1963,13482,13484],{"className":13483},[2125],[1963,13485,13487],{"className":13486,"style":11748},[2129],[1963,13488,13489,13492],{"style":11769},[1963,13490],{"className":13491,"style":2138},[2137],[1963,13493,13495],{"className":13494},[2142,2143,2144,2145],[1963,13496,2052],{"className":13497},[2006,2145]," 次求婚",[1808,13500,13501,13502,13546],{},"每次求婚需要 ",[1963,13503,13505,13525],{"className":13504},[1966],[1963,13506,13508],{"className":13507},[1970],[1972,13509,13510],{"xmlns":1974},[1976,13511,13512,13522],{},[1979,13513,13514,13516,13518,13520],{},[1982,13515,13373],{},[2026,13517,2643],{"stretchy":2031},[2040,13519,2042],{},[2026,13521,2653],{"stretchy":2031},[1986,13523,13524],{"encoding":1988},"O(1)",[1963,13526,13528],{"className":13527,"ariaHidden":1993},[1992],[1963,13529,13531,13534,13537,13540,13543],{"className":13530},[1997],[1963,13532],{"className":13533,"style":2102},[2001],[1963,13535,13373],{"className":13536,"style":13400},[2006,2007],[1963,13538,2643],{"className":13539},[2106],[1963,13541,2042],{"className":13542},[2006],[1963,13544,2653],{"className":13545},[2274]," 时间（假设偏好表已构建）",[1798,13548,13549,1957,13552,13625],{},[1850,13550,13551],{},"空间复杂度",[1963,13553,13555,13578],{"className":13554},[1966],[1963,13556,13558],{"className":13557},[1970],[1972,13559,13560],{"xmlns":1974},[1976,13561,13562,13576],{},[1979,13563,13564,13566,13568,13574],{},[1982,13565,13373],{},[2026,13567,2643],{"stretchy":2031},[11730,13569,13570,13572],{},[1982,13571,1984],{},[2040,13573,2052],{},[2026,13575,2653],{"stretchy":2031},[1986,13577,13386],{"encoding":1988},[1963,13579,13581],{"className":13580,"ariaHidden":1993},[1992],[1963,13582,13584,13587,13590,13593,13622],{"className":13583},[1997],[1963,13585],{"className":13586,"style":13396},[2001],[1963,13588,13373],{"className":13589,"style":13400},[2006,2007],[1963,13591,2643],{"className":13592},[2106],[1963,13594,13596,13599],{"className":13595},[2006],[1963,13597,1984],{"className":13598,"style":2008},[2006,2007],[1963,13600,13602],{"className":13601},[2116],[1963,13603,13605],{"className":13604},[2120],[1963,13606,13608],{"className":13607},[2125],[1963,13609,13611],{"className":13610,"style":11748},[2129],[1963,13612,13613,13616],{"style":11769},[1963,13614],{"className":13615,"style":2138},[2137],[1963,13617,13619],{"className":13618},[2142,2143,2144,2145],[1963,13620,2052],{"className":13621},[2006,2145],[1963,13623,2653],{"className":13624},[2274],"（存储偏好表）",[1794,13627,13629],{"id":13628},"三多对一匹配医院-医生问题-many-to-one-matching","三、多对一匹配：医院-医生问题 (Many-to-One Matching)",[1925,13631,13633],{"id":13632},"_31-问题设定","3.1 问题设定",[1798,13635,13636,1957],{},[1850,13637,13638],{},"医院-医生匹配 (Hospital-Resident Problem)",[1805,13640,13641,13778,13809],{},[1808,13642,13643,13671,13672,13702,13703,13777],{},[1963,13644,13646,13659],{"className":13645},[1966],[1963,13647,13649],{"className":13648},[1970],[1972,13650,13651],{"xmlns":1974},[1976,13652,13653,13657],{},[1979,13654,13655],{},[1982,13656,2024],{},[1986,13658,2024],{"encoding":1988},[1963,13660,13662],{"className":13661,"ariaHidden":1993},[1992],[1963,13663,13665,13668],{"className":13664},[1997],[1963,13666],{"className":13667,"style":2002},[2001],[1963,13669,2024],{"className":13670,"style":2008},[2006,2007]," 个医院，每个医院 ",[1963,13673,13675,13689],{"className":13674},[1966],[1963,13676,13678],{"className":13677},[1970],[1972,13679,13680],{"xmlns":1974},[1976,13681,13682,13687],{},[1979,13683,13684],{},[1982,13685,13686],{},"h",[1986,13688,13686],{"encoding":1988},[1963,13690,13692],{"className":13691,"ariaHidden":1993},[1992],[1963,13693,13695,13699],{"className":13694},[1997],[1963,13696],{"className":13697,"style":13698},[2001],"height:0.6944em;",[1963,13700,13686],{"className":13701},[2006,2007]," 有配额 ",[1963,13704,13706,13725],{"className":13705},[1966],[1963,13707,13709],{"className":13708},[1970],[1972,13710,13711],{"xmlns":1974},[1976,13712,13713,13722],{},[1979,13714,13715],{},[2034,13716,13717,13720],{},[1982,13718,13719],{},"q",[1982,13721,13686],{},[1986,13723,13724],{"encoding":1988},"q_h",[1963,13726,13728],{"className":13727,"ariaHidden":1993},[1992],[1963,13729,13731,13734],{"className":13730},[1997],[1963,13732],{"className":13733,"style":2585},[2001],[1963,13735,13737,13741],{"className":13736},[2006],[1963,13738,13719],{"className":13739,"style":13740},[2006,2007],"margin-right:0.0359em;",[1963,13742,13744],{"className":13743},[2116],[1963,13745,13747,13769],{"className":13746},[2120,2121],[1963,13748,13750,13766],{"className":13749},[2125],[1963,13751,13754],{"className":13752,"style":13753},[2129],"height:0.3361em;",[1963,13755,13757,13760],{"style":13756},"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;",[1963,13758],{"className":13759,"style":2138},[2137],[1963,13761,13763],{"className":13762},[2142,2143,2144,2145],[1963,13764,13686],{"className":13765},[2006,2007,2145],[1963,13767,2153],{"className":13768},[2152],[1963,13770,13772],{"className":13771},[2125],[1963,13773,13775],{"className":13774,"style":2160},[2129],[1963,13776],{},"（可接受多个医生）",[1808,13779,13780,13808],{},[1963,13781,13783,13796],{"className":13782},[1966],[1963,13784,13786],{"className":13785},[1970],[1972,13787,13788],{"xmlns":1974},[1976,13789,13790,13794],{},[1979,13791,13792],{},[1982,13793,1984],{},[1986,13795,1984],{"encoding":1988},[1963,13797,13799],{"className":13798,"ariaHidden":1993},[1992],[1963,13800,13802,13805],{"className":13801},[1997],[1963,13803],{"className":13804,"style":2002},[2001],[1963,13806,1984],{"className":13807,"style":2008},[2006,2007]," 