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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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Start from the design problem",[1798,1832,1833,1834,1838,1839,1842,1843,1846,1847,1850,1851,1854],{},"Agent ",[1835,1836,1837],"code",{},"i"," has private type ",[1835,1840,1841],{},"θ_i",", sends message ",[1835,1844,1845],{},"m_i",", and receives outcome ",[1835,1848,1849],{},"x(m)"," and transfer ",[1835,1852,1853],{},"t_i(m)",". With quasi-linear 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designer must specify:",[2320,2321,2322,2335],"table",{},[2323,2324,2325],"thead",{},[2326,2327,2328,2332],"tr",{},[2329,2330,2331],"th",{},"Element",[2329,2333,2334],{},"Question",[2336,2337,2338,2347,2355,2363,2371,2379],"tbody",{},[2326,2339,2340,2344],{},[2341,2342,2343],"td",{},"type space",[2341,2345,2346],{},"what is privately known?",[2326,2348,2349,2352],{},[2341,2350,2351],{},"message space",[2341,2353,2354],{},"what may participants report or bid?",[2326,2356,2357,2360],{},[2341,2358,2359],{},"outcome rule",[2341,2361,2362],{},"how are goods, positions, or projects assigned?",[2326,2364,2365,2368],{},[2341,2366,2367],{},"transfer rule",[2341,2369,2370],{},"who pays or receives how much?",[2326,2372,2373,2376],{},[2341,2374,2375],{},"objective",[2341,2377,2378],{},"efficiency, revenue, access, fairness, reliability?",[2326,2380,2381,2384],{},[2341,2382,2383],{},"constraints",[2341,2385,2386],{},"IC, IR, budget, privacy, computation, law?",[1798,2388,2389],{},"Mechanism design reverses ordinary game theory: begin with a target, then choose the game whose equilibrium has the desired property.",[1793,2391,2393],{"id":2392},"_2-incentive-and-participation-constraints","2. Incentive and participation constraints",[2395,2396,2398],"h3",{"id":2397},"dominant-strategy-incentive-compatibility","Dominant-strategy incentive compatibility",[1798,2400,2401],{},"Truthful reporting is optimal for every report by others:",[1856,2403,2405],{"className":2404},[1859],[1856,2406,2408,2501],{"className":2407},[1863],[1856,2409,2411],{"className":2410},[1867],[1869,2412,2413],{"xmlns":1871,"display":1872},[1874,2414,2415,2498],{},[1877,2416,2417,2423,2425,2431,2433,2443,2445,2451,2453,2456,2462,2464,2476,2478,2488,2490,2496],{},[1880,2418,2419,2421],{},[1883,2420,1885],{},[1883,2422,1837],{},[1889,2424,1892],{"stretchy":1891},[1880,2426,2427,2429],{},[1883,2428,1914],{},[1883,2430,1837],{},[1889,2432,1899],{"separator":1898},[1880,2434,2435,2437],{},[1883,2436,1914],{},[1877,2438,2439,2441],{},[1889,2440,1946],{},[1883,2442,1837],{},[1889,2444,1909],{"separator":1898},[1880,2446,2447,2449],{},[1883,2448,1914],{},[1883,2450,1837],{},[1889,2452,1919],{"stretchy":1891},[1889,2454,2455],{},"≥",[1880,2457,2458,2460],{},[1883,2459,1885],{},[1883,2461,1837],{},[1889,2463,1892],{"stretchy":1891},[1880,2465,2466,2474],{},[2467,2468,2469,2471],"mover",{"accent":1898},[1883,2470,1914],{},[1889,2472,2473],{},"^",[1883,2475,1837],{},[1889,2477,1899],{"separator":1898},[1880,2479,2480,2482],{},[1883,2481,1914],{},[1877,2483,2484,2486],{},[1889,2485,1946],{},[1883,2487,1837],{},[1889,2489,1909],{"separator":1898},[1880,2491,2492,2494],{},[1883,2493,1914],{},[1883,2495,1837],{},[1889,2497,1919],{"stretchy":1891},[1958,2499,2500],{"encoding":1960},"u_i(\\theta_i,\\theta_{-i};\\theta_i)\n\\ge\nu_i(\\hat\\theta_i,\\theta_{-i};\\theta_i)",[1856,2502,2504,2704],{"className":2503,"ariaHidden":1898},[1965],[1856,2505,2507,2510,2550,2553,2593,2596,2599,2646,2649,2652,2692,2695,2698,2701],{"className":2506},[1969],[1856,2508],{"className":2509,"style":1974},[1973],[1856,2511,2513,2516],{"className":2512},[1978],[1856,2514,1885],{"className":2515},[1978,1982],[1856,2517,2519],{"className":2518},[1986],[1856,2520,2522,2542],{"className":2521},[1990,1991],[1856,2523,2525,2539],{"className":2524},[1995],[1856,2526,2528],{"className":2527,"style":2000},[1999],[1856,2529,2530,2533],{"style":2003},[1856,2531],{"className":2532,"style":2008},[2007],[1856,2534,2536],{"className":2535},[2012,2013,2014,2015],[1856,2537,1837],{"className":2538},[1978,1982,2015],[1856,2540,2023],{"className":2541},[2022],[1856,2543,2545],{"className":2544},[1995],[1856,2546,2548],{"className":2547,"style":2030},[1999],[1856,2549],{},[1856,2551,1892],{"className":2552},[2036],[1856,2554,2556,2559],{"className":2555},[1978],[1856,2557,1914],{"className":2558,"style":2101},[1978,1982],[1856,2560,2562],{"className":2561},[1986],[1856,2563,2565,2585],{"className":2564},[1990,1991],[1856,2566,2568,2582],{"className":2567},[1995],[1856,2569,2571],{"className":2570,"style":2000},[1999],[1856,2572,2573,2576],{"style":2116},[1856,2574],{"className":2575,"style":2008},[2007],[1856,2577,2579],{"className":2578},[2012,2013,2014,2015],[1856,2580,1837],{"className":2581},[1978,1982,2015],[1856,2583,2023],{"className":2584},[2022],[1856,2586,2588],{"className":2587},[1995],[1856,2589,2591],{"className":2590,"style":2030},[1999],[1856,2592],{},[1856,2594,1899],{"className":2595},[2043],[1856,2597],{"className":2598,"style":2048},[2047],[1856,2600,2602,2605],{"className":2601},[1978],[1856,2603,1914],{"className":2604,"style":2101},[1978,1982],[1856,2606,2608],{"className":2607},[1986],[1856,2609,2611,2637],{"className":2610},[1990,1991],[1856,2612,2614,2634],{"className":2613},[1995],[1856,2615,2617],{"className":2616,"style":2000},[1999],[1856,2618,2619,2622],{"style":2116},[1856,2620],{"className":2621,"style":2008},[2007],[1856,2623,2625],{"className":2624},[2012,2013,2014,2015],[1856,2626,2628,2631],{"className":2627},[1978,2015],[1856,2629,1946],{"className":2630},[1978,2015],[1856,2632,1837],{"className":2633},[1978,1982,2015],[1856,2635,2023],{"className":2