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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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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":1585},{"id":1784,"title":757,"body":1785,"description":5037,"extension":5038,"features":5039,"hero":5039,"layout":5039,"locale":5039,"meta":5040,"navigation":5039,"path":758,"published":5041,"seo":5042,"stem":759,"__hash__":5043},"docs\u002Fen\u002Fmicroeconomics\u002F06-oligopoly\u002Findex.md",{"type":1786,"value":1787,"toc":5018},"minimark",[1788,1792,1797,1801,1805,1808,1827,1831,1891,1894,1897,2223,2231,2235,2238,2484,2494,2835,2838,3097,3104,3721,3726,3741,3996,4009,4015,4019,4025,4189,4192,4209,4213,4216,4401,4411,4708,4780,4783,4787,4790,4793,4807,4810,4814,4817,4820,4838,4841,4845,4848,4858,4861,4865,4873,4876,4880,4883,4955,4959,4986,4990,5007],[1789,1790,757],"h1",{"id":1791},"module-6-oligopoly-entry-and-algorithmic-pricing",[1793,1794,1796],"h2",{"id":1795},"core-question","Core question",[1798,1799,1800],"p",{},"How do the strategic variable, timing, product differentiation, capacity, and market rules determine prices, output, entry, and market power?",[1793,1802,1804],{"id":1803},"learning-outcomes","Learning outcomes",[1798,1806,1807],{},"You will be able to:",[1809,1810,1811,1815,1818,1821,1824],"ul",{},[1812,1813,1814],"li",{},"solve and compare Cournot, Bertrand, and Stackelberg benchmarks;",[1812,1816,1817],{},"relate markups to demand elasticity and strategic interaction;",[1812,1819,1820],{},"analyse collusion and entry incentives;",[1812,1822,1823],{},"diagnose platform power beyond market share alone;",[1812,1825,1826],{},"interpret current evidence on algorithmic pricing cautiously.",[1793,1828,1830],{"id":1829},"_1-market-structure-is-a-model-choice","1. Market structure is a model choice",[1832,1833,1834,1847],"table",{},[1835,1836,1837],"thead",{},[1838,1839,1840,1844],"tr",{},[1841,1842,1843],"th",{},"Feature",[1841,1845,1846],{},"Question",[1848,1849,1850,1859,1867,1875,1883],"tbody",{},[1838,1851,1852,1856],{},[1853,1854,1855],"td",{},"strategic variable",[1853,1857,1858],{},"quantity, price, capacity, quality, advertising, ranking?",[1838,1860,1861,1864],{},[1853,1862,1863],{},"timing",[1853,1865,1866],{},"simultaneous, leader–follower, repeated, dynamic entry?",[1838,1868,1869,1872],{},[1853,1870,1871],{},"product relation",[1853,1873,1874],{},"homogeneous, differentiated, complements, ecosystem?",[1838,1876,1877,1880],{},[1853,1878,1879],{},"constraints",[1853,1881,1882],{},"capacity, fixed cost, switching, data, compute, regulation?",[1838,1884,1885,1888],{},[1853,1886,1887],{},"information",[1853,1889,1890],{},"are costs, demand, actions, or algorithm rules observed?",[1798,1892,1893],{},"Counting firms is a starting fact, not a complete theory of competition.",[1798,1895,1896],{},"For a single-price monopolist with differentiable demand, the first-order condition can be written:",[1898,1899,1902],"span",{"className":1900},[1901],"katex-display",[1898,1903,1906,1971],{"className":1904},[1905],"katex",[1898,1907,1910],{"className":1908},[1909],"katex-mathml",[1911,1912,1915],"math",{"xmlns":1913,"display":1914},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML","block",[1916,1917,1918,1966],"semantics",{},[1919,1920,1921,1942,1945,1947,1962],"mrow",{},[1922,1923,1924,1940],"mfrac",{},[1919,1925,1926,1930,1934,1937],{},[1927,1928,1929],"mi",{},"P",[1931,1932,1933],"mo",{},"−",[1927,1935,1936],{},"M",[1927,1938,1939],{},"C",[1927,1941,1929],{},[1931,1943,1944],{},"=",[1931,1946,1933],{},[1922,1948,1949,1953],{},[1950,1951,1952],"mn",{},"1",[1954,1955,1956,1959],"msub",{},[1927,1957,1958],{},"ε",[1927,1960,1961],{},"D",[1931,1963,1965],{"separator":1964},"true",",",[1967,1968,1970],"annotation",{"encoding":1969},"application\u002Fx-tex","\\frac{P-MC}{P}=-\\frac1{\\varepsilon_D},",[1898,1972,1975,2098],{"className":1973,"ariaHidden":1964},[1974],"katex-html",[1898,1976,1979,1984,2087,2091,2095],{"className":1977},[1978],"base",[1898,1980],{"className":1981,"style":1983},[1982],"strut","height:2.0463em;vertical-align:-0.686em;",[1898,1985,1988,1993,2083],{"className":1986},[1987],"mord",[1898,1989],{"className":1990},[1991,1992],"mopen","nulldelimiter",[1898,1994,1996],{"className":1995},[1922],[1898,1997,2001,2074],{"className":1998},[1999,2000],"vlist-t","vlist-t2",[1898,2002,2005,2069],{"className":2003},[2004],"vlist-r",[1898,2006,2010,2026,2037],{"className":2007,"style":2009},[2008],"vlist","height:1.3603em;",[1898,2011,2013,2018],{"style":2012},"top:-2.314em;",[1898,2014],{"className":2015,"style":2017},[2016],"pstrut","height:3em;",[1898,2019,2021],{"className":2020},[1987],[1898,2022,1929],{"className":2023,"style":2025},[1987,2024],"mathnormal","margin-right:0.1389em;",[1898,2027,2029,2032],{"style":2028},"top:-3.23em;",[1898,2030],{"className":2031,"style":2017},[2016],[1898,2033],{"className":2034,"style":2036},[2035],"frac-line","border-bottom-width:0.04em;",[1898,2038,2040,2043],{"style":2039},"top:-3.677em;",[1898,2041],{"className":2042,"style":2017},[2016],[1898,2044,2046,2049,2054,2058,2061,2065],{"className":2045},[1987],[1898,2047,1929],{"className":2048,"style":2025},[1987,2024],[1898,2050],{"className":2051,"style":2053},[2052],"mspace","margin-right:0.2222em;",[1898,2055,1933],{"className":2056},[2057],"mbin",[1898,2059],{"className":2060,"style":2053},[2052],[1898,2062,1936],{"className":2063,"style":2064},[1987,2024],"margin-right:0.109em;",[1898,2066,1939],{"className":2067,"style":2068},[1987,2024],"margin-right:0.0715em;",[1898,2070,2073],{"className":2071},[2