个医生，每个医生只能匹配一个医院",[1808,13810,13811],{},"双方都有偏好排序",[1798,13813,13814,1957],{},[1850,13815,2594,13816],{},[1963,13817,13819,13832],{"className":13818},[1966],[1963,13820,13822],{"className":13821},[1970],[1972,13823,13824],{"xmlns":1974},[1976,13825,13826,13830],{},[1979,13827,13828],{},[1982,13829,2572],{},[1986,13831,2575],{"encoding":1988},[1963,13833,13835],{"className":13834,"ariaHidden":1993},[1992],[1963,13836,13838,13841],{"className":13837},[1997],[1963,13839],{"className":13840,"style":2585},[2001],[1963,13842,2572],{"className":13843},[2006,2007],[1805,13845,13846,13923],{},[1808,13847,13848,13893,13894,13922],{},[1963,13849,13851,13872],{"className":13850},[1966],[1963,13852,13854],{"className":13853},[1970],[1972,13855,13856],{"xmlns":1974},[1976,13857,13858,13869],{},[1979,13859,13860,13862,13864,13867],{},[1982,13861,2572],{},[2026,13863,2643],{"stretchy":2031},[1982,13865,13866],{},"d",[2026,13868,2653],{"stretchy":2031},[1986,13870,13871],{"encoding":1988},"\\mu(d)",[1963,13873,13875],{"className":13874,"ariaHidden":1993},[1992],[1963,13876,13878,13881,13884,13887,13890],{"className":13877},[1997],[1963,13879],{"className":13880,"style":2102},[2001],[1963,13882,2572],{"className":13883},[2006,2007],[1963,13885,2643],{"className":13886},[2106],[1963,13888,13866],{"className":13889},[2006,2007],[1963,13891,2653],{"className":13892},[2274],"：医生 ",[1963,13895,13897,13910],{"className":13896},[1966],[1963,13898,13900],{"className":13899},[1970],[1972,13901,13902],{"xmlns":1974},[1976,13903,13904,13908],{},[1979,13905,13906],{},[1982,13907,13866],{},[1986,13909,13866],{"encoding":1988},[1963,13911,13913],{"className":13912,"ariaHidden":1993},[1992],[1963,13914,13916,13919],{"className":13915},[1997],[1963,13917],{"className":13918,"style":13698},[2001],[1963,13920,13866],{"className":13921},[2006,2007]," 匹配到的医院（或失业）",[1808,13924,13925,13969,13970,13998,13999],{},[1963,13926,13928,13948],{"className":13927},[1966],[1963,13929,13931],{"className":13930},[1970],[1972,13932,13933],{"xmlns":1974},[1976,13934,13935,13945],{},[1979,13936,13937,13939,13941,13943],{},[1982,13938,2572],{},[2026,13940,2643],{"stretchy":2031},[1982,13942,13686],{},[2026,13944,2653],{"stretchy":2031},[1986,13946,13947],{"encoding":1988},"\\mu(h)",[1963,13949,13951],{"className":13950,"ariaHidden":1993},[1992],[1963,13952,13954,13957,13960,13963,13966],{"className":13953},[1997],[1963,13955],{"className":13956,"style":2102},[2001],[1963,13958,2572],{"className":13959},[2006,2007],[1963,13961,2643],{"className":13962},[2106],[1963,13964,13686],{"className":13965},[2006,2007],[1963,13967,2653],{"className":13968},[2274],"：医院 ",[1963,13971,13973,13986],{"className":13972},[1966],[1963,13974,13976],{"className":13975},[1970],[1972,13977,13978],{"xmlns":1974},[1976,13979,13980,13984],{},[1979,13981,13982],{},[1982,13983,13686],{},[1986,13985,13686],{"encoding":1988},[1963,13987,13989],{"className":13988,"ariaHidden":1993},[1992],[1963,13990,13992,13995],{"className":13991},[1997],[1963,13993],{"className":13994,"style":13698},[2001],[1963,13996,13686],{"className":13997},[2006,2007]," 匹配到的医生集合，",[1963,14000,14002,14036],{"className":14001},[1966],[1963,14003,14005],{"className":14004},[1970],[1972,14006,14007],{"xmlns":1974},[1976,14008,14009,14033],{},[1979,14010,14011,14014,14016,14018,14020,14022,14024,14027],{},[1982,14012,14013],{"mathvariant":12468},"∣",[1982,14015,2572],{},[2026,14017,2643],{"stretchy":2031},[1982,14019,13686],{},[2026,14021,2653],{"stretchy":2031},[1982,14023,14013],{"mathvariant":12468},[2026,14025,14026],{},"≤",[2034,14028,14029,14031],{},[1982,14030,13719],{},[1982,14032,13686],{},[1986,14034,14035],{"encoding":1988},"|\\mu(h)| \\leq q_h",[1963,14037,14039,14072],{"className":14038,"ariaHidden":1993},[1992],[1963,14040,14042,14045,14048,14051,14054,14057,14060,14063,14066,14069],{"className":14041},[1997],[1963,14043],{"className":14044,"style":2102},[2001],[1963,14046,14013],{"className":14047},[2006],[1963,14049,2572],{"className":14050},[2006,2007],[1963,14052,2643],{"className":14053},[2106],[1963,14055,13686],{"className":14056},[2006,2007],[1963,14058,2653],{"className":14059},[2274],[1963,14061,14013],{"className":14062},[2006],[1963,14064],{"className":14065,"style":2088},[2087],[1963,14067,14026],{"className":14068},[2092],[1963,14070],{"className":14071,"style":2088},[2087],[1963,14073,14075,14078],{"className":14074},[1997],[1963,14076],{"className":14077,"style":2585},[2001],[1963,14079,14081,14084],{"className":14080},[2006],[1963,14082,13719],{"className":14083,"style":13740},[2006,2007],[1963,14085,14087],{"className":14086},[2116],[1963,14088,14090,14110],{"className":14089},[2120,2121],[1963,14091,14093,14107],{"className":14092},[2125],[1963,14094,14096],{"className":14095,"style":13753},[2129],[1963,14097,14098,14101],{"style":13756},[1963,14099],{"className":14100,"style":2138},[2137],[1963,14102,14104],{"className":14103},[2142,2143,2144,2145],[1963,14105,13686],{"className":14106},[2006,2007,2145],[1963,14108,2153],{"className":14109},[2152],[1963,14111,14113],{"className":14112},[2125],[1963,14114,14116],{"className":14115,"style":2160},[2129],[1963,14117],{},[1798,14119,14120,6396,14123,3362],{},[1850,14121,14122],{},"阻塞对",[1963,14124,14126,14148],{"className":14125},[1966],[1963,14127,14129],{"className":14128},[1970],[1972,14130,14131],{"xmlns":1974},[1976,14132,14133,14145],{},[1979,14134,14135,14137,14139,14141,14143],{},[2026,14136,2643],{"stretchy":2031},[1982,14138,13866],{},[2026,14140,2045],{"separator":1993},[1982,14142,13686],{},[2026,14144,2653],{"stretchy":2031},[1986,14146,14147],{"encoding":1988},"(d, h)",[1963,14149,14151],{"className":14150,"ariaHidden":1993},[1992],[1963,14152,14154,14157,14160,14163,14166,14169,14172],{"className":14153},[1997],[1963,14155],{"className":14156,"style":2102},[2001],[1963,14158,2643],{"className":14159},[2106],[1963,14161,13866],{"className":14162},[2006,2007],[1963,14164,2045],{"className":14165},[2166],[1963,14167],{"className":14168,"style":2170},[2087],[1963,14170,13686],{"className":14171},[2006,2007],[1963,14173,2653],{"className":14174},[2274],[1888,14176,14177,14278],{},[1808,14178,14179,3436,14207,5512,14235],{},[1963,14180,14182,14195],{"className":14181},[1966],[1963,14183,14185],{"className":14184},[1970],[1972,14186,14187],{"xmlns":1974},[1976,14188,14189,14193],{},[1979,14190,14191],{},[1982,14192,13866],{},[1986,14194,13866],{"encoding":1988},[1963,14196,14198],{"className":14197,"ariaHidden":1993},[1992],[1963,14199,14201,14204