636},[2022],[1856,2638,2640],{"className":2639},[1995],[1856,2641,2644],{"className":2642,"style":2643},[1999],"height:0.2083em;",[1856,2645],{},[1856,2647,1909],{"className":2648},[2043],[1856,2650],{"className":2651,"style":2048},[2047],[1856,2653,2655,2658],{"className":2654},[1978],[1856,2656,1914],{"className":2657,"style":2101},[1978,1982],[1856,2659,2661],{"className":2660},[1986],[1856,2662,2664,2684],{"className":2663},[1990,1991],[1856,2665,2667,2681],{"className":2666},[1995],[1856,2668,2670],{"className":2669,"style":2000},[1999],[1856,2671,2672,2675],{"style":2116},[1856,2673],{"className":2674,"style":2008},[2007],[1856,2676,2678],{"className":2677},[2012,2013,2014,2015],[1856,2679,1837],{"className":2680},[1978,1982,2015],[1856,2682,2023],{"className":2683},[2022],[1856,2685,2687],{"className":2686},[1995],[1856,2688,2690],{"className":2689,"style":2030},[1999],[1856,2691],{},[1856,2693,1919],{"className":2694},[2140],[1856,2696],{"className":2697,"style":2144},[2047],[1856,2699,2455],{"className":2700},[2148],[1856,2702],{"className":2703,"style":2144},[2047],[1856,2705,2707,2711,2751,2754,2829,2832,2835,2881,2884,2887,2927],{"className":2706},[1969],[1856,2708],{"className":2709,"style":2710},[1973],"height:1.2079em;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rationality",[1798,3814,3815],{},"Participation must beat the outside option:",[1856,3817,3819],{"className":3818},[1859],[1856,3820,3822,3861],{"className":3821},[1863],[1856,3823,3825],{"className":3824},[1867],[1869,3826,3827],{"xmlns":1871,"display":1872},[1874,3828,3829,3858],{},[1877,3830,3831,3833,3835,3841,3843,3845,3856],{},[1883,3832,2969],{},[1889,3834,2993],{"stretchy":1891},[1880,3836,3837,3839],{},[1883,3838,1885],{},[1883,3840,1837],{},[1889,3842,3032],{"stretchy":1891},[1889,3844,2455],{},[1880,3846,3847,3854],{},[2467,3848,3849,3851],{"accent":1898},[1883,3850,1885],{},[1889,3852,3853],{},"ˉ",[1883,3855,1837],{},[1883,3857,1956],{"mathvariant":1955},[1958,3859,3860],{"encoding":1960},"E[u_i]\\ge \\bar u_i.",[1856,3862,3864,3928],{"className":3863,"ariaHidden":1898},[1965],[1856,3865,3867,3870,3873,3876,3916,3919,3922,3925],{"className":3866},[1969],[1856,3868],{"className":3869,"style":1974},[1973],[1856,3871,2969],{"className":3872,"style":3124},[1978,1982],[1856,3874,2993],{"className":3875},[2036],[1856,3877,3879,3882],{"className":3878},[1978],[1856,3880,1885],{"className":3881},[1978,1982],[1856,3883,3885],{"className":3884},[1986],[1856,3886,3888,3908],{"className":3887},[1990,1991],[1856,3889,3891,3905],{"className":3890},[1995],[1856,3892,3894],{"className":3893,"style":2000},[1999],[1856,3895,3896,3899],{"style":2003},[1856,3897],{"className":3898,"style":2008},[2007],[1856,3900,3902],{"className":3901},[2012,2013,2014,2015],[1856,3903,1837],{"className":3904},[1978,1982,2015],[1856,3906,2023],{"className":3907},[2022],[1856,3909,3911],{"className":3910},[1995],[1856,3912,3914],{"className":3913,"style":2030},[1999],[1856,3915],{},[1856,3917,3032],{"className":3918},[2140],[1856,3920],{"className":3921,"style":2144},[2047],[1856,3923,2455],{"className":3924},[2148],[1856,3926],{"className":3927,"style":2144},[2047],[1856,3929,3931,3935,4005],{"className":3930},[1969],[1856,3932],{"className":3933,"style":3934},[1973],"height:0.7178em;vertical-align:-0.15em;",[1856,3936,3938,3971],{"className":3937},[1978],[1856,3939,3941],{"className":3940},[1978,2760],[1856,3942,3944],{"className":3943},[1990],[1856,3945,3947],{"className":3946},[1995],[1856,3948,3951,3959],{"className":3949,"style":3950},[1999],"height:0.5678em;",[1856,3952,3953,3956],{"style":2773},[1856,3954],{"className":3955,"style":2777},[2007],[1856,3957,1885],{"className":3958},[1978,1982],[1856,3960,3961,3964],{"style":2773},[1856,3962],{"className":3963,"style":2777},[2007],[1856,3965,3968],{"className":3966,"style":3967},[2790],"left:-0.2222em;",[1856,3969,3853],{"className":3970},[1978],[1856,3972,3974],{"className":3973},[1986],[1856,3975,3977,3997],{"className":3976},[1990,1991],[1856,3978,3980,3994],{"className":3979},[1995],[1856,3981,3983],{"className":3982,"style":2000},[1999],[1856,3984,3985,3988],{"style":2003},[1856,3986],{"className":3987,"style":2008},[2007],[1856,3989,3991],{"className":3990},[2012,2013,2014,2015],[1856,3992,1837],{"className":3993},[1978,1982,2015],[1856,3995,2023],{"className":3996},[2022],[1856,3998,4000],{"className":3999},[1995],[1856,4001,4003],{"className":4002,"style":2030},[1999],[1856,4004],{},[1856,4006,1956],{"className":4007},[1978],[1798,4009,4010],{},"Dominant-strategy truthfulness is more robust to beliefs but can restrict achievable outcomes more severely.",[1793,4012,4014],{"id":4013},"_3-revelation-principle","3. Revelation principle",[1798,4016,4017],{},"If an outcome can be implemented by some mechanism and equilibrium, a direct mechanism exists in which agents report types and truthful reporting is an equilibrium producing the same outcome.",[1798,4019,4020,4021,4025],{},"The principle lets theorists search over truthful direct mechanisms. It does ",[4022,4023,4024],"strong",{},"not"," say:",[1809,4027,4028,4031,4034,4037],{},[1812,4029,4030],{},"every desirable allocation is implementable;",[1812,4032,4033],{},"truth is the unique equilibrium;",[1812,4035,4036],{},"participants understand the mechanism;",[1812,4038,4039],{},"communication, computation, collusion, or privacy is costless.",[1793,4041,4043],{"id":4042},"_4-vickrey-auction-pay-the-opportunity-cost","4. Vickrey auction: pay the opportunity cost",[1798,4045,4046],{},"One indivisible object is valued at 10 by A, 7 by B, and 4 by C. In a sealed-bid second-price auction:",[1809,4048,4049,4052],{},[1812,4050,4051],{},"highest bid wins;",[1812,4053,4054],{},"winner