072],"vlist-s","​",[1898,2075,2077],{"className":2076},[2004],[1898,2078,2081],{"className":2079,"style":2080},[2008],"height:0.686em;",[1898,2082],{},[1898,2084],{"className":2085},[2086,1992],"mclose",[1898,2088],{"className":2089,"style":2090},[2052],"margin-right:0.2778em;",[1898,2092,1944],{"className":2093},[2094],"mrel",[1898,2096],{"className":2097,"style":2090},[2052],[1898,2099,2101,2105,2108,2219],{"className":2100},[1978],[1898,2102],{"className":2103,"style":2104},[1982],"height:2.1574em;vertical-align:-0.836em;",[1898,2106,1933],{"className":2107},[1987],[1898,2109,2111,2114,2216],{"className":2110},[1987],[1898,2112],{"className":2113},[1991,1992],[1898,2115,2117],{"className":2116},[1922],[1898,2118,2120,2207],{"className":2119},[1999,2000],[1898,2121,2123,2204],{"className":2122},[2004],[1898,2124,2127,2185,2193],{"className":2125,"style":2126},[2008],"height:1.3214em;",[1898,2128,2129,2132],{"style":2012},[1898,2130],{"className":2131,"style":2017},[2016],[1898,2133,2135],{"className":2134},[1987],[1898,2136,2138,2141],{"className":2137},[1987],[1898,2139,1958],{"className":2140},[1987,2024],[1898,2142,2145],{"className":2143},[2144],"msupsub",[1898,2146,2148,2176],{"className":2147},[1999,2000],[1898,2149,2151,2173],{"className":2150},[2004],[1898,2152,2155],{"className":2153,"style":2154},[2008],"height:0.3283em;",[1898,2156,2158,2162],{"style":2157},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[1898,2159],{"className":2160,"style":2161},[2016],"height:2.7em;",[1898,2163,2169],{"className":2164},[2165,2166,2167,2168],"sizing","reset-size6","size3","mtight",[1898,2170,1961],{"className":2171,"style":2172},[1987,2024,2168],"margin-right:0.0278em;",[1898,2174,2073],{"className":2175},[2072],[1898,2177,2179],{"className":2178},[2004],[1898,2180,2183],{"className":2181,"style":2182},[2008],"height:0.15em;",[1898,2184],{},[1898,2186,2187,2190],{"style":2028},[1898,2188],{"className":2189,"style":2017},[2016],[1898,2191],{"className":2192,"style":2036},[2035],[1898,2194,2195,2198],{"style":2039},[1898,2196],{"className":2197,"style":2017},[2016],[1898,2199,2201],{"className":2200},[1987],[1898,2202,1952],{"className":2203},[1987],[1898,2205,2073],{"className":2206},[2072],[1898,2208,2210],{"className":2209},[2004],[1898,2211,2214],{"className":2212,"style":2213},[2008],"height:0.836em;",[1898,2215],{},[1898,2217],{"className":2218},[2086,1992],[1898,2220,1965],{"className":2221},[2222],"mpunct",[1798,2224,2225,2226,2230],{},"where ",[2227,2228,2229],"code",{},"ε_D\u003C0"," is the price elasticity at the chosen point. This Lerner relation is a benchmark; multi-product pricing, dynamic demand, regulation, and imperfect measurement complicate empirical markups.",[1793,2232,2234],{"id":2233},"_2-cournot-firms-choose-quantities","2. Cournot: firms choose quantities",[1798,2236,2237],{},"Let inverse demand be:",[1898,2239,2241],{"className":2240},[1901],[1898,2242,2244,2298],{"className":2243},[1905],[1898,2245,2247],{"className":2246},[1909],[1911,2248,2249],{"xmlns":1913,"display":1914},[1916,2250,2251,2295],{},[1919,2252,2253,2255,2257,2260,2262,2265,2268,2270,2273,2275,2277,2286,2293],{},[1927,2254,1929],{},[1931,2256,1944],{},[1927,2258,2259],{},"a",[1931,2261,1933],{},[1927,2263,2264],{},"b",[1927,2266,2267],{},"Q",[1931,2269,1965],{"separator":1964},[2052,2271],{"width":2272},"2em",[1927,2274,2267],{},[1931,2276,1944],{},[2278,2279,2280,2283],"munder",{},[1931,2281,2282],{},"∑",[1927,2284,2285],{},"i",[1954,2287,2288,2291],{},[1927,2289,2290],{},"q",[1927,2292,2285],{},[1931,2294,1965],{"separator":1964},[1967,2296,2297],{"encoding":1969},"P=a-bQ,\\qquad Q=\\sum_iq_i,",[1898,2299,2301,2320,2339,2375],{"className":2300,"ariaHidden":1964},[1974],[1898,2302,2304,2308,2311,2314,2317],{"className":2303},[1978],[1898,2305],{"className":2306,"style":2307},[1982],"height:0.6833em;",[1898,2309,1929],{"className":2310,"style":2025},[1987,2024],[1898,2312],{"className":2313,"style":2090},[2052],[1898,2315,1944],{"className":2316},[2094],[1898,2318],{"className":2319,"style":2090},[2052],[1898,2321,2323,2327,2330,2333,2336],{"className":2322},[1978],[1898,2324],{"className":2325,"style":2326},[1982],"height:0.6667em;vertical-align:-0.0833em;",[1898,2328,2259],{"className":2329},[1987,2024],[1898,2331],{"className":2332,"style":2053},[2052],[1898,2334,1933],{"className":2335},[2057],[1898,2337],{"className":2338,"style":2053},[2052],[1898,2340,2342,2346,2349,2352,2355,2359,2363,2366,2369,2372],{"className":2341},[1978],[1898,2343],{"className":2344,"style":2345},[1982],"height:0.8889em;vertical-align:-0.1944em;",[1898,2347,2264],{"className":2348},[1987,2024],[1898,2350,2267],{"className":2351},[1987,2024],[1898,2353,1965],{"className":2354},[2222],[1898,2356],{"className":2357,"style":2358},[2052],"margin-right:2em;",[1898,2360],{"className":2361,"style":2362},[2052],"margin-right:0.1667em;",[1898,2364,2267],{"className":2365},[1987,2024],[1898,2367],{"className":2368,"style":2090},[2052],[1898,2370,1944],{"className":2371},[2094],[1898,2373],{"className":2374,"style":2090},[2052],[1898,2376,2378,2382,2435,2438,2481],{"className":2377},[1978],[1898,2379],{"className":2380,"style":2381},[1982],"height:2.3277em;vertical-align:-1.2777em;",[1898,2383,2387],{"className":2384},[2385,2386],"mop","op-limits",[1898,2388,2390,2426],{"className":2389},[1999,2000],[1898,2391,2393,2423],{"className":2392},[2004],[1898,2394,2397,2410],{"className":2395,"style":2396},[2008],"height:1.05em;",[1898,2398,2400,2404],{"style":2399},"top:-1.8723em;margin-left:0em;",[1898,2401],{"className":2402,"style":2403},[2016],"height:3.05em;",[1898,2405