],{"className":14200},[1997],[1963,14202],{"className":14203,"style":13698},[2001],[1963,14205,13866],{"className":14206},[2006,2007],[1963,14208,14210,14223],{"className":14209},[1966],[1963,14211,14213],{"className":14212},[1970],[1972,14214,14215],{"xmlns":1974},[1976,14216,14217,14221],{},[1979,14218,14219],{},[1982,14220,13686],{},[1986,14222,13686],{"encoding":1988},[1963,14224,14226],{"className":14225,"ariaHidden":1993},[1992],[1963,14227,14229,14232],{"className":14228},[1997],[1963,14230],{"className":14231,"style":13698},[2001],[1963,14233,13686],{"className":14234},[2006,2007],[1963,14236,14238,14257],{"className":14237},[1966],[1963,14239,14241],{"className":14240},[1970],[1972,14242,14243],{"xmlns":1974},[1976,14244,14245,14255],{},[1979,14246,14247,14249,14251,14253],{},[1982,14248,2572],{},[2026,14250,2643],{"stretchy":2031},[1982,14252,13866],{},[2026,14254,2653],{"stretchy":2031},[1986,14256,13871],{"encoding":1988},[1963,14258,14260],{"className":14259,"ariaHidden":1993},[1992],[1963,14261,14263,14266,14269,14272,14275],{"className":14262},[1997],[1963,14264],{"className":14265,"style":2102},[2001],[1963,14267,2572],{"className":14268},[2006,2007],[1963,14270,2643],{"className":14271},[2106],[1963,14273,13866],{"className":14274},[2006,2007],[1963,14276,2653],{"className":14277},[2274],[1808,14279,14280,14281],{},"且以下之一成立：\n",[1805,14282,14283,14404],{},[1808,14284,14285,14403],{},[1963,14286,14288,14321],{"className":14287},[1966],[1963,14289,14291],{"className":14290},[1970],[1972,14292,14293],{"xmlns":1974},[1976,14294,14295,14318],{},[1979,14296,14297,14299,14301,14303,14305,14307,14309,14312],{},[1982,14298,14013],{"mathvariant":12468},[1982,14300,2572],{},[2026,14302,2643],{"stretchy":2031},[1982,14304,13686],{},[2026,14306,2653],{"stretchy":2031},[1982,14308,14013],{"mathvariant":12468},[2026,14310,14311],{},"\u003C",[2034,14313,14314,14316],{},[1982,14315,13719],{},[1982,14317,13686],{},[1986,14319,14320],{"encoding":1988},"|\\mu(h)| \u003C q_h",[1963,14322,14324,14357],{"className":14323,"ariaHidden":1993},[1992],[1963,14325,14327,14330,14333,14336,14339,14342,14345,14348,14351,14354],{"className":14326},[1997],[1963,14328],{"className":14329,"style":2102},[2001],[1963,14331,14013],{"className":14332},[2006],[1963,14334,2572],{"className":14335},[2006,2007],[1963,14337,2643],{"className":14338},[2106],[1963,14340,13686],{"className":14341},[2006,2007],[1963,14343,2653],{"className":14344},[2274],[1963,14346,14013],{"className":14347},[2006],[1963,14349],{"className":14350,"style":2088},[2087],[1963,14352,14311],{"className":14353},[2092],[1963,14355],{"className":14356,"style":2088},[2087],[1963,14358,14360,14363],{"className":14359},[1997],[1963,14361],{"className":14362,"style":2585},[2001],[1963,14364,14366,14369],{"className":14365},[2006],[1963,14367,13719],{"className":14368,"style":13740},[2006,2007],[1963,14370,14372],{"className":14371},[2116],[1963,14373,14375,14395],{"className":14374},[2120,2121],[1963,14376,14378,14392],{"className":14377},[2125],[1963,14379,14381],{"className":14380,"style":13753},[2129],[1963,14382,14383,14386],{"style":13756},[1963,14384],{"className":14385,"style":2138},[2137],[1963,14387,14389],{"className":14388},[2142,2143,2144,2145],[1963,14390,13686],{"className":14391},[2006,2007,2145],[1963,14393,2153],{"className":14394},[2152],[1963,14396,14398],{"className":14397},[2125],[1963,14399,14401],{"className":14400,"style":2160},[2129],[1963,14402],{},"（医院有空位）",[1808,14405,14406,14407,14508,14509,3436,14537,5512,14565],{},"存在 ",[1963,14408,14410,14439],{"className":14409},[1966],[1963,14411,14413],{"className":14412},[1970],[1972,14414,14415],{"xmlns":1974},[1976,14416,14417,14436],{},[1979,14418,14419,14425,14428,14430,14432,14434],{},[11730,14420,14421,14423],{},[1982,14422,13866],{},[2026,14424,12470],{"mathvariant":12468,"lspace":12469,"rspace":12469},[2026,14426,14427],{},"∈",[1982,14429,2572],{},[2026,14431,2643],{"stretchy":2031},[1982,14433,13686],{},[2026,14435,2653],{"stretchy":2031},[1986,14437,14438],{"encoding":1988},"d' \\in \\mu(h)",[1963,14440,14442,14490],{"className":14441,"ariaHidden":1993},[1992],[1963,14443,14445,14449,14481,14484,14487],{"className":14444},[1997],[1963,14446],{"className":14447,"style":14448},[2001],"height:0.791em;vertical-align:-0.0391em;",[1963,14450,14452,14455],{"className":14451},[2006],[1963,14453,13866],{"className":14454},[2006,2007],[1963,14456,14458],{"className":14457},[2116],[1963,14459,14461],{"className":14460},[2120],[1963,14462,14464],{"className":14463},[2125],[1963,14465,14467],{"className":14466,"style":12483},[2129],[1963,14468,14469,14472],{"style":11769},[1963,14470],{"className":14471,"style":2138},[2137],[1963,14473,14475],{"className":14474},[2142,2143,2144,2145],[1963,14476,14478],{"className":14477},[2006,2145],[1963,14479,12470],{"className":14480},[2006,2145],[1963,14482],{"className":14483,"style":2088},[2087],[1963,14485,14427],{"className":14486},[2092],[1963,14488],{"className":14489,"style":2088},[2087],[1963,14491,14493,14496,14499,14502,14505],{"className":14492},[1997],[1963,14494],{"className":14495,"style":2102},[2001],[1963,14497,2572],{"className":14498},[2006,2007],[1963,14500,2643],{"className":14501},[2106],[1963,14503,13686],{"className":14504},[2006,2007],[1963,14506,2653],{"className":14507},[2274]," 使得 ",[1963,14510,14512,14525],{"className":14511},[1966],[1963,14513,14515],{"className":14514},[1970],[1972,14516,14517],{"xmlns":1974},[1976,14518,14519,14523],{},[1979,14520,14521],{},[1982,14522,13686],{},[1986,14524,13686],{"encoding":1988},[1963,14526,14528],{"className":14527,"ariaHidden":1993},[1992],[1963,14529,14531,14534],{"className":14530},[1997],[1963,14532],{"className":14533,"style":13698},[2001],[1963,14535,13686],{"className":14536},[2006,2007],[1963,14538,14540,14553],{"className":14539},[1966],[1963,14541,14543],{"className":14542},[1970],[1972,14544,14545],{"xmlns":1974},[1976,14546,14547,14551],{},[1979,14548,14549],{},[1982,14550,13866],{},[1986,14552,13866],{"encoding":1988},[1963,14554,14556],{"className":14555,"ariaHidden":1993},[1992],[1963,14557,14559,14562],{"className":14558},[1997],[1963,14560],{"className":14561,"style":13698},[2001],[1963,14563,13866],{"className":14564},[2006,2007],[1963,14566,14568,14586],{"className":14567},[1966],[1963,14569,14571],{"className":14570},[1970],[1972,14572,14573],{"xmlns":1974},[1976,14574,14575,14583],{},[1979,14576,14577],{},[11730,14578,14579,14581],{},[1982,14580,13866],{},[2026,14582,12470],{"mathvariant":12468,"lspace":12469,"rspace":12469},[1986,14584,14585],{"encoding":1988},"d'",[1963,14587,14589],{"className":14588,"ariaHidden":1993},[1992],[1963,14590,14592,14595],{"className":14591},[1997],[1963,14593],{"className":14594,"style":12483},[2001],[1963,14596,14598,14601],{"className":14597},[2006],[1963,14599,13866],{"className":14600},[2006,2007],[1963,14602,14604],{"className":14603},[2116],[1963,14605,14607],{"className":14606},[2120],[1963,14608,14610],{"className":14609},[2125],[1963,14611,14613],{"className":14612,"style":12483},[2129],[1963,14614,14615,14618],{"style":11769},[1963,14616],{"className":14617,"style":2138},[2137],[1963,14619,14621],{"className":14620},[2142,2143,2144,2145],[1963,14622,14624],{"className":14623},[2006,2145],[1963,14625,12470],{"className":14626},[2006,2145],[1925,14628,14630],{"id":14629},"_32-da算法推广","3.2 DA算法推广",[1798,14632,14633,1957],{},[1850,14634,14635],{},"医生求婚版本",[1805,14637,14638,14641,14714],{},[1808,14639,14640],{},"医生向医院求婚",[1808,14642,14643,14644,14713],{},"医院持有最优的 ",[1963,14645,14647,14664],{"className":14646},[1966],[1963,14648,14650],{"className":14649},[1970],[1972,14651,14652],{"xmlns":1974},[1976,14653,14654,14662],{},[1979,14655,14656],{},[2034,14657,14658,14660],{},[1982,14659,13719],{},[1982,14661,13686],{},[1986,14663,13724],{"encoding":1988},[1963,14665,14667],{"className":14666,"ariaHidden":1993},[1992],[1963,14668,14670,14673],{"className":14669},[1997],[1963,14671],{"className":14672,"style":2585},[2001],[1963,14674,14676,14679],{"className":14675},[2006],[1963,14677,13719],{"className":14678,"style":13740},[2006,2007],[1963,14680,14682],{"className":14681},[2116],[1963,14683,14685,14705],{"className":14684},[2120,2121],[1963,14686,14688,14702],{"className":14687},[2125],[1963,14689,14691],{"className":14690,"style":13753},[2129],[1963,14692,14693,14696],{"style":13756},[1963,14694],{"className":14695,"style":2138},[2137],[1963,14697,14699],{"className":14698},[2142,2143,2144,2145],[1963,14700,13686],{"className":14701},[2006,2007,2145],[1963,14703,2153],{"className":14704},[2152],[1963,14706,14708],{"className":14707},[2125],[1963,14709,14711],{"className":14710,"style":2160},[2129],[1963,14712],{}," 个医生，拒绝其余",[1808,14715,14716],{},"被拒绝的医生向次优医院求婚",[1798,14718,14719,1957],{},[1850,14720,14721],{},"性质",[1805,14723,14724,14727],{},[1808,14725,14726],{},"算法终止且产生稳定匹配",[1808,14728,14729],{},"对医生最优（对医院悲观）",[1925,14731,14733],{"id":14732},"_33-实际应用nrmp","3.3 实际应用：NRMP",[1798,14735,14736,1957],{},[1850,14737,14738],{},"National Resident Matching Program (美国医生匹配)",[1798,14740,14741,1957],{},[1850,14742,14743],{},"历史",[1805,14745,14746,14749,14752,14755],{},[1808,14747,14748],{},"1950年代前：混乱，医院提前抢人，医生毁约",[1808,14750,14751],{},"1952年：引入集中匹配",[1808,14753,14754],{},"1984年：Roth证明NRMP使用的算法等价于DA算法",[1808,14756,14757],{},"1990年代：改革，加入夫妇匹配、优先级等复杂约束",[1798,14759,14760,1957],{},[1850,14761,14762],{},"成功原因",[1805,14764,14765,14768,14771],{},[1808,14766,14767],{},"稳定性 → 减少毁约",[1808,14769,14770],{},"透明性 → 参与者信任",[1808,14772,14773],{},"适应性 → 不断改进",[1794,14775,14777],{"id":14776},"四学校选择机制-school-choice","四、学校选择机制 (School Choice)",[1925,14779,14781],{"id":14780},"_41-问题背景","4.1 问题背景",[1798,14783,14784,14787],{},[1850,14785,14786],{},"传统机制","（波士顿、纽约等）：",[1805,14789,14790,14793],{},[1808,14791,14792],{},"学生提交偏好排序",[1808,14794,14795],{},"学校按\"接近性\"（如家庭住址）或先到先得分配",[1798,14797,14798,1957],{},[1850,14799,14800],{},"问题",[1805,14802,14803,14809,14815],{},[1808,14804,14805,14808],{},[1850,14806,14807],{},"策略性","：学生不能真实报告偏好",[1808,14810,14811,14814],{},[1850,14812,14813],{},"不公平","：信息不对称，有经验的家长占优",[1808,14816,14817,14820],{},[1850,14818,14819],{},"不稳定","：存在阻塞对",[1925,14822,14824],{"id":14823},"_42-学生最优稳定机制-student-optimal-stable-mechanism-sosm","4.2 学生最优稳定机制 (Student-Optimal Stable Mechanism, SOSM)",[1798,14826,14827,14830],{},[1850,14828,14829],{},"机制","：DA算法，学生求婚",[1798,14832,14833,1957],{},[1850,14834,14835],{},"优点",[1888,14837,14838,14844,14849],{},[1808,14839,14840,14843],{},[1850,14841,14842],{},"激励相容","：真实报告偏好是优势策略（在单方面偏好下）",[1808,14845,14846,14848],{},[1850,14847,5933],{},"：无阻塞对",[1808,14850,14851,14854],{},[1850,14852,14853],{},"学生最优","：所有稳定匹配中学生最满意",[1798,14856,14857,1957],{},[1850,14858,14859],{},"改革实例",[1798,14861,14862,1957],{},[1850,14863,14864],{},"波士顿 (2005)",[1805,14866,14867,14870,14873],{},[1808,14868,14869],{},"旧机制：立即接受算法 → 策略性报告",[1808,14871,14872],{},"新机制：SOSM",[1808,14874,14875],{},"结果：更多学生报告真实第一志愿",[1798,14877,14878,1957],{},[1850,14879,14880],{},"纽约 (2003)",[1805,14882,14883,14886,14889],{},[1808,14884,14885],{},"高中匹配系统改革",[1808,14887,14888],{},"参与学校从17个增加到500+",[1808,14890,14891],{},"学生满意度大幅提升",[1925,14893,14895],{"id":14894},"_43-优先级设计","4.3 优先级设计",[1798,14897,14898,14901],{},[1850,14899,14900],{},"关键问题","：学校如何排序学生？",[1798,14903,14904,1957],{},[1850,14905,14906],{},"常见优先级规则",[1888,14908,14909,14915,14921],{},[1808,14910,14911,14914],{},[1850,14912,14913],{},"兄弟姐妹优先","：有兄弟姐妹在该校的学生优先",[1808,14916,14917,14920],{},[1850,14918,14919],{},"步行距离","：居住地离学校近的优先",[1808,14922,14923,14926],{},[1850,14924,14925],{},"抽签","：随机决定",[1798,14928,14929,1957],{},[1850,14930,14931],{},"权衡",[1805,14933,14934,14937],{},[1808,14935,14936],{},"公平性 vs. 效率",[1808,14938,14939],{},"社区稳定 vs. 