pays the second-highest bid.",[1798,4056,4057,4058,1956],{},"With truthful bids, A wins and pays 7, receiving utility ",[1835,4059,4060],{},"10−7=3",[1798,4062,4063],{},"Why truth is weakly dominant for A:",[1809,4065,4066,4069,4072],{},[1812,4067,4068],{},"if the highest rival bid is below 10, A wants to win and the payment is that rival bid, not A's own bid;",[1812,4070,4071],{},"if it is above 10, A wants to lose;",[1812,4073,4074],{},"misreporting only risks changing the win\u002Floss decision in the wrong direction.",[1798,4076,4077],{},"This logic assumes private values, enforceable payment, no spite or externality from who wins, and no binding budget below value.",[1793,4079,4081],{"id":4080},"_5-vcg-generalises-the-externality-payment","5. VCG generalises the externality payment",[1798,4083,4084],{},"Choose the outcome that maximises reported total value:",[1856,4086,4088],{"className":4087},[1859],[1856,4089,4091,4176],{"className":4090},[1863],[1856,4092,4094],{"className":4093},[1867],[1869,4095,4096],{"xmlns":1871,"display":1872},[1874,4097,4098,4173],{},[1877,4099,4100,4108,4110,4116,4118,4121,4124,4127,4139,4147,4153,4155,4157,4159,4169,4171],{},[4101,4102,4103,4105],"msup",{},[1883,4104,1895],{},[1889,4106,4107],{},"∗",[1889,4109,1892],{"stretchy":1891},[2467,4111,4112,4114],{"accent":1898},[1883,4113,1914],{},[1889,4115,2473],{},[1889,4117,1919],{"stretchy":1891},[1889,4119,4120],{},"∈",[1883,4122,4123],{},"arg",[1889,4125,4126],{},"⁡",[4128,4129,4130,4137],"munder",{},[1877,4131,4132,4135],{},[1883,4133,4134],{},"max",[1889,4136,4126],{},[1883,4138,1895],{},[4128,4140,4141,4144],{},[1889,4142,4143],{},"∑",[1883,4145,4146],{},"j",[1880,4148,4149,4151],{},[1883,4150,1927],{},[1883,4152,4146],{},[1889,4154,1892],{"stretchy":1891},[1883,4156,1895],{},[1889,4158,1909],{"separator":1898},[1880,4160,4161,4167],{},[2467,4162,4163,4165],{"accent":1898},[1883,4164,1914],{},[1889,4166,2473],{},[1883,4168,4146],{},[1889,4170,1919],{"stretchy":1891},[1883,4172,1956],{"mathvariant":1955},[1958,4174,4175],{"encoding":1960},"x^*(\\hat\\theta)\\in\\arg\\max_x\\sum_jv_j(x;\\hat\\theta_j).",[1856,4177,4179,4262],{"className":4178,"ariaHidden":1898},[1965],[1856,4180,4182,4185,4216,4219,4250,4253,4256,4259],{"className":4181},[1969],[1856,4183],{"className":4184,"style":2710},[1973],[1856,4186,4188,4191],{"className":4187},[1978],[1856,4189,1895],{"className":4190},[1978,1982],[1856,4192,4194],{"className":4193},[1986],[1856,4195,4197],{"className":4196},[1990],[1856,4198,4200],{"className":4199},[1995],[1856,4201,4204],{"className":4202,"style":4203},[1999],"height:0.7387em;",[1856,4205,4207,4210],{"style":4206},"top:-3.113em;margin-right:0.05em;",[1856,4208],{"className":4209,"style":2008},[2007],[1856,4211,4213],{"className":4212},[2012,2013,2014,2015],[1856,4214,4107],{"className":4215},[2262,2015],[1856,4217,1892],{"className":4218},[2036],[1856,4220,4222],{"className":4221},[1978,2760],[1856,4223,4225],{"className":4224},[1990],[1856,4226,4228],{"className":4227},[1995],[1856,4229,4231,4239],{"className":4230,"style":2770},[1999],[1856,4232,4233,4236],{"style":2773},[1856,4234],{"className":4235,"style":2777},[2007],[1856,4237,1914],{"className":4238,"style":2101},[1978,1982],[1856,4240,4241,4244],{"style":2783},[1856,4242],{"className":4243,"style":2777},[2007],[1856,4245,4247],{"className":4246,"style":2791},[2790],[1856,4248,2473],{"className":4249},[1978],[1856,4251,1919],{"className":4252},[2140],[1856,4254],{"className":4255,"style":2144},[2047],[1856,4257,4120],{"className":4258},[2148],[1856,4260],{"className":4261,"style":2144},[2047],[1856,4263,4265,4269,4278,4281,4329,4332,4384,4387,4428,4431,4434,4437,4440,4508,4511],{"className":4264},[1969],[1856,4266],{"className":4267,"style":4268},[1973],"height:2.4638em;vertical-align:-1.4138em;",[1856,4270,4273,4274],{"className":4271},[4272],"mop","ar",[1856,4275,4277],{"style":4276},"margin-right:0.0139em;","g",[1856,4279],{"className":4280,"style":2048},[2047],[1856,4282,4285],{"className":4283},[4272,4284],"op-limits",[1856,4286,4288,4320],{"className":4287},[1990,1991],[1856,4289,4291,4317],{"className":4290},[1995],[1856,4292,4295,4307],{"className":4293,"style":4294},[1999],"height:0.4306em;",[1856,4296,4298,4301],{"style":4297},"top:-2.4em;margin-left:0em;",[1856,4299],{"className":4300,"style":2777},[2007],[1856,4302,4304],{"className":4303},[2012,2013,2014,2015],[1856,4305,1895],{"className":4306},[1978,1982,2015],[1856,4308,4309,4312],{"style":2773},[1856,4310],{"className":4311,"style":2777},[2007],[1856,4313,4314],{},[1856,4315,4134],{"className":4316},[4272],[1856,4318,2023],{"className":4319},[2022],[1856,4321,4323],{"className":4322},[1995],[1856,4324,4327],{"className":4325,"style":4326},[1999],"height:0.7em;",[1856,4328],{},[1856,4330],{"className":4331,"style":2048},[2047],[1856,4333,4335],{"className":4334},[4272,4284],[1856,4336,4338,4375],{"className":4337},[1990,1991],[1856,4339,4341,4372],{"className":4340},[1995],[1856,4342,4345,4359],{"className":4343,"style":4344},[1999],"height:1.05em;",[1856,4346,4348,4352],{"style":4347},"top:-1.8723em;margin-left:0em;",[1856,4349],{"className":4350,"style":4351},[2007],"height:3.05em;",[1856,4353,4355],{"className":4354},[2012,2013,2014,2015],[1856,4356,4146],{"className":4357,"style":4358},[1978,1982,2015],"margin-right:0.0572em;",[1856,4360,4362,4365],{"style":4361},"top:-3.05em;",[1856,4363],{"className":4364,"style":4351},[2007],[1856,4366,4367],{},[1856,4368,4143],{"className":4369},[4272,4370,4371],"op-symbol","large-op",[1856,4373,2023],{"className":4374},[2022],[1856,4376,4378],{"className":4377},[1995],[1856,4379,4382],{"className":4380,"style":4381},[1999],"height:1.4138em;",[1856,4383],{},[1856,4385],