,2407],{"className":2406},[2165,2166,2167,2168],[1898,2408,2285],{"className":2409},[1987,2024,2168],[1898,2411,2413,2416],{"style":2412},"top:-3.05em;",[1898,2414],{"className":2415,"style":2403},[2016],[1898,2417,2418],{},[1898,2419,2282],{"className":2420},[2385,2421,2422],"op-symbol","large-op",[1898,2424,2073],{"className":2425},[2072],[1898,2427,2429],{"className":2428},[2004],[1898,2430,2433],{"className":2431,"style":2432},[2008],"height:1.2777em;",[1898,2434],{},[1898,2436],{"className":2437,"style":2362},[2052],[1898,2439,2441,2445],{"className":2440},[1987],[1898,2442,2290],{"className":2443,"style":2444},[1987,2024],"margin-right:0.0359em;",[1898,2446,2448],{"className":2447},[2144],[1898,2449,2451,2473],{"className":2450},[1999,2000],[1898,2452,2454,2470],{"className":2453},[2004],[1898,2455,2458],{"className":2456,"style":2457},[2008],"height:0.3117em;",[1898,2459,2461,2464],{"style":2460},"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;",[1898,2462],{"className":2463,"style":2161},[2016],[1898,2465,2467],{"className":2466},[2165,2166,2167,2168],[1898,2468,2285],{"className":2469},[1987,2024,2168],[1898,2471,2073],{"className":2472},[2072],[1898,2474,2476],{"className":2475},[2004],[1898,2477,2479],{"className":2478,"style":2182},[2008],[1898,2480],{},[1898,2482,1965],{"className":2483},[2222],[1798,2485,2486,2487,2490,2491,2493],{},"with constant marginal cost ",[2227,2488,2489],{},"c",". Firm ",[2227,2492,2285],{}," maximises:",[1898,2495,2497],{"className":2496},[1901],[1898,2498,2500,2573],{"className":2499},[1905],[1898,2501,2503],{"className":2502},[1909],[1911,2504,2505],{"xmlns":1913,"display":1914},[1916,2506,2507,2570],{},[1919,2508,2509,2516,2518,2522,2524,2526,2528,2531,2537,2540,2550,2553,2555,2557,2560,2566],{},[1954,2510,2511,2514],{},[1927,2512,2513],{},"π",[1927,2515,2285],{},[1931,2517,1944],{},[1931,2519,2521],{"stretchy":2520},"false","[",[1927,2523,2259],{},[1931,2525,1933],{},[1927,2527,2264],{},[1931,2529,2530],{"stretchy":2520},"(",[1954,2532,2533,2535],{},[1927,2534,2290],{},[1927,2536,2285],{},[1931,2538,2539],{},"+",[1954,2541,2542,2544],{},[1927,2543,2267],{},[1919,2545,2546,2548],{},[1931,2547,1933],{},[1927,2549,2285],{},[1931,2551,2552],{"stretchy":2520},")",[1931,2554,1933],{},[1927,2556,2489],{},[1931,2558,2559],{"stretchy":2520},"]",[1954,2561,2562,2564],{},[1927,2563,2290],{},[1927,2565,2285],{},[1927,2567,2569],{"mathvariant":2568},"normal",".",[1967,2571,2572],{"encoding":1969},"\\pi_i=[a-b(q_i+Q_{-i})-c]q_i.",[1898,2574,2576,2632,2654,2715,2780],{"className":2575,"ariaHidden":1964},[1974],[1898,2577,2579,2583,2623,2626,2629],{"className":2578},[1978],[1898,2580],{"className":2581,"style":2582},[1982],"height:0.5806em;vertical-align:-0.15em;",[1898,2584,2586,2589],{"className":2585},[1987],[1898,2587,2513],{"className":2588,"style":2444},[1987,2024],[1898,2590,2592],{"className":2591},[2144],[1898,2593,2595,2615],{"className":2594},[1999,2000],[1898,2596,2598,2612],{"className":2597},[2004],[1898,2599,2601],{"className":2600,"style":2457},[2008],[1898,2602,2603,2606],{"style":2460},[1898,2604],{"className":2605,"style":2161},[2016],[1898,2607,2609],{"className":2608},[2165,2166,2167,2168],[1898,2610,2285],{"className":2611},[1987,2024,2168],[1898,2613,2073],{"className":2614},[2072],[1898,2616,2618],{"className":2617},[2004],[1898,2619,2621],{"className":2620,"style":2182},[2008],[1898,2622],{},[1898,2624],{"className":2625,"style":2090},[2052],[1898,2627,1944],{"className":2628},[2094],[1898,2630],{"className":2631,"style":2090},[2052],[1898,2633,2635,2639,2642,2645,2648,2651],{"className":2634},[1978],[1898,2636],{"className":2637,"style":2638},[1982],"height:1em;vertical-align:-0.25em;",[1898,2640,2521],{"className":2641},[1991],[1898,2643,2259],{"className":2644},[1987,2024],[1898,2646],{"className":2647,"style":2053},[2052],[1898,2649,1933],{"className":2650},[2057],[1898,2652],{"className":2653,"style":2053},[2052],[1898,2655,2657,2660,2663,2666,2706,2709,2712],{"className":2656},[1978],[1898,2658],{"className":2659,"style":2638},[1982],[1898,2661,2264],{"className":2662},[1987,2024],[1898,2664,2530],{"className":2665},[1991],[1898,2667,2669,2672],{"className":2668},[1987],[1898,2670,2290],{"className":2671,"style":2444},[1987,2024],[1898,2673,2675],{"className":2674},[2144],[1898,2676,2678,2698],{"className":2677},[1999,2000],[1898,2679,2681,2695],{"className":2680},[2004],[1898,2682,2684],{"className":2683,"style":2457},[2008],[1898,2685,2686,2689],{"style":2460},[1898,2687],{"className":2688,"style":2161},[2016],[1898,2690,2692],{"className":2691},[2165,2166,2167,2168],[1898,2693,2285],{"className":2694},[1987,2024,2168],[1898,2696,2073],{"className":2697},[2072],[1898,2699,2701],{"className":2700},[2004],[1898,2702,2704],{"className":2703,"style":2182},[2008],[1898,2705],{},[1898,2707],{"className":2708,"style":2053},[2052],[1898,2710,2539],{"className":2711},[2057],[1898,2713],{"className":2714,"style":2053},[2052],[1898,2716,2718,2721,2768,2771,2774,2777],{"className":2717},[1978],[1898,2719],{"className":2720,"style":2638},[1982],[1898,2722,2724,2727],{"className":2723},[1987],[1898,2725,2267],{"className":2726},[1987,2024],[1898,2728,2730],{"className":2729},[2144],[1898,2731,2733,2759],{"className":2732},[1999,2000],[1898,2734,2736,2756],{"className":2735},[2004],[1898,2737,2739],{"className":2738,"style":2457},[2008],[1898,2740,2741,2744],{"style":2157},[1898,2742],{"className":2743,"style":2161},[2016],[1898,2745,2747],{"className":2746},[2165,2166,2167,2168],[1898,2748,2750,2753],{"className":2749},[1987,2168],[1898,2751,1933],{"className":2752},[1987,2168],