择校自由",[1794,14941,14943],{"id":14942},"五器官交换-kidney-exchange","五、器官交换 (Kidney Exchange)",[1925,14945,14947],{"id":14946},"_51-问题设定","5.1 问题设定",[1798,14949,14950,1957],{},[1850,14951,14952],{},"背景",[1805,14954,14955,14958],{},[1808,14956,14957],{},"肾脏移植需求远超供给",[1808,14959,14960],{},"很多患者有愿意捐赠的亲友，但血型\u002F组织不兼容",[1798,14962,14963,1957,14966],{},[1850,14964,14965],{},"解决方案",[1850,14967,14968],{},"配对捐赠 (Paired Donation)",[1805,14970,14971,14974],{},[1808,14972,14973],{},"患者A的捐赠者 → 患者B",[1808,14975,14976],{},"患者B的捐赠者 → 患者A",[1798,14978,14979,1957],{},[1850,14980,14981],{},"挑战",[1805,14983,14984,14987,14990],{},[1808,14985,14986],{},"两对以上的循环交换（3对、4对）",[1808,14988,14989],{},"物流复杂性（同时手术）",[1808,14991,14992],{},"激励相容（如何防止捐赠者反悔？）",[1925,14994,14996],{"id":14995},"_52-顶级交易循环算法-top-trading-cycles-ttc","5.2 顶级交易循环算法 (Top Trading Cycles, TTC)",[1798,14998,14999,15002],{},[1850,15000,15001],{},"Shapley-Scarf (1974)"," 房屋交换问题的推广：",[1798,15004,15005,1957],{},[1850,15006,15007],{},"算法",[7403,15009,15012],{"className":15010,"code":15011,"language":7408},[7406],"while 存在未匹配的对:\n    每对指向其最偏好的未匹配对\n    找到所有循环（A → B → C → A）\n    执行循环中的交换\n    移除已匹配的对\n",[7410,15013,15011],{"__ignoreMap":10},[1798,15015,15016,1957],{},[1850,15017,14721],{},[1805,15019,15020,15023,15026],{},[1808,15021,15022],{},"Pareto有效",[1808,15024,15025],{},"激励相容（真实报告偏好是优势策略）",[1808,15027,15028],{},"策略简单（指向最优）",[1925,15030,15032],{"id":15031},"_53-实际系统","5.3 实际系统",[1798,15034,15035,1957],{},[1850,15036,15037],{},"New England Program for Kidney Exchange (2005)",[1805,15039,15040,15043,15046],{},[1808,15041,15042],{},"Roth等人设计",[1808,15044,15045],{},"整合多个医院",[1808,15047,15048],{},"允许3-way交换",[1798,15050,15051,1957],{},[1850,15052,15053],{},"全国性网络",[1805,15055,15056,15059],{},[1808,15057,15058],{},"UNOS（美国）",[1808,15060,15061],{},"NHS（英国）",[1798,15063,15064,1957],{},[1850,15065,15066],{},"成果",[1805,15068,15069,15072],{},[1808,15070,15071],{},"大幅增加移植数量",[1808,15073,15074],{},"提高匹配质量（更好的组织兼容性）",[1794,15076,15078],{"id":15077},"六市场设计的原则-market-design-principles","六、市场设计的原则 (Market Design Principles)",[1925,15080,15082],{"id":15081},"_61-市场厚度-thickness","6.1 市场厚度 (Thickness)",[1798,15084,15085,15088],{},[1850,15086,15087],{},"定义","：有足够多的参与者同时存在于市场中",[1798,15090,15091,1957],{},[1850,15092,14800],{},[1805,15094,15095,15098],{},[1808,15096,15097],{},"市场太薄 → 难以找到好匹配",[1808,15099,15100],{},"市场分散（时间\u002F空间）→ 效率低",[1798,15102,15103,1957],{},[1850,15104,15105],{},"解决",[1805,15107,15108,15114],{},[1808,15109,15110,15113],{},[1850,15111,15112],{},"集中化","：统一平台（如NRMP）",[1808,15115,15116,15119],{},[1850,15117,15118],{},"时间集中","：统一时间点（如高考志愿填报）",[1925,15121,15123],{"id":15122},"_62-避免拥堵-congestion","6.2 避免拥堵 (Congestion)",[1798,15125,15126,15128],{},[1850,15127,15087],{},"：市场处理速度快，不让参与者等待",[1798,15130,15131,1957],{},[1850,15132,14800],{},[1805,15134,15135,15138],{},[1808,15136,15137],{},"算法太慢 → 参与者绕过机制",[1808,15139,15140],{},"信息过载 → 决策质量下降",[1798,15142,15143,1957],{},[1850,15144,15105],{},[1805,15146,15147,15150],{},[1808,15148,15149],{},"限制排名长度（如NRMP限制12个）",[1808,15151,15152,15153,15226],{},"高效算法（DA是 ",[1963,15154,15156,15179],{"className":15155},[1966],[1963,15157,15159],{"className":15158},[1970],[1972,15160,15161],{"xmlns":1974},[1976,15162,15163,15177],{},[1979,15164,15165,15167,15169,15175],{},[1982,15166,13373],{},[2026,15168,2643],{"stretchy":2031},[11730,15170,15171,15173],{},[1982,15172,1984],{},[2040,15174,2052],{},[2026,15176,2653],{"stretchy":2031},[1986,15178,13386],{"encoding":1988},[1963,15180,15182],{"className":15181,"ariaHidden":1993},[1992],[1963,15183,15185,15188,15191,15194,15223],{"className":15184},[1997],[1963,15186],{"className":15187,"style":13396},[2001],[1963,15189,13373],{"className":15190,"style":13400},[2006,2007],[1963,15192,2643],{"className":15193},[2106],[1963,15195,15197,15200],{"className":15196},[2006],[1963,15198,1984],{"className":15199,"style":2008},[2006,2007],[1963,15201,15203],{"className":15202},[2116],[1963,15204,15206],{"className":15205},[2120],[1963,15207,15209],{"className":15208},[2125],[1963,15210,15212],{"className":15211,"style":11748},[2129],[1963,15213,15214,15217],{"style":11769},[1963,15215],{"className":15216,"style":2138},[2137],[1963,15218,15220],{"className":15219},[2142,2143,2144,2145],[1963,15221,2052],{"className":15222},[2006,2145],[1963,15224,2653],{"className":15225},[2274],"，可接受）",[1925,15228,15230],{"id":15229},"_63-安全性-safety","6.3 安全性 (Safety)",[1798,15232,15233,15235],{},[1850,15234,15087],{},"：参与者愿意真实报告偏好",[1798,15237,15238,1957],{},[1850,15239,14800],{},[1805,15241,15242,15245],{},[1808,15243,15244],{},"策略性报告 → 低效率",[1808,15246,15247],{},"复杂策略 → 不公平（有经验者占优）",[1798,15249,15250,1957],{},[1850,15251,15105],{},[1805,15253,15254,15257],{},[1808,15255,15256],{},"激励相容机制（DA、TTC）",[1808,15258,15259],{},"简单明了的规则",[1925,15261,15263],{"id":15262},"_64-roth的市场设计失败案例","6.4 Roth的市场设计失败案例",[1798,15265,15266,15269],{},[1850,15267,15268],{},"英国肾脏交换","（早期）：",[1805,15271,15272,15275],{},[1808,15273,15274],{},"设计复杂，难以理解",[1808,15276,15277],{},"医院不信任 → 参与率低",[1798,15279,15280,1957],{},[1850,15281,15282],{},"加州大学招生",[1805,15284,15285,15288],{},[1808,15286,15287],{},"时间分散 → 提前抢人",[1808,15289,15290],{},"缺乏集中机制",[1798,15292,15293,15296],{},[1850,15294,15295],{},"教训","：理论正确不够，还需考虑实践约束和参与者心理。",[1794,15298,15300],{"id":15299},"七前沿话题-advanced-topics","七、前沿话题 (Advanced Topics)",[1925,15302,15304],{"id":15303},"_70-论文精读从匹配机制到平台治理","7.0 论文精读：从匹配机制到平台治理",[1798,15306,15307],{},"市场设计的 fundamental 不是“写一个算法把双方配起来”，而是设计一套规则，使市场足够厚、参与者愿意进入、策略行为不至于毁掉结果，并且匹配结果能被参与者接受。DA、TTC、肾脏交换和学校选择都围绕这几个标准展开。",[1798,15309,15310],{},"数字平台把这些标准放进了一个更复杂的环境。平台不仅决定“谁和谁匹配”，还决定谁先被看见、信息披露到什么程度、评价如何影响未来机会、佣金和补贴如何改变参与者激励。