{"className":4386,"style":2048},[2047],[1856,4388,4390,4393],{"className":4389},[1978],[1856,4391,1927],{"className":4392,"style":2164},[1978,1982],[1856,4394,4396],{"className":4395},[1986],[1856,4397,4399,4419],{"className":4398},[1990,1991],[1856,4400,4402,4416],{"className":4401},[1995],[1856,4403,4405],{"className":4404,"style":2000},[1999],[1856,4406,4407,4410],{"style":2179},[1856,4408],{"className":4409,"style":2008},[2007],[1856,4411,4413],{"className":4412},[2012,2013,2014,2015],[1856,4414,4146],{"className":4415,"style":4358},[1978,1982,2015],[1856,4417,2023],{"className":4418},[2022],[1856,4420,4422],{"className":4421},[1995],[1856,4423,4426],{"className":4424,"style":4425},[1999],"height:0.2861em;",[1856,4427],{},[1856,4429,1892],{"className":4430},[2036],[1856,4432,1895],{"className":4433},[1978,1982],[1856,4435,1909],{"className":4436},[2043],[1856,4438],{"className":4439,"style":2048},[2047],[1856,4441,4443,4474],{"className":4442},[1978],[1856,4444,4446],{"className":4445},[1978,2760],[1856,4447,4449],{"className":4448},[1990],[1856,4450,4452],{"className":4451},[1995],[1856,4453,4455,4463],{"className":4454,"style":2770},[1999],[1856,4456,4457,4460],{"style":2773},[1856,4458],{"className":4459,"style":2777},[2007],[1856,4461,1914],{"className":4462,"style":2101},[1978,1982],[1856,4464,4465,4468],{"style":2783},[1856,4466],{"className":4467,"style":2777},[2007],[1856,4469,4471],{"className":4470,"style":2791},[2790],[1856,4472,2473],{"className":4473},[1978],[1856,4475,4477],{"className":4476},[1986],[1856,4478,4480,4500],{"className":4479},[1990,1991],[1856,4481,4483,4497],{"className":4482},[1995],[1856,4484,4486],{"className":4485,"style":2000},[1999],[1856,4487,4488,4491],{"style":2116},[1856,4489],{"className":4490,"style":2008},[2007],[1856,4492,4494],{"className":4493},[2012,2013,2014,2015],[1856,4495,4146],{"className":4496,"style":4358},[1978,1982,2015],[1856,4498,2023],{"className":4499},[2022],[1856,4501,4503],{"className":4502},[1995],[1856,4504,4506],{"className":4505,"style":4425},[1999],[1856,4507],{},[1856,4509,1919],{"className":4510},[2140],[1856,4512,1956],{"className":4513},[1978],[1798,4515,1833,4516,4518],{},[1835,4517,1837],{}," pays the harm their presence imposes on others:",[1856,4520,4522],{"className":4521},[1859],[1856,4523,4525,4636],{"className":4524},[1863],[1856,4526,4528],{"className":4527},[1867],[1869,4529,4530],{"xmlns":1871,"display":1872},[1874,4531,4532,4633],{},[1877,4533,4534,4540,4542,4552,4565,4571,4573,4575,4577,4587,4589,4591,4603,4609,4611,4617,4619,4629,4631],{},[1880,4535,4536,4538],{},[1883,4537,1904],{},[1883,4539,1837],{},[1889,4541,1922],{},[4128,4543,4544,4550],{},[1877,4545,4546,4548],{},[1883,4547,4134],{},[1889,4549,4126],{},[1883,4551,1895],{},[4128,4553,4554,4556],{},[1889,4555,4143],{},[1877,4557,4558,4560,4563],{},[1883,4559,4146],{},[1889,4561,4562],{"mathvariant":1955},"≠",[1883,4564,1837],{},[1880,4566,4567,4569],{},[1883,4568,1927],{},[1883,4570,4146],{},[1889,4572,1892],{"stretchy":1891},[1883,4574,1895],{},[1889,4576,1909],{"separator":1898},[1880,4578,4579,4585],{},[2467,4580,4581,4583],{"accent":1898},[1883,4582,1914],{},[1889,4584,2473],{},[1883,4586,4146],{},[1889,4588,1919],{"stretchy":1891},[1889,4590,1946],{},[4128,4592,4593,4595],{},[1889,4594,4143],{},[1877,4596,4597,4599,4601],{},[1883,4598,4146],{},[1889,4600,4562],{"mathvariant":1955},[1883,4602,1837],{},[1880,4604,4605,4607],{},[1883,4606,1927],{},[1883,4608,4146],{},[1889,4610,1892],{"stretchy":1891},[4101,4612,4613,4615],{},[1883,4614,1895],{},[1889,4616,4107],{},[1889,4618,1909],{"separator":1898},[1880,4620,4621,4627],{},[2467,4622,4623,4625],{"accent":1898},[1883,4624,1914],{},[1889,4626,2473],{},[1883,4628,4146],{},[1889,4630,1919],{"stretchy":1891},[1883,4632,1956],{"mathvariant":1955},[1958,4634,4635],{"encoding":1960},"t_i=\n\\max_x\\sum_{j\\ne i}v_j(x;\\hat\\theta_j)\n-\\sum_{j\\ne i}v_j(x^*;\\hat\\theta_j).",[1856,4637,4639,4694,4979],{"className":4638,"ariaHidden":1898},[1965],[1856,4640,4642,4645,4685,4688,4691],{"className":4641},[1969],[1856,4643],{"className":4644,"style":2272},[1973],[1856,4646,4648,4651],{"className":4647},[1978],[1856,4649,1904],{"className":4650},[1978,1982],[1856,4652,4654],{"className":4653},[1986],[1856,4655,4657,4677],{"className":4656},[1990,1991],[1856,4658,4660,4674],{"className":4659},[1995],[1856,4661,4663],{"className":4662,"style":2000},[1999],[1856,4664,4665,4668],{"style":2003},[1856,4666],{"className":4667,"style":2008},[2007],[1856,4669,4671],{"className":4670},[2012,2013,2014,2015],[1856,4672,1837],{"className":4673},[1978,1982,2015],[1856,4675,2023],{"className":4676},[2022],[1856,4678,4680],{"className":4679},[1995],[1856,4681,4683],{"className":4682,"style":2030},[1999],[1856,4684],{},[1856,4686],{"className":4687,"style":2144},[2047],[1856,4689,1922],{"className":4690},[2148],[1856,4692],{"className":4693,"style":2144},[2047],[1856,4695,4697,4701,4745,4748,4844,4847,4887,4890,4893,4896,4899,4967,4970,4973,4976],{"className":4696},[1969],[1856,4698],{"className":4699,"style":4700},[1973],"height:2.4882em;vertical-align:-1.4382em;",[1856,4702,4704],{"className":4703},[4272,4284],[1856,4705,4707,4737],{"className":4706},[1990,1991],[1856,4708,4710,4734],{"className":4709},[1995],[1856,4711,4713,4724],{"className":4712,"style":4294},[1999],[1856,4714,4715,4718],{"style":4297},[1856,4716],{"className":4717,"style":2777},[2007],[1856,4719,4721],{"className":4720},[2012,2013,2014,2015],[1856,4722,1895],{"className":4723},[1978,1982,2015],[1856,4725,4726,4729],{"style":2773},[1856,4727],{"className":4728,"style":2777},[2007],[1856,4730,4731],{},[1856,4732,4134],{"className":4733},[4272],[1856,4735,2023],{"className":4736},[2022],[1856,4738,4740