[1898,2754,2285],{"className":2755},[1987,2024,2168],[1898,2757,2073],{"className":2758},[2072],[1898,2760,2762],{"className":2761},[2004],[1898,2763,2766],{"className":2764,"style":2765},[2008],"height:0.2083em;",[1898,2767],{},[1898,2769,2552],{"className":2770},[2086],[1898,2772],{"className":2773,"style":2053},[2052],[1898,2775,1933],{"className":2776},[2057],[1898,2778],{"className":2779,"style":2053},[2052],[1898,2781,2783,2786,2789,2792,2832],{"className":2782},[1978],[1898,2784],{"className":2785,"style":2638},[1982],[1898,2787,2489],{"className":2788},[1987,2024],[1898,2790,2559],{"className":2791},[2086],[1898,2793,2795,2798],{"className":2794},[1987],[1898,2796,2290],{"className":2797,"style":2444},[1987,2024],[1898,2799,2801],{"className":2800},[2144],[1898,2802,2804,2824],{"className":2803},[1999,2000],[1898,2805,2807,2821],{"className":2806},[2004],[1898,2808,2810],{"className":2809,"style":2457},[2008],[1898,2811,2812,2815],{"style":2460},[1898,2813],{"className":2814,"style":2161},[2016],[1898,2816,2818],{"className":2817},[2165,2166,2167,2168],[1898,2819,2285],{"className":2820},[1987,2024,2168],[1898,2822,2073],{"className":2823},[2072],[1898,2825,2827],{"className":2826},[2004],[1898,2828,2830],{"className":2829,"style":2182},[2008],[1898,2831],{},[1898,2833,2569],{"className":2834},[1987],[1798,2836,2837],{},"Its best response is:",[1898,2839,2841],{"className":2840},[1901],[1898,2842,2844,2895],{"className":2843},[1905],[1898,2845,2847],{"className":2846},[1909],[1911,2848,2849],{"xmlns":1913,"display":1914},[1916,2850,2851,2892],{},[1919,2852,2853,2859,2861],{},[1954,2854,2855,2857],{},[1927,2856,2290],{},[1927,2858,2285],{},[1931,2860,1944],{},[1922,2862,2863,2885],{},[1919,2864,2865,2867,2869,2871,2873,2875],{},[1927,2866,2259],{},[1931,2868,1933],{},[1927,2870,2489],{},[1931,2872,1933],{},[1927,2874,2264],{},[1954,2876,2877,2879],{},[1927,2878,2267],{},[1919,2880,2881,2883],{},[1931,2882,1933],{},[1927,2884,2285],{},[1919,2886,2887,2890],{},[1950,2888,2889],{},"2",[1927,2891,2264],{},[1967,2893,2894],{"encoding":1969},"q_i=\\frac{a-c-bQ_{-i}}{2b}",[1898,2896,2898,2954],{"className":2897,"ariaHidden":1964},[1974],[1898,2899,2901,2905,2945,2948,2951],{"className":2900},[1978],[1898,2902],{"className":2903,"style":2904},[1982],"height:0.625em;vertical-align:-0.1944em;",[1898,2906,2908,2911],{"className":2907},[1987],[1898,2909,2290],{"className":2910,"style":2444},[1987,2024],[1898,2912,2914],{"className":2913},[2144],[1898,2915,2917,2937],{"className":2916},[1999,2000],[1898,2918,2920,2934],{"className":2919},[2004],[1898,2921,2923],{"className":2922,"style":2457},[2008],[1898,2924,2925,2928],{"style":2460},[1898,2926],{"className":2927,"style":2161},[2016],[1898,2929,2931],{"className":2930},[2165,2166,2167,2168],[1898,2932,2285],{"className":2933},[1987,2024,2168],[1898,2935,2073],{"className":2936},[2072],[1898,2938,2940],{"className":2939},[2004],[1898,2941,2943],{"className":2942,"style":2182},[2008],[1898,2944],{},[1898,2946],{"className":2947,"style":2090},[2052],[1898,2949,1944],{"className":2950},[2094],[1898,2952],{"className":2953,"style":2090},[2052],[1898,2955,2957,2961],{"className":2956},[1978],[1898,2958],{"className":2959,"style":2960},[1982],"height:2.0574em;vertical-align:-0.686em;",[1898,2962,2964,2967,3094],{"className":2963},[1987],[1898,2965],{"className":2966},[1991,1992],[1898,2968,2970],{"className":2969},[1922],[1898,2971,2973,3086],{"className":2972},[1999,2000],[1898,2974,2976,3083],{"className":2975},[2004],[1898,2977,2980,2994,3002],{"className":2978,"style":2979},[2008],"height:1.3714em;",[1898,2981,2982,2985],{"style":2012},[1898,2983],{"className":2984,"style":2017},[2016],[1898,2986,2988,2991],{"className":2987},[1987],[1898,2989,2889],{"className":2990},[1987],[1898,2992,2264],{"className":2993},[1987,2024],[1898,2995,2996,2999],{"style":2028},[1898,2997],{"className":2998,"style":2017},[2016],[1898,3000],{"className":3001,"style":2036},[2035],[1898,3003,3004,3007],{"style":2039},[1898,3005],{"className":3006,"style":2017},[2016],[1898,3008,3010,3013,3016,3019,3022,3025,3028,3031,3034,3037],{"className":3009},[1987],[1898,3011,2259],{"className":3012},[1987,2024],[1898,3014],{"className":3015,"style":2053},[2052],[1898,3017,1933],{"className":3018},[2057],[1898,3020],{"className":3021,"style":2053},[2052],[1898,3023,2489],{"className":3024},[1987,2024],[1898,3026],{"className":3027,"style":2053},[2052],[1898,3029,1933],{"className":3030},[2057],[1898,3032],{"className":3033,"style":2053},[2052],[1898,3035,2264],{"className":3036},[1987,2024],[1898,3038,3040,3043],{"className":3039},[1987],[1898,3041,2267],{"className":3042},[1987,2024],[1898,3044,3046],{"className":3045},[2144],[1898,3047,3049,3075],{"className":3048},[1999,2000],[1898,3050,3052,3072],{"className":3051},[2004],[1898,3053,3055],{"className":3054,"style":2457},[2008],[1898,3056,3057,3060],{"style":2157},[1898,3058],{"className":3059,"style":2161},[2016],[1898,3061,3063],{"className":3062},[2165,2166,2167,2168],[1898,3064,3066,3069],{"className":3065},[1987,2168],[1898,3067,1933],{"className":3068},[1987,2168],[1898,3070,2285],{"className":3071},[1987,2024,2168],[1898,3073,2073],{"className":3074},[2072],[1898,3076,3078],{"className":3077},[2004],[1898,3079,3081],{"className":3080,"style":2765},[2008],[1898,3082],{},[1898,3084,2073],{"className":3085},[2072],[1898,3087,3089],{"className":3088},[2004],[1898,3090,3092],{"className":3091,"style":2080},[2008],[1898,3093],{},[1898,3095],{"className":3096},[2086,1992],[1798,3098,3099,3100,3103],{},"when the expression is positive. With ",[2227,3101,3102],{},"n"," symmetric