用机制设计语言写，可以把平台规则看作：",[1963,15312,15315],{"className":15313},[15314],"katex-display",[1963,15316,15318,15369],{"className":15317},[1966],[1963,15319,15321],{"className":15320},[1970],[1972,15322,15324],{"xmlns":1974,"display":15323},"block",[1976,15325,15326,15366],{},[1979,15327,15328,15332,15334,15336,15338,15341,15343,15346,15348,15351,15353,15356,15358,15361,15363],{},[15329,15330,15331],"mtext",{},"outcome",[2026,15333,2028],{},[1982,15335,2024],{},[2026,15337,2643],{"stretchy":2031},[15329,15339,15340],{},"preferences",[2026,15342,2045],{"separator":1993},[15329,15344,15345],{},"information",[2026,15347,2045],{"separator":1993},[15329,15349,15350],{},"ranking rule",[2026,15352,2045],{"separator":1993},[15329,15354,15355],{},"prices",[2026,15357,2045],{"separator":1993},[15329,15359,15360],{},"reputation",[2026,15362,2653],{"stretchy":2031},[1982,15364,15365],{"mathvariant":12468},".",[1986,15367,15368],{"encoding":1988},"\\text{outcome}=M(\\text{preferences},\\text{information},\\text{ranking rule},\\text{prices},\\text{reputation}).",[1963,15370,15372,15394],{"className":15371,"ariaHidden":1993},[1992],[1963,15373,15375,15379,15385,15388,15391],{"className":15374},[1997],[1963,15376],{"className":15377,"style":15378},[2001],"height:0.6151em;",[1963,15380,15382],{"className":15381},[2006,7408],[1963,15383,15331],{"className":15384},[2006],[1963,15386],{"className":15387,"style":2088},[2087],[1963,15389,2028],{"className":15390},[2092],[1963,15392],{"className":15393,"style":2088},[2087],[1963,15395,15397,15400,15403,15406,15412,15415,15418,15424,15427,15430,15436,15439,15442,15448,15451,15454,15460,15463],{"className":15396},[1997],[1963,15398],{"className":15399,"style":2102},[2001],[1963,15401,2024],{"className":15402,"style":2008},[2006,2007],[1963,15404,2643],{"className":15405},[2106],[1963,15407,15409],{"className":15408},[2006,7408],[1963,15410,15340],{"className":15411},[2006],[1963,15413,2045],{"className":15414},[2166],[1963,15416],{"className":15417,"style":2170},[2087],[1963,15419,15421],{"className":15420},[2006,7408],[1963,15422,15345],{"className":15423},[2006],[1963,15425,2045],{"className":15426},[2166],[1963,15428],{"className":15429,"style":2170},[2087],[1963,15431,15433],{"className":15432},[2006,7408],[1963,15434,15350],{"className":15435},[2006],[1963,15437,2045],{"className":15438},[2166],[1963,15440],{"className":15441,"style":2170},[2087],[1963,15443,15445],{"className":15444},[2006,7408],[1963,15446,15355],{"className":15447},[2006],[1963,15449,2045],{"className":15450},[2166],[1963,15452],{"className":15453,"style":2170},[2087],[1963,15455,15457],{"className":15456},[2006,7408],[1963,15458,15360],{"className":15459},[2006],[1963,15461,2653],{"className":15462},[2274],[1963,15464,15365],{"className":15465},[2006],[1798,15467,15468],{},"这比传统匹配多了几个变量。学校选择中，学生提交偏好列表，机制给出学校；外卖平台中，消费者看到的商家列表本身已经被排序规则加工过，商家的“偏好”也会被佣金、配送费、流量和评分影响。",[1798,15470,15471],{},"读平台经济论文时，可以把 fundamental 和前沿问题一一对应：",[15473,15474,15475,15491],"table",{},[15476,15477,15478],"thead",{},[15479,15480,15481,15485,15488],"tr",{},[15482,15483,15484],"th",{},"市场设计基础问题",[15482,15486,15487],{},"平台里的对应问题",[15482,15489,15490],{},"读论文时要看",[15492,15493,15494,15506,15517,15527],"tbody",{},[15479,15495,15496,15500,15503],{},[15497,15498,15499],"td",{},"厚度",[15497,15501,15502],{},"是否有足够买家和卖家同时参与",[15497,15504,15505],{},"平台补贴、准入规则和多归属是否影响参与。",[15479,15507,15508,15511,15514],{},[15497,15509,15510],{},"拥堵",[15497,15512,15513],{},"参与者太多时如何筛选和排序",[15497,15515,15516],{},"搜索排序、推荐系统和默认展示是否改变可见性。",[15479,15518,15519,15521,15524],{},[15497,15520,14842],{},[15497,15522,15523],{},"参与者是否愿意真实报告偏好或质量",[15497,15525,15526],{},"评分操纵、刷单、策略性定价和虚假披露。",[15479,15528,15529,15532,15535],{},[15497,15530,15531],{},"安全与信任",[15497,15533,15534],{},"参与者是否相信机制可执行",[15497,15536,15537],{},"申诉、处罚、评价纠错和数据透明度。",[1798,15539,15540],{},"Martin (2024, DOI: 10.1111\u002F1756-2171.12485) 关于市场透明度和消费者搜索的研究，可以这样放进本章：传统直觉常以为信息越透明越好，但市场设计会问更细的问题：披露哪些信息、以什么顺序披露、消费者是否真的处理得了这些信息、卖家会不会因为披露规则改变价格。它对应的是本章的“信息结构设计”，不是一句普通的市场背景。",[1798,15542,15543],{},"Wessel et al. (2025, DOI: 10.1080\u002F07421222.2025.2487315) 讨论生成式 AI 对数字平台价值创造的影响，也可以用同样方式读。生成式 AI 让平台从“匹配用户和内容\u002F商家”进一步走向“替用户生成、筛选和代理行动”。这会改变偏好表达方式：过去用户显式搜索，现在用户可能让 AI agent 替自己筛选。市场设计问题随之变成：AI 代理代表谁的偏好？平台是否能操纵代理看到的选择集？推荐结果是否仍然可解释、可申诉？",[1798,15545,15546],{},"Tang and Xu (2025, DOI: 10.1111\u002Fjems.12630) 则连接到市场势力。数字技术如果只是降低交易成本，平台会提高效率；但如果它同时让头部企业积累数据、优化定价、锁定用户，就可能提高进入壁垒和议价能力。把这篇论文放进市场设计章节，关键是理解：机制不只是分配效率问题，也是权力分配问题。",[1798,15548,15549],{},"因此，平台治理论文的系统读法不是“用了算法，所以是前沿”。而是：",[1888,15551,15552,15555,15558,15561],{},[1808,15553,15554],{},"平台规则如何改变参与者看到的选择集；",[1808,15556,15557],{},"平台规则如何改变参与者报告信息和采取行动的激励；",[1808,15559,15560],{},"平台规则如何改变市场厚度、拥堵和信任；",[1808,15562,15563],{},"平台规则是否把效率提升转化成某一方的市场势力。",[1798,15565,15566],{},"这条线把 DA、TTC 这类经典机制和生成式 AI 平台接在一起：二者都在回答同一个问题，只是现代平台把信息、价格、排序、声誉和自动代理全部放进了机制本身。",[1925,15568,15570],{"id":15569},"_71-匹配与契约-matching-with-contracts","7.1 匹配与契约 (Matching with Contracts)",[1798,15572,15573,15576],{},[1850,15574,15575],{},"推广","：匹配不仅是\"谁和谁\"，还包括合同条款（如工资、工作时间）",[1798,15578,15579,1957],{},[1850,15580,15581],{},"应用",[1805,15583,15584,15587],{},[1808,15585,15586],{},"医生匹配中加入薪资谈判",[1808,15588,15589],{},"学校选择中加入课程包",[1925,15591,15593],{"id":15592},"_72-动态匹配-dynamic-matching","7.2 动态匹配 (Dynamic Matching)",[1798,15595,15596,15598],{},[1850,15597,14800],{},"：参与者随时间到达和离开",[1798,15600,15601,1957],{},[1850,15602,15581],{},[1805,15604,15605,15608],{},[1808,15606,15607],{},"器官移植（器官供给随机到达）",[1808,15609,15610],{},"在线约会平台",[1798,15612,15613,1957],{},[1850,15614,14981],{},[1805,15616,15617,15620],{},[1808,15618,15619],{},"何时匹配vs.等待更好选项",[1808,15621,15622],{},"厚度 vs. 及时性的权衡",[1925,15624,15626],{"id":15625},"_73-匹配与货币-matching-with-transfers","7.3 匹配与货币 (Matching with Transfers)",[1798,15628,15629,1957],{},[1850,15630,15631],{},"放松无货币约束",[1805,15633,15634,15637],{},[1808,15635,15636],{},"允许一方支付另一方",[1808,15638,15639],{},"例：肾脏交换中允许\"链\"（利他捐赠启动）",[1798,15641,15642,15645],{},[1850,15643,15644],{},"理论","：结合匹配理论和机制设计",[1925,15647,15649],{"id":15648},"_74-在线平台的匹配","7.4 在线平台的匹配",[1798,15651,15652,1957],{},[1850,15653,15654],{},"例子",[1805,15656,15657,15660,15663],{},[1808,15658,15659],{},"Airbnb：房东-房客匹配",[1808,15661,15662],{},"Uber：司机-乘客匹配",[1808,15664,15665],{},"在线约会：Tinder、探探",[1798,15667,15668,1957],{},[1850,15669,15670],{},"特点",[1805,15672,15673,15676,15679],{},[1808,15674,15675],{},"实时、大规模",[1808,15677,15678],{},"机器学习辅助偏好推断",[1808,15680,15681],{},"双边评级系统",[1798,15683,15684],{},[1850,15685,15686],{},"近年前沿：平台规则和算法定价",[1798,15688,15689],{},"在线平台不只是把买卖双方“放在一起”，它还会决定搜索排序、流量分配、佣金、处罚、推荐和价格展示方式。Chen et al. (2021) 把数字平台治理和设计放在同一个框架里讨论；Bonina et al. (2021) 进一步提醒我们，平台能不能带来发展收益，还取决于制度环境、参与者能力和治理规则。",[1798,15691,15692],{},"算法定价让这个问题更复杂。