],{"className":4739},[1995],[1856,4741,4743],{"className":4742,"style":4326},[1999],[1856,4744],{},[1856,4746],{"className":4747,"style":2048},[2047],[1856,4749,4751],{"className":4750},[4272,4284],[1856,4752,4754,4835],{"className":4753},[1990,1991],[1856,4755,4757,4832],{"className":4756},[1995],[1856,4758,4760,4822],{"className":4759,"style":4344},[1999],[1856,4761,4763,4766],{"style":4762},"top:-1.8479em;margin-left:0em;",[1856,4764],{"className":4765,"style":4351},[2007],[1856,4767,4769],{"className":4768},[2012,2013,2014,2015],[1856,4770,4772,4775,4819],{"className":4771},[1978,2015],[1856,4773,4146],{"className":4774,"style":4358},[1978,1982,2015],[1856,4776,4778,4812,4816],{"className":4777},[2148,2015],[1856,4779,4781],{"className":4780},[2148,2015],[1856,4782,4785],{"className":4783},[1978,4784,2015],"vbox",[1856,4786,4789],{"className":4787},[4788,2015],"thinbox",[1856,4790,4793,4797,4808],{"className":4791},[4792,2015],"rlap",[1856,4794],{"className":4795,"style":4796},[1973],"height:0.8889em;vertical-align:-0.1944em;",[1856,4798,4801],{"className":4799},[4800],"inner",[1856,4802,4804],{"className":4803},[1978,2015],[1856,4805,4807],{"className":4806},[2148,2015],"",[1856,4809],{"className":4810},[4811],"fix",[1856,4813],{"className":4814},[2047,4815,2015],"nobreak",[1856,4817,1922],{"className":4818},[2148,2015],[1856,4820,1837],{"className":4821},[1978,1982,2015],[1856,4823,4824,4827],{"style":4361},[1856,4825],{"className":4826,"style":4351},[2007],[1856,4828,4829],{},[1856,4830,4143],{"className":4831},[4272,4370,4371],[1856,4833,2023],{"className":4834},[2022],[1856,4836,4838],{"className":4837},[1995],[1856,4839,4842],{"className":4840,"style":4841},[1999],"height:1.4382em;",[1856,4843],{},[1856,4845],{"className":4846,"style":2048},[2047],[1856,4848,4850,4853],{"className":4849},[1978],[1856,4851,1927],{"className":4852,"style":2164},[1978,1982],[1856,4854,4856],{"className":4855},[1986],[1856,4857,4859,4879],{"className":4858},[1990,1991],[1856,4860,4862,4876],{"className":4861},[1995],[1856,4863,4865],{"className":4864,"style":2000},[1999],[1856,4866,4867,4870],{"style":2179},[1856,4868],{"className":4869,"style":2008},[2007],[1856,4871,4873],{"className":4872},[2012,2013,2014,2015],[1856,4874,4146],{"className":4875,"style":4358},[1978,1982,2015],[1856,4877,2023],{"className":4878},[2022],[1856,4880,4882],{"className":4881},[1995],[1856,4883,4885],{"className":4884,"style":4425},[1999],[1856,4886],{},[1856,4888,1892],{"className":4889},[2036],[1856,4891,1895],{"className":4892},[1978,1982],[1856,4894,1909],{"className":4895},[2043],[1856,4897],{"className":4898,"style":2048},[2047],[1856,4900,4902,4933],{"className":4901},[1978],[1856,4903,4905],{"className":4904},[1978,2760],[1856,4906,4908],{"className":4907},[1990],[1856,4909,4911],{"className":4910},[1995],[1856,4912,4914,4922],{"className":4913,"style":2770},[1999],[1856,4915,4916,4919],{"style":2773},[1856,4917],{"className":4918,"style":2777},[2007],[1856,4920,1914],{"className":4921,"style":2101},[1978,1982],[1856,4923,4924,4927],{"style":2783},[1856,4925],{"className":4926,"style":2777},[2007],[1856,4928,4930],{"className":4929,"style":2791},[2790],[1856,4931,2473],{"className":4932},[1978],[1856,4934,4936],{"className":4935},[1986],[1856,4937,4939,4959],{"className":4938},[1990,1991],[1856,4940,4942,4956],{"className":4941},[1995],[1856,4943,4945],{"className":4944,"style":2000},[1999],[1856,4946,4947,4950],{"style":2116},[1856,4948],{"className":4949,"style":2008},[2007],[1856,4951,4953],{"className":4952},[2012,2013,2014,2015],[1856,4954,4146],{"className":4955,"style":4358},[1978,1982,2015],[1856,4957,2023],{"className":4958},[2022],[1856,4960,4962],{"className":4961},[1995],[1856,4963,4965],{"className":4964,"style":4425},[1999],[1856,4966],{},[1856,4968,1919],{"className":4969},[2140],[1856,4971],{"className":4972,"style":2258},[2047],[1856,4974,1946],{"className":4975},[2262],[1856,4977],{"className":4978,"style":2258},[2047],[1856,4980,4982,4985,5071,5074,5114,5117,5146,5149,5152,5220,5223],{"className":4981},[1969],[1856,4983],{"className":4984,"style":4700},[1973],[1856,4986,4988],{"className":4987},[4272,4284],[1856,4989,4991,5063],{"className":4990},[1990,1991],[1856,4992,4994,5060],{"className":4993},[1995],[1856,4995,4997,5050],{"className":4996,"style":4344},[1999],[1856,4998,4999,5002],{"style":4762},[1856,5000],{"className":5001,"style":4351},[2007],[1856,5003,5005],{"className":5004},[2012,2013,2014,2015],[1856,5006,5008,5011,5047],{"className":5007},[1978,2015],[1856,5009,4146],{"className":5010,"style":4358},[1978,1982,2015],[1856,5012,5014,5041,5044],{"className":5013},[2148,2015],[1856,5015,5017],{"className":5016},[2148,2015],[1856,5018,5020],{"className":5019},[1978,4784,2015],[1856,5021,5023],{"className":5022},[4788,2015],[1856,5024,5026,5029,5038],{"className":5025},[4792,2015],[1856,5027],{"className":5028,"style":4796},[1973],[1856,5030,5032],{"className":5031},[4800],[1856,5033,5035],{"className":5034},[1978,2015],[1856,5036,4807],{"className":5037},[2148,2015],[1856,5039],{"className":5040},[4811],[1856,5042],{"className":5043},[2047,4815,2015],[1856,5045,1922],{"className":5046},[2148,2015],[1856,5048,1837],{"className":5049},[1978,1982,2015],[1856,5051,5052,5055],{"style":4361},[1856,5053],{"className":5054,"style":4351},[2007],[1856,5056,5057],{},[1856,5058,4143],{"className":5059},[4272,4370,4371],[1856,5061,2023],{"className":5062},[2022],[1856,5064,5066],{"className":5065},[1995],[1856,5067,5069],{"className":5068,"style":4841},[1999],[1856,5070],{},[1856,5072],{"className":5073,"style":2048},[2047],[1856,5075,5077,5080],{"className":5076},[1978],[1856,5078,1927],{"className":5079,"style":2164},[1978,1982],[1856,5081,