firms:",[1898,3105,3107],{"className":3106},[1901],[1898,3108,3110,3236],{"className":3109},[1905],[1898,3111,3113],{"className":3112},[1909],[1911,3114,3115],{"xmlns":1913,"display":1914},[1916,3116,3117,3233],{},[1919,3118,3119,3129,3131,3155,3157,3160,3167,3169,3199,3201,3203,3209,3211,3231],{},[3120,3121,3122,3124,3126],"msubsup",{},[1927,3123,2290],{},[1927,3125,2285],{},[1931,3127,3128],{},"∗",[1931,3130,1944],{},[1922,3132,3133,3141],{},[1919,3134,3135,3137,3139],{},[1927,3136,2259],{},[1931,3138,1933],{},[1927,3140,2489],{},[1919,3142,3143,3145,3147,3149,3151,3153],{},[1927,3144,2264],{},[1931,3146,2530],{"stretchy":2520},[1927,3148,3102],{},[1931,3150,2539],{},[1950,3152,1952],{},[1931,3154,2552],{"stretchy":2520},[1931,3156,1965],{"separator":1964},[2052,3158],{"width":3159},"1em",[3161,3162,3163,3165],"msup",{},[1927,3164,2267],{},[1931,3166,3128],{},[1931,3168,1944],{},[1922,3170,3171,3185],{},[1919,3172,3173,3175,3177,3179,3181,3183],{},[1927,3174,3102],{},[1931,3176,2530],{"stretchy":2520},[1927,3178,2259],{},[1931,3180,1933],{},[1927,3182,2489],{},[1931,3184,2552],{"stretchy":2520},[1919,3186,3187,3189,3191,3193,3195,3197],{},[1927,3188,2264],{},[1931,3190,2530],{"stretchy":2520},[1927,3192,3102],{},[1931,3194,2539],{},[1950,3196,1952],{},[1931,3198,2552],{"stretchy":2520},[1931,3200,1965],{"separator":1964},[2052,3202],{"width":3159},[3161,3204,3205,3207],{},[1927,3206,1929],{},[1931,3208,3128],{},[1931,3210,1944],{},[1922,3212,3213,3223],{},[1919,3214,3215,3217,3219,3221],{},[1927,3216,2259],{},[1931,3218,2539],{},[1927,3220,3102],{},[1927,3222,2489],{},[1919,3224,3225,3227,3229],{},[1927,3226,3102],{},[1931,3228,2539],{},[1950,3230,1952],{},[1927,3232,2569],{"mathvariant":2568},[1967,3234,3235],{"encoding":1969},"q_i^*=\\frac{a-c}{b(n+1)},\n\\quad Q^*=\\frac{n(a-c)}{b(n+1)},\n\\quad P^*=\\frac{a+nc}{n+1}.",[1898,3237,3239,3310,3462,3621],{"className":3238,"ariaHidden":1964},[1974],[1898,3240,3242,3246,3301,3304,3307],{"className":3241},[1978],[1898,3243],{"className":3244,"style":3245},[1982],"height:0.9857em;vertical-align:-0.247em;",[1898,3247,3249,3252],{"className":3248},[1987],[1898,3250,2290],{"className":3251,"style":2444},[1987,2024],[1898,3253,3255],{"className":3254},[2144],[1898,3256,3258,3292],{"className":3257},[1999,2000],[1898,3259,3261,3289],{"className":3260},[2004],[1898,3262,3265,3277],{"className":3263,"style":3264},[2008],"height:0.7387em;",[1898,3266,3268,3271],{"style":3267},"top:-2.453em;margin-left:-0.0359em;margin-right:0.05em;",[1898,3269],{"className":3270,"style":2161},[2016],[1898,3272,3274],{"className":3273},[2165,2166,2167,2168],[1898,3275,2285],{"className":3276},[1987,2024,2168],[1898,3278,3280,3283],{"style":3279},"top:-3.113em;margin-right:0.05em;",[1898,3281],{"className":3282,"style":2161},[2016],[1898,3284,3286],{"className":3285},[2165,2166,2167,2168],[1898,3287,3128],{"className":3288},[2057,2168],[1898,3290,2073],{"className":3291},[2072],[1898,3293,3295],{"className":3294},[2004],[1898,3296,3299],{"className":3297,"style":3298},[2008],"height:0.247em;",[1898,3300],{},[1898,3302],{"className":3303,"style":2090},[2052],[1898,3305,1944],{"className":3306},[2094],[1898,3308],{"className":3309,"style":2090},[2052],[1898,3311,3313,3317,3414,3417,3421,3424,3453,3456,3459],{"className":3312},[1978],[1898,3314],{"className":3315,"style":3316},[1982],"height:2.1963em;vertical-align:-0.936em;",[1898,3318,3320,3323,3411],{"className":3319},[1987],[1898,3321],{"className":3322},[1991,1992],[1898,3324,3326],{"className":3325},[1922],[1898,3327,3329,3402],{"className":3328},[1999,2000],[1898,3330,3332,3399],{"className":3331},[2004],[1898,3333,3336,3368,3376],{"className":3334,"style":3335},[2008],"height:1.2603em;",[1898,3337,3338,3341],{"style":2012},[1898,3339],{"className":3340,"style":2017},[2016],[1898,3342,3344,3347,3350,3353,3356,3359,3362,3365],{"className":3343},[1987],[1898,3345,2264],{"className":3346},[1987,2024],[1898,3348,2530],{"className":3349},[1991],[1898,3351,3102],{"className":3352},[1987,2024],[1898,3354],{"className":3355,"style":2053},[2052],[1898,3357,2539],{"className":3358},[2057],[1898,3360],{"className":3361,"style":2053},[2052],[1898,3363,1952],{"className":3364},[1987],[1898,3366,2552],{"className":3367},[2086],[1898,3369,3370,3373],{"style":2028},[1898,3371],{"className":3372,"style":2017},[2016],[1898,3374],{"className":3375,"style":2036},[2035],[1898,3377,3378,3381],{"style":2039},[1898,3379],{"className":3380,"style":2017},[2016],[1898,3382,3384,3387,3390,3393,3396],{"className":3383},[1987],[1898,3385,2259],{"className":3386},[1987,2024],[1898,3388],{"className":3389,"style":2053},[2052],[1898,3391,1933],{"className":3392},[2057],[1898,3394],{"className":3395,"style":2053},[2052],[1898,3397,2489],{"className":3398},[1987,2024],[1898,3400,2073],{"className":3401},[2072],[1898,3403,3405],{"className":3404},[2004],[1898,3406,3409],{"className":3407,"style":3408},[2008],"height:0.936em;",[1898,3410],{},[1898,3412],{"className":3413},[2086,1992],[1898,3415,1965],{"className":3416},[2222],[1898,3418],{"className":3419,"style":3420},[2052],"margin-right:1em;",[1898,3422],{"className":3423,"style":2362},[2052],[1898,3425,3427,3430],{"className":3426},[1987],[1898,3428,2267],{"className":3429},[1987,2024],[1898,3431,3433],{"className":3432},[2144],[1898,3434,3436],{"className":3435},[1999],[1898,3437,3439],{"className":3438},[2004],[1898,3440,3442],{"className":3441,"style":3264},[2008],[1898,3443,3444,3447],{"style":3279},[1898,3445],{"className":3446,"style":2161},[2016],[1898,3448,3450],{"className":3449},[2165,2166,2167,2168],[1898,3451,3128],{"className