Assad, Clark, Ershov & Xu (2023) 研究德国汽油市场时发现，算法定价会改变竞争过程；Johnson, Rhodes & Wildenbeest (2023) 则说明，当卖家使用定价算法时，平台如何分配需求会影响算法之间是否更容易形成类似合谋的结果。对本章来说，这些研究把“市场设计”从学校选择、医生匹配扩展到了日常数字市场。",[15473,15694,15695,15708],{},[15476,15696,15697],{},[15479,15698,15699,15702,15705],{},[15482,15700,15701],{},"平台设计问题",[15482,15703,15704],{},"对应的市场设计语言",[15482,15706,15707],{},"学生应关注的点",[15492,15709,15710,15721,15732,15743],{},[15479,15711,15712,15715,15718],{},[15497,15713,15714],{},"搜索排序和推荐",[15497,15716,15717],{},"厚度、拥堵、信息披露",[15497,15719,15720],{},"排名规则会改变谁被看见，也会改变参与者策略。",[15479,15722,15723,15726,15729],{},[15497,15724,15725],{},"平台导流规则",[15497,15727,15728],{},"机制约束、激励相容",[15497,15730,15731],{},"规则不只是技术细节，可能抑制或放大算法合谋。",[15479,15733,15734,15737,15740],{},[15497,15735,15736],{},"双边评价系统",[15497,15738,15739],{},"信任、安全性、声誉机制",[15497,15741,15742],{},"评分能降低信息不对称，也可能带来歧视和策略性评价。",[15479,15744,15745,15748,15751],{},[15497,15746,15747],{},"平台治理",[15497,15749,15750],{},"准入、处罚、申诉和数据权利",[15497,15752,15753],{},"一个市场能否长期运行，取决于参与者是否相信规则。",[1794,15755,15757],{"id":15756},"直觉总结-intuitive-summary","直觉总结 (Intuitive Summary)",[1925,15759,15760],{"id":15760},"匹配理论的核心洞见",[1888,15762,15763,15776,15789,15802],{},[1808,15764,15765,15768],{},[1850,15766,15767],{},"稳定性是关键",[1805,15769,15770,15773],{},[1808,15771,15772],{},"不稳定的匹配会瓦解",[1808,15774,15775],{},"稳定匹配作为均衡概念",[1808,15777,15778,15781],{},[1850,15779,15780],{},"延迟接受的智慧",[1805,15782,15783,15786],{},[1808,15784,15785],{},"不立即决定 → 收集更多信息",[1808,15787,15788],{},"女性\"待价而沽\" → 持有最优",[1808,15790,15791,15794],{},[1850,15792,15793],{},"求婚方占优",[1805,15795,15796,15799],{},[1808,15797,15798],{},"DA算法的不对称性",[1808,15800,15801],{},"设计时选择哪方求婚很重要",[1808,15803,15804,15807],{},[1850,15805,15806],{},"激励相容的价值",[1805,15808,15809,15812],{},[1808,15810,15811],{},"真实报告 → 简化决策、提高参与",[1808,15813,15814],{},"不是所有机制都激励相容",[1925,15816,15817],{"id":15817},"匹配机制比较",[15473,15819,15820,15836],{},[15476,15821,15822],{},[15479,15823,15824,15826,15829,15831,15834],{},[15482,15825,14829],{},[15482,15827,15828],{},"稳定性",[15482,15830,14842],{},[15482,15832,15833],{},"效率",[15482,15835,15581],{},[15492,15837,15838,15857,15873,15890,15907],{},[15479,15839,15840,15845,15848,15851,15854],{},[15497,15841,15842],{},[1850,15843,15844],{},"DA (男求婚)",[15497,15846,15847],{},"✓",[15497,15849,15850],{},"✓*",[15497,15852,15853],{},"男性最优稳定",[15497,15855,15856],{},"医生匹配",[15479,15858,15859,15864,15866,15868,15871],{},[15497,15860,15861],{},[1850,15862,15863],{},"DA (女求婚)",[15497,15865,15847],{},[15497,15867,15850],{},[15497,15869,15870],{},"女性最优稳定",[15497,15872,1860],{},[15479,15874,15875,15880,15883,15885,15887],{},[15497,15876,15877],{},[1850,15878,15879],{},"TTC",[15497,15881,15882],{},"✗",[15497,15884,15847],{},[15497,15886,15022],{},[15497,15888,15889],{},"器官交换、学校选择",[15479,15891,15892,15897,15899,15901,15904],{},[15497,15893,15894],{},[1850,15895,15896],{},"立即接受",[15497,15898,15882],{},[15497,15900,15882],{},[15497,15902,15903],{},"低",[15497,15905,15906],{},"旧波士顿机制",[15479,15908,15909,15914,15916,15918,15921],{},[15497,15910,15911],{},[1850,15912,15913],{},"Serial Dictatorship",[15497,15915,15882],{},[15497,15917,15847],{},[15497,15919,15920],{},"独裁者最优",[15497,15922,15923],{},"宿舍分配",[1798,15925,15926],{},"*在单方面偏好或特定条件下",[1925,15928,15930],{"id":15929},"理论-vs-实践","理论 vs. 实践",[1798,15932,15933,1957],{},[1850,15934,15935],{},"理论提供",[1805,15937,15938,15941,15944],{},[1808,15939,15940],{},"稳定性概念",[1808,15942,15943],{},"算法保证",[1808,15945,15946],{},"性质分析",[1798,15948,15949,1957],{},[1850,15950,15951],{},"实践需要",[1805,15953,15954,15957,15960],{},[1808,15955,15956],{},"简单易懂",[1808,15958,15959],{},"适应约束（如夫妇匹配）",[1808,15961,15962],{},"获得参与者信任",[1798,15964,15965,15968],{},[1850,15966,15967],{},"成功案例","：理论与实践紧密结合（如Roth的工作）",[1794,15970,15972],{"id":15971},"文献导读-literature-guide","文献导读 (Literature Guide)",[1798,15974,15975,1957],{},[1850,15976,15977],{},"奠基性论文",[1805,15979,15980,15987,15994],{},[1808,15981,15982,15983,15365],{},"Gale, D., & Shapley, L. (1962). \"College Admissions and the Stability of Marriage.\" ",[15984,15985,15986],"em",{},"American Mathematical Monthly",[1808,15988,15989,15990,15993],{},"Shapley, L., & Scarf, H. (1974). \"On Cores and Indivisibility.\" ",[15984,15991,15992],{},"Journal of Mathematical Economics",". (TTC)",[1808,15995,15996,15997,15365],{},"Roth, A. (1984). \"The Evolution of the Labor Market for Medical Interns and Residents.\" ",[15984,15998,15999],{},"JPE",[1798,16001,16002,1957],{},[1850,16003,16004],{},"应用文献",[1805,16006,16007,16013,16019],{},[1808,16008,16009,16010,15365],{},"Abdulkadiroğlu, A., & Sönmez, T. (2003). \"School Choice: A Mechanism Design Approach.\" ",[15984,16011,16012],{},"AER",[1808,16014,16015,16016,15365],{},"Roth, A., Sönmez, T., & Ünver, M. (2004). \"Kidney Exchange.\" ",[15984,16017,16018],{},"QJE",[1808,16020,16021,16022,15365],{},"Pathak, P., & Sönmez, T. (2008). \"Leveling the Playing Field: Sincere and Sophisticated Players in the Boston Mechanism.\" ",[15984,16023,16012],{},[1798,16025,16026,1957],{},[1850,16027,16028],{},"综述",[1805,16030,16031,16037],{},[1808,16032,16033,16034,15365],{},"Roth, A. (2008). \"Deferred Acceptance Algorithms: History, Theory, Practice, and Open Questions.\" ",[15984,16035,16036],{},"International Journal of Game Theory",[1808,16038,16039,16040,15365],{},"Sönmez, T., & Ünver, M. (2011). \"Matching, Allocation, and Exchange of Discrete Resources.\" In ",[15984,16041,16042],{},"Handbook of Social Economics",[1798,16044,16045,1957],{},[1850,16046,16047],{},"教科书\u002F通俗读物",[1805,16049,16050,16057],{},[1808,16051,16052,16053,16056],{},"Roth, A. (2015). ",[15984,16054,16055],{},"Who Gets What — and Why: The New Economics of Matchmaking and Market Design",". Houghton Mifflin. (畅销书)",[1808,16058,16059,16060,15365],{},"Kojima, F., & Pathak, P. (2009). \"Incentives and Stability in Large Two-Sided Matching Markets.\" ",[15984,16061,16012],{},[1798,16063,16064,1957],{},[1850,16065,16066],{},"前沿",[1805,16068,16069],{},[1808,16070,16071],{},"动态匹配、在线平台、机器学习与匹配",[1794,16073,16074],{"id":16074},"本章小结",[1798,16076,16077,16078,16080,16081,16084,16085,16088,16089,16162],{},"匹配理论研究在",[1850,16079,1900],{},"的市场中如何进行资源配置。",[1850,16082,16083],{},"Gale-Shapley算法","（延迟接受算法）通过系统性地消除阻塞对，保证找到",[1850,16086,16087],{},"稳定匹配","，并具有对求婚方最优的性质。