5083],{"className":5082},[1986],[1856,5084,5086,5106],{"className":5085},[1990,1991],[1856,5087,5089,5103],{"className":5088},[1995],[1856,5090,5092],{"className":5091,"style":2000},[1999],[1856,5093,5094,5097],{"style":2179},[1856,5095],{"className":5096,"style":2008},[2007],[1856,5098,5100],{"className":5099},[2012,2013,2014,2015],[1856,5101,4146],{"className":5102,"style":4358},[1978,1982,2015],[1856,5104,2023],{"className":5105},[2022],[1856,5107,5109],{"className":5108},[1995],[1856,5110,5112],{"className":5111,"style":4425},[1999],[1856,5113],{},[1856,5115,1892],{"className":5116},[2036],[1856,5118,5120,5123],{"className":5119},[1978],[1856,5121,1895],{"className":5122},[1978,1982],[1856,5124,5126],{"className":5125},[1986],[1856,5127,5129],{"className":5128},[1990],[1856,5130,5132],{"className":5131},[1995],[1856,5133,5135],{"className":5134,"style":4203},[1999],[1856,5136,5137,5140],{"style":4206},[1856,5138],{"className":5139,"style":2008},[2007],[1856,5141,5143],{"className":5142},[2012,2013,2014,2015],[1856,5144,4107],{"className":5145},[2262,2015],[1856,5147,1909],{"className":5148},[2043],[1856,5150],{"className":5151,"style":2048},[2047],[1856,5153,5155,5186],{"className":5154},[1978],[1856,5156,5158],{"className":5157},[1978,2760],[1856,5159,5161],{"className":5160},[1990],[1856,5162,5164],{"className":5163},[1995],[1856,5165,5167,5175],{"className":5166,"style":2770},[1999],[1856,5168,5169,5172],{"style":2773},[1856,5170],{"className":5171,"style":2777},[2007],[1856,5173,1914],{"className":5174,"style":2101},[1978,1982],[1856,5176,5177,5180],{"style":2783},[1856,5178],{"className":5179,"style":2777},[2007],[1856,5181,5183],{"className":5182,"style":2791},[2790],[1856,5184,2473],{"className":5185},[1978],[1856,5187,5189],{"className":5188},[1986],[1856,5190,5192,5212],{"className":5191},[1990,1991],[1856,5193,5195,5209],{"className":5194},[1995],[1856,5196,5198],{"className":5197,"style":2000},[1999],[1856,5199,5200,5203],{"style":2116},[1856,5201],{"className":5202,"style":2008},[2007],[1856,5204,5206],{"className":5205},[2012,2013,2014,2015],[1856,5207,4146],{"className":5208,"style":4358},[1978,1982,2015],[1856,5210,2023],{"className":5211},[2022],[1856,5213,5215],{"className":5214},[1995],[1856,5216,5218],{"className":5217,"style":4425},[1999],[1856,5219],{},[1856,5221,1919],{"className":5222},[2140],[1856,5224,1956],{"className":5225},[1978],[1798,5227,5228],{},"The payment removes the gain from manipulating how one's report affects everyone else, producing dominant-strategy truthfulness under the benchmark.",[1798,5230,5231],{},"VCG can fail practical desiderata: revenue may be low or negative, budget balance can fail, collusion and false identities can matter, and combinatorial valuation may be difficult to report or compute.",[1793,5233,5235],{"id":5234},"_6-first-price-auction-shade-the-bid","6. First-price auction: shade the bid",[1798,5237,5238,5239,5242,5243,5246],{},"Suppose ",[1835,5240,5241],{},"n"," risk-neutral bidders have independent private values uniformly distributed on ",[1835,5244,5245],{},"[0,1]",". In the symmetric equilibrium of a first-price sealed-bid auction:",[1856,5248,5250],{"className":5249},[1859],[1856,5251,5253,5295],{"className":5252},[1863],[1856,5254,5256],{"className":5255},[1867],[1869,5257,5258],{"xmlns":1871,"display":1872},[1874,5259,5260,5292],{},[1877,5261,5262,5265,5267,5269,5271,5273,5288,5290],{},[1883,5263,5264],{},"b",[1889,5266,1892],{"stretchy":1891},[1883,5268,1927],{},[1889,5270,1919],{"stretchy":1891},[1889,5272,1922],{},[5274,5275,5276,5286],"mfrac",{},[1877,5277,5278,5280,5282],{},[1883,5279,5241],{},[1889,5281,1946],{},[5283,5284,5285],"mn",{},"1",[1883,5287,5241],{},[1883,5289,1927],{},[1883,5291,1956],{"mathvariant":1955},[1958,5293,5294],{"encoding":1960},"b(v)=\\frac{n-1}{n}v.",[1856,5296,5298,5325],{"className":5297,"ariaHidden":1898},[1965],[1856,5299,5301,5304,5307,5310,5313,5316,5319,5322],{"className":5300},[1969],[1856,5302],{"className":5303,"style":1974},[1973],[1856,5305,5264],{"className":5306},[1978,1982],[1856,5308,1892],{"className":5309},[2036],[1856,5311,1927],{"className":5312,"style":2164},[1978,1982],[1856,5314,1919],{"className":5315},[2140],[1856,5317],{"className":5318,"style":2144},[2047],[1856,5320,1922],{"className":5321},[2148],[1856,5323],{"className":5324,"style":2144},[2047],[1856,5326,5328,5332,5414,5417],{"className":5327},[1969],[1856,5329],{"className":5330,"style":5331},[1973],"height:2.0074em;vertical-align:-0.686em;",[1856,5333,5335,5339,5411],{"className":5334},[1978],[1856,5336],{"className":5337},[2036,5338],"nulldelimiter",[1856,5340,5342],{"className":5341},[5274],[1856,5343,5345,5402],{"className":5344},[1990,1991],[1856,5346,5348,5399],{"className":5347},[1995],[1856,5349,5352,5364,5375],{"className":5350,"style":5351},[1999],"height:1.3214em;",[1856,5353,5355,5358],{"style":5354},"top:-2.314em;",[1856,5356],{"className":5357,"style":2777},[2007],[1856,5359,5361],{"className":5360},[1978],[1856,5362,5241],{"className":5363},[1978,1982],[1856,5365,5367,5370],{"style":5366},"top:-3.23em;",[1856,5368],{"className":5369,"style":2777},[2007],[1856,5371],{"className":5372,"style":5374},[5373],"frac-line","border-bottom-width:0.04em;",[1856,5376,5378,5381],{"style":5377},"top:-3.677em;",[1856,5379],{"className":5380,"style":2777},[2007],[1856,5382,5384,5387,5390,5393,5396],{"className":5383},[1978],[1856,5385,5241],{"className":5386},[1978,1982],[1856,5388],{"className":5389,"style":2258},[2047],[1856,5391,1946],{"className":5392},[2262],[1856,5394],{"className":5395,"style":2258},[2047],[1856,5397,5285],{"className":5398},[1978],[1856,5400,2023],{"className":5401},[2022],[1856,5403,5405],{"className":5404},[1995],[1856,5406,5409],{"className":5407,"style":5408},[1999],"height:0.686em;",[1856,5410],{},[1856,5412],{"className":5413},[2140,5338],[1856,5415,1927],{"className":5416,"style":2164},[1978,1982],[1856,5418,1956],{"className":5419},[1978],[1798,5421,5422,5423,5426,5427,5430],{},"With