":3452},[2057,2168],[1898,3454],{"className":3455,"style":2090},[2052],[1898,3457,1944],{"className":3458},[2094],[1898,3460],{"className":3461,"style":2090},[2052],[1898,3463,3465,3469,3574,3577,3580,3583,3612,3615,3618],{"className":3464},[1978],[1898,3466],{"className":3467,"style":3468},[1982],"height:2.363em;vertical-align:-0.936em;",[1898,3470,3472,3475,3571],{"className":3471},[1987],[1898,3473],{"className":3474},[1991,1992],[1898,3476,3478],{"className":3477},[1922],[1898,3479,3481,3563],{"className":3480},[1999,2000],[1898,3482,3484,3560],{"className":3483},[2004],[1898,3485,3488,3520,3528],{"className":3486,"style":3487},[2008],"height:1.427em;",[1898,3489,3490,3493],{"style":2012},[1898,3491],{"className":3492,"style":2017},[2016],[1898,3494,3496,3499,3502,3505,3508,3511,3514,3517],{"className":3495},[1987],[1898,3497,2264],{"className":3498},[1987,2024],[1898,3500,2530],{"className":3501},[1991],[1898,3503,3102],{"className":3504},[1987,2024],[1898,3506],{"className":3507,"style":2053},[2052],[1898,3509,2539],{"className":3510},[2057],[1898,3512],{"className":3513,"style":2053},[2052],[1898,3515,1952],{"className":3516},[1987],[1898,3518,2552],{"className":3519},[2086],[1898,3521,3522,3525],{"style":2028},[1898,3523],{"className":3524,"style":2017},[2016],[1898,3526],{"className":3527,"style":2036},[2035],[1898,3529,3530,3533],{"style":2039},[1898,3531],{"className":3532,"style":2017},[2016],[1898,3534,3536,3539,3542,3545,3548,3551,3554,3557],{"className":3535},[1987],[1898,3537,3102],{"className":3538},[1987,2024],[1898,3540,2530],{"className":3541},[1991],[1898,3543,2259],{"className":3544},[1987,2024],[1898,3546],{"className":3547,"style":2053},[2052],[1898,3549,1933],{"className":3550},[2057],[1898,3552],{"className":3553,"style":2053},[2052],[1898,3555,2489],{"className":3556},[1987,2024],[1898,3558,2552],{"className":3559},[2086],[1898,3561,2073],{"className":3562},[2072],[1898,3564,3566],{"className":3565},[2004],[1898,3567,3569],{"className":3568,"style":3408},[2008],[1898,3570],{},[1898,3572],{"className":3573},[2086,1992],[1898,3575,1965],{"className":3576},[2222],[1898,3578],{"className":3579,"style":3420},[2052],[1898,3581],{"className":3582,"style":2362},[2052],[1898,3584,3586,3589],{"className":3585},[1987],[1898,3587,1929],{"className":3588,"style":2025},[1987,2024],[1898,3590,3592],{"className":3591},[2144],[1898,3593,3595],{"className":3594},[1999],[1898,3596,3598],{"className":3597},[2004],[1898,3599,3601],{"className":3600,"style":3264},[2008],[1898,3602,3603,3606],{"style":3279},[1898,3604],{"className":3605,"style":2161},[2016],[1898,3607,3609],{"className":3608},[2165,2166,2167,2168],[1898,3610,3128],{"className":3611},[2057,2168],[1898,3613],{"className":3614,"style":2090},[2052],[1898,3616,1944],{"className":3617},[2094],[1898,3619],{"className":3620,"style":2090},[2052],[1898,3622,3624,3628,3718],{"className":3623},[1978],[1898,3625],{"className":3626,"style":3627},[1982],"height:2.0297em;vertical-align:-0.7693em;",[1898,3629,3631,3634,3715],{"className":3630},[1987],[1898,3632],{"className":3633},[1991,1992],[1898,3635,3637],{"className":3636},[1922],[1898,3638,3640,3706],{"className":3639},[1999,2000],[1898,3641,3643,3703],{"className":3642},[2004],[1898,3644,3646,3669,3677],{"className":3645,"style":3335},[2008],[1898,3647,3648,3651],{"style":2012},[1898,3649],{"className":3650,"style":2017},[2016],[1898,3652,3654,3657,3660,3663,3666],{"className":3653},[1987],[1898,3655,3102],{"className":3656},[1987,2024],[1898,3658],{"className":3659,"style":2053},[2052],[1898,3661,2539],{"className":3662},[2057],[1898,3664],{"className":3665,"style":2053},[2052],[1898,3667,1952],{"className":3668},[1987],[1898,3670,3671,3674],{"style":2028},[1898,3672],{"className":3673,"style":2017},[2016],[1898,3675],{"className":3676,"style":2036},[2035],[1898,3678,3679,3682],{"style":2039},[1898,3680],{"className":3681,"style":2017},[2016],[1898,3683,3685,3688,3691,3694,3697,3700],{"className":3684},[1987],[1898,3686,2259],{"className":3687},[1987,2024],[1898,3689],{"className":3690,"style":2053},[2052],[1898,3692,2539],{"className":3693},[2057],[1898,3695],{"className":3696,"style":2053},[2052],[1898,3698,3102],{"className":3699},[1987,2024],[1898,3701,2489],{"className":3702},[1987,2024],[1898,3704,2073],{"className":3705},[2072],[1898,3707,3709],{"className":3708},[2004],[1898,3710,3713],{"className":3711,"style":3712},[2008],"height:0.7693em;",[1898,3714],{},[1898,3716],{"className":3717},[2086,1992],[1898,3719,2569],{"className":3720},[1987],[3722,3723,3725],"h3",{"id":3724},"numerical-duopoly","Numerical duopoly",[1798,3727,3728,3729,3732,3733,3736,3737,3740],{},"Let ",[2227,3730,3731],{},"a=100",", ",[2227,3734,3735],{},"b=1",", and ",[2227,3738,3739],{},"c=20",":",[1898,3742,3744],{"className":3743},[1901],[1898,3745,3747,3791],{"className":3746},[1905],[1898,3748,3750],{"className":3749},[1909],[1911,3751,3752],{"xmlns":1913,"display":1914},[1916,3753,3754,3788],{},[1919,3755,3756,3762,3764,3770,3772,3780,3783,3786],{},[1954,3757,3758,3760],{},[1927,3759,2290],{},[1950,3761,1952],{},[1931,3763,1944],{},[1954,3765,3766,3768],{},[1927,3767,2290],{},[1950,3769,2889],{},[1931,3771,1944],{},[1922,3773,3774,3777],{},[1950,3775,3776],{},"80",[1950,3778,3779],{},"3",[1931,3781,3782],{},"≈",[1950,3784,3785],{},"26.67",[1931,3787,1965],{"separator":1964},[1967,3789,3790],{"encoding":1969},"q_1=q_2=\\frac{80}{3}\\approx26.67,",[1898,3792,3794,3850,3905,3983],{"className":3793,"ariaHidden":1964},[1974],[1898,3795,3797,3800,3841,3844,3847],{"className":3796},[1978],[1898,3798],{"className":3799,"style":2904},[1982],