该算法在 ",[1963,16090,16092,16115],{"className":16091},[1966],[1963,16093,16095],{"className":16094},[1970],[1972,16096,16097],{"xmlns":1974},[1976,16098,16099,16113],{},[1979,16100,16101,16103,16105,16111],{},[1982,16102,13373],{},[2026,16104,2643],{"stretchy":2031},[11730,16106,16107,16109],{},[1982,16108,1984],{},[2040,16110,2052],{},[2026,16112,2653],{"stretchy":2031},[1986,16114,13386],{"encoding":1988},[1963,16116,16118],{"className":16117,"ariaHidden":1993},[1992],[1963,16119,16121,16124,16127,16130,16159],{"className":16120},[1997],[1963,16122],{"className":16123,"style":13396},[2001],[1963,16125,13373],{"className":16126,"style":13400},[2006,2007],[1963,16128,2643],{"className":16129},[2106],[1963,16131,16133,16136],{"className":16132},[2006],[1963,16134,1984],{"className":16135,"style":2008},[2006,2007],[1963,16137,16139],{"className":16138},[2116],[1963,16140,16142],{"className":16141},[2120],[1963,16143,16145],{"className":16144},[2125],[1963,16146,16148],{"className":16147,"style":11748},[2129],[1963,16149,16150,16153],{"style":11769},[1963,16151],{"className":16152,"style":2138},[2137],[1963,16154,16156],{"className":16155},[2142,2143,2144,2145],[1963,16157,2052],{"className":16158},[2006,2145],[1963,16160,2653],{"className":16161},[2274]," 时间内终止，且可推广到多对一匹配。",[1798,16164,16165],{},"匹配理论有广泛的实际应用：",[1805,16167,16168,16173,16178],{},[1808,16169,16170,16172],{},[1850,16171,15856],{},"：NRMP使用DA算法，减少毁约和市场混乱",[1808,16174,16175,16177],{},[1850,16176,1860],{},"：波士顿、纽约等改革，采用学生最优稳定机制，提高公平性和激励相容性",[1808,16179,16180,16183],{},[1850,16181,16182],{},"器官交换","：TTC算法支持配对捐赠，大幅增加肾脏移植数量",[1798,16185,16186,16187,16190,16191,16194,16195,16198],{},"成功的市场设计需要遵循关键原则：",[1850,16188,16189],{},"市场厚度","（足够参与者）、",[1850,16192,16193],{},"避免拥堵","（快速处理）、",[1850,16196,16197],{},"安全性","（激励相容）。Alvin Roth等经济学家展示了如何将深刻的理论洞见转化为解决现实问题的有效工具，产生了巨大的社会效益。",[1798,16200,16201],{},"匹配理论仍在不断发展，前沿研究包括动态匹配、在线平台设计、以及将匹配与机器学习相结合，为数字经济时代的市场设计提供新的工具和洞见。",[1794,16203,16204],{"id":16204},"自学检查",[1798,16206,16207,16210],{},[1850,16208,16209],{},"核心直觉回看","：市场设计关注“价格机制不够用或不能用”的配置问题。好的机制需要让市场足够厚、运行不拥堵，并让参与者觉得如实参与是安全的。",[1798,16212,16213,16216],{},[1850,16214,16215],{},"关键模型提醒","：稳定匹配要求不存在阻塞对。延迟接受算法的基本逻辑是：一方依偏好逐轮申请，另一方暂留当前最优申请者，直到没有新的申请。算法终止时得到稳定匹配，并对申请方最优。",[1925,16218,16219],{"id":16219},"常见误区",[1805,16221,16222,16225,16228,16231],{},[1808,16223,16224],{},"把稳定匹配等同于总福利最大化。稳定强调没有阻塞对，不一定最大化所有人的效用总和。",[1808,16226,16227],{},"认为 DA 算法对双方都策略无关。标准学生申请版本通常对学生方策略安全，对学校方不一定。",[1808,16229,16230],{},"混淆偏好和优先级。学校选择中，学生有偏好，学校常有由政策决定的优先顺序。",[1808,16232,16233],{},"忽略现实约束，例如容量、夫妇匹配、地区公平和信息提交成本。",[1925,16235,16236],{"id":16236},"自测题",[1888,16238,16239,16242,16245,16248,16251],{},[1808,16240,16241],{},"什么是阻塞对？为什么它会破坏匹配的稳定性？",[1808,16243,16244],{},"用三名学生和三所学校构造一个 DA 算法的执行过程。",[1808,16246,16247],{},"学生最优稳定机制中的“学生最优”是什么意思？",[1808,16249,16250],{},"TTC 算法为什么适合住房交换或肾脏交换这类问题？",[1808,16252,16253],{},"一个真实市场设计项目为什么要同时考虑厚度、拥堵和安全性？",[1925,16255,16256],{"id":16256},"下一步学习提示",[1798,16258,16259],{},"最后一章会把全课程工具放到数字平台、算法和数据市场中。复习时请练习为每个现实问题选择合适工具：是价格问题、策略问题、信息问题，还是匹配问题？",[16261,16262],"hr",{},[1798,16264,16265,16268,16269,16272],{},[1850,16266,16267],{},"下一章","（最后一章）我们将对整个微观经济学课程进行",[1850,16270,16271],{},"系统总结","，回顾核心理论框架，探讨跨章节的综合应用，并分析数字经济时代的新挑战和政策含义。",{"title":10,"searchDepth":16274,"depth":16274,"links":16275},2,[16276,16277,16281,16286,16292,16297,16302,16307,16313,16320,16325,16326,16327],{"id":1796,"depth":16274,"text":1796},{"id":1844,"depth":16274,"text":1845,"children":16278},[16279],{"id":1927,"depth":16280,"text":1927},3,{"id":1946,"depth":16274,"text":1947,"children":16282},[16283,16284,16285],{"id":1950,"depth":16280,"text":1951},{"id":3220,"depth":16280,"text":3221},{"id":3844,"depth":16280,"text":3845},{"id":7391,"depth":16274,"text":7392,"children":16287},[16288,16289,16290,16291],{"id":7395,"depth":16280,"text":7396},{"id":7439,"depth":16280,"text":7440},{"id":11693,"depth":16280,"text":11694},{"id":13352,"depth":16280,"text":13353},{"id":13628,"depth":16274,"text":13629,"children":16293},[16294,16295,16296],{"id":13632,"depth":16280,"text":13633},{"id":14629,"depth":16280,"text":14630},{"id":14732,"depth":16280,"text":14733},{"id":14776,"depth":16274,"text":14777,"children":16298},[16299,16300,16301],{"id":14780,"depth":16280,"text":14781},{"id":14823,"depth":16280,"text":14824},{"id":14894,"depth":16280,"text":14895},{"id":14942,"depth":16274,"text":14943,"children":16303},[16304,16305,16306],{"id":14946,"depth":16280,"text":14947},{"id":14995,"depth":16280,"text":14996},{"id":15031,"depth":16280,"text":15032},{"id":15077,"depth":16274,"text":15078,"children":16308},[16309,16310,16311,16312],{"id":15081,"depth":16280,"text":15082},{"id":15122,"depth":16280,"text":15123},{"id":15229,"depth":16280,"text":15230},{"id":15262,"depth":16280,"text":15263},{"id":15299,"depth":16274,"text":15300,"children":16314},[16315,16316,16317,16318,16319],{"id":15303,"depth":16280,"text":15304},{"id":15569,"depth":16280,"text":15570},{"id":15592,"depth":16280,"text":15593},{"id":15625,"depth":16280,"text":15626},{"id":15648,"depth":16280,"text":15649},{"id":15756,"depth":16274,"text":15757,"children":16321},[16322,16323,16324],{"id":15760,"depth":16280,"text":15760},{"id":15817,"depth":16280,"text":15817},{"id":15929,"depth":16280,"text":15930},{"id":15971,"depth":16274,"text":15972},{"id":16074,"depth":16274,"text":16074},{"id":16204,"depth":16274,"text":16204,"children":16328},[16329,16330,16331],{"id":16219,"depth":16280,"text":16219},{"id":16236,"depth":16280,"text":16236},{"id":16256,"depth":16280,"text":16256},"稳定匹配、延迟接受算法、学校选择、器官交换与市场设计原则","md",null,{},true,{"title":1614,"description":16332},"3MDuEc7M4Xy0MRrHx6n4B3hA8vAeKSU9QwbKSUf6X8Y",[16340,16342],{"title":1608,"path":1609,"stem":1610,"description":16341,"children":-1},"外部性、庇古税、科斯定理、公共物品供给与VCG机制",{"title":1620,"path":1621,"stem":1622,"description":16343,"children":-1},"微观经济学核心框架回顾，以及数字平台、数据资产、在线广告与算法治理应用",1785754755783]