three bidders and value ",[1835,5424,5425],{},"v=0.9",", the equilibrium bid is ",[1835,5428,5429],{},"0.6",". A higher bid increases the probability of winning but lowers surplus conditional on winning.",[1798,5432,5433],{},"In a second-price auction, truthful bidding is weakly dominant; in a first-price auction, bidding depends on beliefs about rivals, risk attitude, number of bidders, and value distribution.",[1793,5435,5437],{"id":5436},"_7-revenue-equivalence-is-conditional","7. Revenue equivalence is conditional",[1798,5439,5440],{},"Standard auctions have the same expected revenue when:",[1809,5442,5443,5446,5449,5452,5455],{},[1812,5444,5445],{},"bidders are risk-neutral;",[1812,5447,5448],{},"values are independent and identically distributed;",[1812,5450,5451],{},"the highest-value bidder wins;",[1812,5453,5454],{},"the lowest type receives zero expected surplus;",[1812,5456,5457],{},"participation and payment assumptions match.",[1798,5459,5460],{},"Risk aversion, affiliated\u002Fcommon values, asymmetry, budgets, entry, reserve prices, and dynamic learning can break equivalence.",[2395,5462,5464],{"id":5463},"optimal-reserve-in-a-benchmark","Optimal reserve in a benchmark",[1798,5466,5467,5468,5471,5472,5475],{},"For distribution ",[1835,5469,5470],{},"F"," with density ",[1835,5473,5474],{},"f",", Myerson's virtual value is:",[1856,5477,5479],{"className":5478},[1859],[1856,5480,5482,5537],{"className":5481},[1863],[1856,5483,5485],{"className":5484},[1867],[1869,5486,5487],{"xmlns":1871,"display":1872},[1874,5488,5489,5534],{},[1877,5490,5491,5494,5496,5498,5500,5502,5504,5506,5532],{},[1883,5492,5493],{},"ϕ",[1889,5495,1892],{"stretchy":1891},[1883,5497,1927],{},[1889,5499,1919],{"stretchy":1891},[1889,5501,1922],{},[1883,5503,1927],{},[1889,5505,1946],{},[5274,5507,5508,5522],{},[1877,5509,5510,5512,5514,5516,5518,5520],{},[5283,5511,5285],{},[1889,5513,1946],{},[1883,5515,5470],{},[1889,5517,1892],{"stretchy":1891},[1883,5519,1927],{},[1889,5521,1919],{"stretchy":1891},[1877,5523,5524,5526,5528,5530],{},[1883,5525,5474],{},[1889,5527,1892],{"stretchy":1891},[1883,5529,1927],{},[1889,5531,1919],{"stretchy":1891},[1883,5533,1956],{"mathvariant":1955},[1958,5535,5536],{"encoding":1960},"\\phi(v)=v-\\frac{1-F(v)}{f(v)}.",[1856,5538,5540,5567,5586],{"className":5539,"ariaHidden":1898},[1965],[1856,5541,5543,5546,5549,5552,5555,5558,5561,5564],{"className":5542},[1969],[1856,5544],{"className":5545,"style":1974},[1973],[1856,5547,5493],{"className":5548},[1978,1982],[1856,5550,1892],{"className":5551},[2036],[1856,5553,1927],{"className":5554,"style":2164},[1978,1982],[1856,5556,1919],{"className":5557},[2140],[1856,5559],{"className":5560,"style":2144},[2047],[1856,5562,1922],{"className":5563},[2148],[1856,5565],{"className":5566,"style":2144},[2047],[1856,5568,5570,5574,5577,5580,5583],{"className":5569},[1969],[1856,5571],{"className":5572,"style":5573},[1973],"height:0.6667em;vertical-align:-0.0833em;",[1856,5575,1927],{"className":5576,"style":2164},[1978,1982],[1856,5578],{"className":5579,"style":2258},[2047],[1856,5581,1946],{"className":5582},[2262],[1856,5584],{"className":5585,"style":2258},[2047],[1856,5587,5589,5593,5689],{"className":5588},[1969],[1856,5590],{"className":5591,"style":5592},[1973],"height:2.363em;vertical-align:-0.936em;",[1856,5594,5596,5599,5686],{"className":5595},[1978],[1856,5597],{"className":5598},[2036,5338],[1856,5600,5602],{"className":5601},[5274],[1856,5603,5605,5677],{"className":5604},[1990,1991],[1856,5606,5608,5674],{"className":5607},[1995],[1856,5609,5612,5633,5641],{"className":5610,"style":5611},[1999],"height:1.427em;",[1856,5613,5614,5617],{"style":5354},[1856,5615],{"className":5616,"style":2777},[2007],[1856,5618,5620,5624,5627,5630],{"className":5619},[1978],[1856,5621,5474],{"className":5622,"style":5623},[1978,1982],"margin-right:0.1076em;",[1856,5625,1892],{"className":5626},[2036],[1856,5628,1927],{"className":5629,"style":2164},[1978,1982],[1856,5631,1919],{"className":5632},[2140],[1856,5634,5635,5638],{"style":5366},[1856,5636],{"className":5637,"style":2777},[2007],[1856,5639],{"className":5640,"style":5374},[5373],[1856,5642,5643,5646],{"style":5377},[1856,5644],{"className":5645,"style":2777},[2007],[1856,5647,5649,5652,5655,5658,5661,5665,5668,5671],{"className":5648},[1978],[1856,5650,5285],{"className":5651},[1978],[1856,5653],{"className":5654,"style":2258},[2047],[1856,5656,1946],{"className":5657},[2262],[1856,5659],{"className":5660,"style":2258},[2047],[1856,5662,5470],{"className":5663,"style":5664},[1978,1982],"margin-right:0.1389em;",[1856,5666,1892],{"className":5667},[2036],[1856,5669,1927],{"className":5670,"style":2164},[1978,1982],[1856,5672,1919],{"className":5673},[2140],[1856,5675,2023],{"className":5676},[2022],[1856,5678,5680],{"className":5679},[1995],[1856,5681,5684],{"className":5682,"style":5683},[1999],"height:0.936em;",[1856,5685],{},[1856,5687],{"className":5688},[2140,5338],[1856,5690,1956],{"className":5691},[1978],[1798,5693,5694,5695,2935,5698,5701,5702,5705],{},"For ",[1835,5696,5697],{},"U[0,1]",[1835,5699,5700],{},"φ(v)=2v−1","; the seller-optimal reserve is therefore ",[1835,5703,5704],{},"v=1\u002F2"," under regularity. The reserve can leave the object unsold even when trade would create positive surplus: revenue and allocative efficiency differ.",[1793,5707,5709],{"id":5708},"_8-a-fundamental-impossibility","8. A fundamental impossibility",[1798,5711,5712],{},"In