[1898,3801,3803,3806],{"className":3802},[1987],[1898,3804,2290],{"className":3805,"style":2444},[1987,2024],[1898,3807,3809],{"className":3808},[2144],[1898,3810,3812,3833],{"className":3811},[1999,2000],[1898,3813,3815,3830],{"className":3814},[2004],[1898,3816,3819],{"className":3817,"style":3818},[2008],"height:0.3011em;",[1898,3820,3821,3824],{"style":2460},[1898,3822],{"className":3823,"style":2161},[2016],[1898,3825,3827],{"className":3826},[2165,2166,2167,2168],[1898,3828,1952],{"className":3829},[1987,2168],[1898,3831,2073],{"className":3832},[2072],[1898,3834,3836],{"className":3835},[2004],[1898,3837,3839],{"className":3838,"style":2182},[2008],[1898,3840],{},[1898,3842],{"className":3843,"style":2090},[2052],[1898,3845,1944],{"className":3846},[2094],[1898,3848],{"className":3849,"style":2090},[2052],[1898,3851,3853,3856,3896,3899,3902],{"className":3852},[1978],[1898,3854],{"className":3855,"style":2904},[1982],[1898,3857,3859,3862],{"className":3858},[1987],[1898,3860,2290],{"className":3861,"style":2444},[1987,2024],[1898,3863,3865],{"className":3864},[2144],[1898,3866,3868,3888],{"className":3867},[1999,2000],[1898,3869,3871,3885],{"className":3870},[2004],[1898,3872,3874],{"className":3873,"style":3818},[2008],[1898,3875,3876,3879],{"style":2460},[1898,3877],{"className":3878,"style":2161},[2016],[1898,3880,3882],{"className":3881},[2165,2166,2167,2168],[1898,3883,2889],{"className":3884},[1987,2168],[1898,3886,2073],{"className":3887},[2072],[1898,3889,3891],{"className":3890},[2004],[1898,3892,3894],{"className":3893,"style":2182},[2008],[1898,3895],{},[1898,3897],{"className":3898,"style":2090},[2052],[1898,3900,1944],{"className":3901},[2094],[1898,3903],{"className":3904,"style":2090},[2052],[1898,3906,3908,3912,3974,3977,3980],{"className":3907},[1978],[1898,3909],{"className":3910,"style":3911},[1982],"height:2.0074em;vertical-align:-0.686em;",[1898,3913,3915,3918,3971],{"className":3914},[1987],[1898,3916],{"className":3917},[1991,1992],[1898,3919,3921],{"className":3920},[1922],[1898,3922,3924,3963],{"className":3923},[1999,2000],[1898,3925,3927,3960],{"className":3926},[2004],[1898,3928,3930,3941,3949],{"className":3929,"style":2126},[2008],[1898,3931,3932,3935],{"style":2012},[1898,3933],{"className":3934,"style":2017},[2016],[1898,3936,3938],{"className":3937},[1987],[1898,3939,3779],{"className":3940},[1987],[1898,3942,3943,3946],{"style":2028},[1898,3944],{"className":3945,"style":2017},[2016],[1898,3947],{"className":3948,"style":2036},[2035],[1898,3950,3951,3954],{"style":2039},[1898,3952],{"className":3953,"style":2017},[2016],[1898,3955,3957],{"className":3956},[1987],[1898,3958,3776],{"className":3959},[1987],[1898,3961,2073],{"className":3962},[2072],[1898,3964,3966],{"className":3965},[2004],[1898,3967,3969],{"className":3968,"style":2080},[2008],[1898,3970],{},[1898,3972],{"className":3973},[2086,1992],[1898,3975],{"className":3976,"style":2090},[2052],[1898,3978,3782],{"className":3979},[2094],[1898,3981],{"className":3982,"style":2090},[2052],[1898,3984,3986,3990,3993],{"className":3985},[1978],[1898,3987],{"className":3988,"style":3989},[1982],"height:0.8389em;vertical-align:-0.1944em;",[1898,3991,3785],{"className":3992},[1987],[1898,3994,1965],{"className":3995},[2222],[1798,3997,3998,3999,3732,4002,4005,4006,2569],{},"so ",[2227,4000,4001],{},"Q≈53.33",[2227,4003,4004],{},"P≈46.67",", and each profit is about ",[2227,4007,4008],{},"£711.11",[1798,4010,4011,4012,4014],{},"As ",[2227,4013,3102],{}," grows, price approaches marginal cost in this benchmark. Fixed costs and endogenous entry can prevent the number of active firms from growing without bound.",[1793,4016,4018],{"id":4017},"_3-bertrand-firms-choose-prices","3. Bertrand: firms choose prices",[1798,4020,4021,4022,4024],{},"With homogeneous products, constant identical marginal cost, sufficient capacity, and consumers buying from the cheapest seller, any price above ",[2227,4023,2489],{}," can be undercut. The Nash equilibrium is:",[1898,4026,4028],{"className":4027},[1901],[1898,4029,4031,4063],{"className":4030},[1905],[1898,4032,4034],{"className":4033},[1909],[1911,4035,4036],{"xmlns":1913,"display":1914},[1916,4037,4038,4060],{},[1919,4039,4040,4046,4048,4054,4056,4058],{},[1954,4041,4042,4044],{},[1927,4043,1798],{},[1950,4045,1952],{},[1931,4047,1944],{},[1954,4049,4050,4052],{},[1927,4051,1798],{},[1950,4053,2889],{},[1931,4055,1944],{},[1927,4057,2489],{},[1927,4059,2569],{"mathvariant":2568},[1967,4061,4062],{"encoding":1969},"p_1=p_2=c.",[1898,4064,4066,4121,4176],{"className":4065,"ariaHidden":1964},[1974],[1898,4067,4069,4072,4112,4115,4118],{"className":4068},[1978],[1898,4070],{"className":4071,"style":2904},[1982],[1898,4073,4075,4078],{"className":4074},[1987],[1898,4076,1798],{"className":4077},[1987,2024],[1898,4079,4081],{"className":4080},[2144],[1898,4082,4084,4104],{"className":4083},[1999,2000],[1898,4085,4087,4101],{"className":4086},[2004],[1898,4088,4090],{"className":4089,"style":3818},[2008],[1898,4091,4092,4095],{"style":2157},[1898,4093],{"className":4094,"style":2161},[2016],[1898,4096,4098],{"className":4097},[2165,2166,2167,2168],[1898,4099,1952],{"className":4100},[1987,2168],[1898,4102,2073],{"className":4103},[2072],[1898,4105,4107],{"className":4106},[2004],[1898,4108,4110],{"className":4109,"style":2182},[2008],[1898,4111],{},[1898,4113],{"className":4114,"style":2090},[2052],[1898,4116,1944],{"className":4117},[2094],[1898,4119],{"className":4120,"style":2090},[2052],[1898,4122,4124,4127,4167,4170,4173],{"className":4123},[1978],[1898,4125],{"className":4126,"style":2904},[1982],[1898,4128,4130