bilateral trade with private buyer and seller values whose distributions overlap, no mechanism can simultaneously guarantee efficiency, Bayesian incentive compatibility, individual rationality, and budget balance under the Myerson–Satterthwaite conditions.",[1798,5714,5715],{},"The lesson is not “design is futile.” It is that a real institution must identify which desideratum to relax and who bears the resulting loss.",[1793,5717,5719],{"id":5718},"_9-current-case-digital-ad-auction-rules-affect-product-prices","9. Current case: digital-ad auction rules affect product prices",[1798,5721,5722,5723,5730],{},"Bergemann, Bonatti, and Wu model a platform with on- and off-platform consumer contact, data-enhanced matching, and auction-like ad allocation. Their platform-optimal managed campaign achieves efficient on-platform matching but conditions sponsored-product pricing on advertisers' off-platform prices; relative to data-augmented auctions, it raises off-platform prices and lowers consumer surplus (",[5724,5725,5729],"a",{"href":5726,"rel":5727},"https:\u002F\u002Fdoi.org\u002F10.1093\u002Frestud\u002Frdae087",[5728],"nofollow","2025",").",[1798,5732,5733],{},"The example broadens auction evaluation: do not stop at auction revenue or click allocation. The mechanism can change advertisers' downstream product prices. The result is theoretical and rests on the model's data, contact, and commitment structure; it is not an estimate of one platform's realised price effect.",[2395,5735,5737],{"id":5736},"frontier-design-result","Frontier design result",[1798,5739,5740,5741,5745],{},"Echenique and Núñez's “Price and Choose” mechanism sequentially lets agents define outcome prices before a final choice and implements efficient outcomes in a broad quasi-linear environment (",[5724,5742,5729],{"href":5743,"rel":5744},"https:\u002F\u002Fdoi.org\u002F10.1257\u002Fmic.20230095",[5728],"). It illustrates that mechanism design remains an active search for simpler information and implementation structures—not only a catalogue of classic auctions.",[1793,5747,5749],{"id":5748},"_10-implementation-checklist","10. Implementation checklist",[1798,5751,5752],{},"Before recommending a mechanism, test:",[5754,5755,5756,5759,5762,5765,5768,5771,5774,5777],"ol",{},[1812,5757,5758],{},"incentive concept and equilibrium multiplicity;",[1812,5760,5761],{},"participation and opt-out;",[1812,5763,5764],{},"budget balance and payment risk;",[1812,5766,5767],{},"collusion, shill bids, and false identities;",[1812,5769,5770],{},"computational and communication burden;",[1812,5772,5773],{},"privacy, auditability, and appeals;",[1812,5775,5776],{},"dynamic entry and investment;",[1812,5778,5779],{},"outcomes outside the auction itself.",[1793,5781,5783],{"id":5782},"practice","Practice",[5754,5785,5786,5789,5798,5804,5807],{},[1812,5787,5788],{},"Explain truthfulness in a second-price auction for every possible rival bid.",[1812,5790,5791,5792,5795,5796,1956],{},"Derive ",[1835,5793,5794],{},"b(v)=(n−1)v\u002Fn"," using a deviation by type ",[1835,5797,1927],{},[1812,5799,5800,5801,1956],{},"Calculate VCG allocation and payments for values ",[1835,5802,5803],{},"(14,9,6,2)",[1812,5805,5806],{},"Show how risk aversion changes first-price bid shading qualitatively.",[1812,5808,5809],{},"Design an ad-auction evaluation with one auction outcome and two downstream-market outcomes.",[1793,5811,5813],{"id":5812},"quick-check","Quick check",[1809,5815,5816,5819,5822,5825,5828],{},[1812,5817,5818],{},"A mechanism specifies messages, allocations, and transfers.",[1812,5820,5821],{},"IC aligns a participant's optimal message with the designer's interpretation.",[1812,5823,5824],{},"VCG charges opportunity cost but may violate other practical goals.",[1812,5826,5827],{},"Revenue equivalence depends on a narrow common benchmark.",[1812,5829,5830],{},"Auction rules can alter prices and competition outside the auction.",[1798,5832,5833,5836,5837,1956],{},[4022,5834,5835],{},"Next:"," ",[5724,5838,5840],{"href":5839},"..\u002F09-behavioural-economics\u002F","test where standard choice models fail and how evidence scales",{"title":10,"searchDepth":5842,"depth":5842,"links":5843},2,[5844,5845,5846,5847,5853,5854,5855,5856,5857,5860,5861,5864,5865,5866],{"id":1795,"depth":5842,"text":1796},{"id":1803,"depth":5842,"text":1804},{"id":1829,"depth":5842,"text":1830},{"id":2392,"depth":5842,"text":2393,"children":5848},[5849,5851,5852],{"id":2397,"depth":5850,"text":2398},3,{"id":2945,"depth":5850,"text":2946},{"id":3811,"depth":5850,"text":3812},{"id":4013,"depth":5842,"text":4014},{"id":4042,"depth":5842,"text":4043},{"id":4080,"depth":5842,"text":4081},{"id":5234,"depth":5842,"text":5235},{"id":5436,"depth":5842,"text":5437,"children":5858},[5859],{"id":5463,"depth":5850,"text":5464},{"id":5708,"depth":5842,"text":5709},{"id":5718,"depth":5842,"text":5719,"children":5862},[5863],{"id":5736,"depth":5850,"text":5737},{"id":5748,"depth":5842,"text":5749},{"id":5782,"depth":5842,"text":5783},{"id":5812,"depth":5842,"text":5813},"Revelation, incentive compatibility, Vickrey–Clarke–Groves mechanisms, first-price bidding, revenue equivalence, optimal auctions, and digital advertising.","md",null,{},true,{"title":769,"description":5867},"YdR4JR8V7hy4IOiVJA4edH2kL8eoRch08x0hbBJTezU",[5875,5877],{"title":763,"path":764,"stem":765,"description":5876,"children":-1},"Adverse selection, signalling, screening, moral hazard, incentive compatibility, and machine-learning credit evidence.",{"title":775,"path":776,"stem":777,"description":5878,"children":-1},"Reference dependence, probability weighting, present bias, social preferences, limited attention, experiments, nudges, and welfare.",1785754732930]