,4133],{"className":4129},[1987],[1898,4131,1798],{"className":4132},[1987,2024],[1898,4134,4136],{"className":4135},[2144],[1898,4137,4139,4159],{"className":4138},[1999,2000],[1898,4140,4142,4156],{"className":4141},[2004],[1898,4143,4145],{"className":4144,"style":3818},[2008],[1898,4146,4147,4150],{"style":2157},[1898,4148],{"className":4149,"style":2161},[2016],[1898,4151,4153],{"className":4152},[2165,2166,2167,2168],[1898,4154,2889],{"className":4155},[1987,2168],[1898,4157,2073],{"className":4158},[2072],[1898,4160,4162],{"className":4161},[2004],[1898,4163,4165],{"className":4164,"style":2182},[2008],[1898,4166],{},[1898,4168],{"className":4169,"style":2090},[2052],[1898,4171,1944],{"className":4172},[2094],[1898,4174],{"className":4175,"style":2090},[2052],[1898,4177,4179,4183,4186],{"className":4178},[1978],[1898,4180],{"className":4181,"style":4182},[1982],"height:0.4306em;",[1898,4184,2489],{"className":4185},[1987,2024],[1898,4187,2569],{"className":4188},[1987],[1798,4190,4191],{},"This “Bertrand paradox” is not a claim that two real firms always create perfect competition. Relax one assumption:",[1809,4193,4194,4197,4200,4203,4206],{},[1812,4195,4196],{},"differentiated products soften price competition;",[1812,4198,4199],{},"capacity constraints make undercutting unable to serve the market;",[1812,4201,4202],{},"search or switching costs create local power;",[1812,4204,4205],{},"repeated interaction can support coordination;",[1812,4207,4208],{},"asymmetric costs can leave the efficient firm with a markup.",[1793,4210,4212],{"id":4211},"_4-stackelberg-commitment-changes-best-responses","4. Stackelberg: commitment changes best responses",[1798,4214,4215],{},"The leader chooses quantity first and anticipates the follower's Cournot response. In the same numerical market:",[1898,4217,4219],{"className":4218},[1901],[1898,4220,4222,4264],{"className":4221},[1905],[1898,4223,4225],{"className":4224},[1909],[1911,4226,4227],{"xmlns":1913,"display":1914},[1916,4228,4229,4261],{},[1919,4230,4231,4238,4240,4243,4245,4247,4254,4256,4259],{},[1954,4232,4233,4235],{},[1927,4234,2290],{},[1927,4236,4237],{},"L",[1931,4239,1944],{},[1950,4241,4242],{},"40",[1931,4244,1965],{"separator":1964},[2052,4246],{"width":2272},[1954,4248,4249,4251],{},[1927,4250,2290],{},[1927,4252,4253],{},"F",[1931,4255,1944],{},[1950,4257,4258],{},"20",[1931,4260,1965],{"separator":1964},[1967,4262,4263],{"encoding":1969},"q_L=40,\\qquad q_F=20,",[1898,4265,4267,4322,4389],{"className":4266,"ariaHidden":1964},[1974],[1898,4268,4270,4273,4313,4316,4319],{"className":4269},[1978],[1898,4271],{"className":4272,"style":2904},[1982],[1898,4274,4276,4279],{"className":4275},[1987],[1898,4277,2290],{"className":4278,"style":2444},[1987,2024],[1898,4280,4282],{"className":4281},[2144],[1898,4283,4285,4305],{"className":4284},[1999,2000],[1898,4286,4288,4302],{"className":4287},[2004],[1898,4289,4291],{"className":4290,"style":2154},[2008],[1898,4292,4293,4296],{"style":2460},[1898,4294],{"className":4295,"style":2161},[2016],[1898,4297,4299],{"className":4298},[2165,2166,2167,2168],[1898,4300,4237],{"className":4301},[1987,2024,2168],[1898,4303,2073],{"className":4304},[2072],[1898,4306,4308],{"className":4307},[2004],[1898,4309,4311],{"className":4310,"style":2182},[2008],[1898,4312],{},[1898,4314],{"className":4315,"style":2090},[2052],[1898,4317,1944],{"className":4318},[2094],[1898,4320],{"className":4321,"style":2090},[2052],[1898,4323,4325,4328,4331,4334,4337,4340,4380,4383,4386],{"className":4324},[1978],[1898,4326],{"className":4327,"style":3989},[1982],[1898,4329,4242],{"className":4330},[1987],[1898,4332,1965],{"className":4333},[2222],[1898,4335],{"className":4336,"style":2358},[2052],[1898,4338],{"className":4339,"style":2362},[2052],[1898,4341,4343,4346],{"className":4342},[1987],[1898,4344,2290],{"className":4345,"style":2444},[1987,2024],[1898,4347,4349],{"className":4348},[2144],[1898,4350,4352,4372],{"className":4351},[1999,2000],[1898,4353,4355,4369],{"className":4354},[2004],[1898,4356,4358],{"className":4357,"style":2154},[2008],[1898,4359,4360,4363],{"style":2460},[1898,4361],{"className":4362,"style":2161},[2016],[1898,4364,4366],{"className":4365},[2165,2166,2167,2168],[1898,4367,4253],{"className":4368,"style":2025},[1987,2024,2168],[1898,4370,2073],{"className":4371},[2072],[1898,4373,4375],{"className":4374},[2004],[1898,4376,4378],{"className":4377,"style":2182},[2008],[1898,4379],{},[1898,4381],{"className":4382,"style":2090},[2052],[1898,4384,1944],{"className":4385},[2094],[1898,4387],{"className":4388,"style":2090},[2052],[1898,4390,4392,4395,4398],{"className":4391},[1978],[1898,4393],{"className":4394,"style":3989},[1982],[1898,4396,4258],{"className":4397},[1987],[1898,4399,1965],{"className":4400},[2222],[1798,4402,3998,4403,4406,4407,4410],{},[2227,4404,4405],{},"Q=60"," and ",[2227,4408,4409],{},"P=40",". Profits are:",[1898,4412,4414],{"className":4413},[1901],[1898,4415,4417,4483],{"className":4416},[1905],[1898,4418,4420],{"className":4419},[1909],[1911,4421,4422],{"xmlns":1913,"display":1914},[1916,4423,4424,4480],{},[1919,4425,4426,4432,4434,4436,4438,4440,4442,4444,4446,4448,4451,4453,4455,4461,4463,4465,4467,4469,4471,4473,4475,4477],{},[1954,4427,4428,4430],{},[1927,4429,2513],{},[1927,4431,4237],{},[1931,4433,1944],{},[1931,4435,2530],{"stretchy":2520},[1950,4437,4242],{},[1931,4439,1933],{},[1950,4441,4258],{},[1931,4443,2552],{"stretchy":2520},[1950,4445,4242],{},[1931,4447,1944],{},[1950,4449,4450],{},"800",[1931,4452,1965],{"separator":1964},[2052,4454],{"width":2272},[1954,4456,4457,4459],{},[1927,4458,2513],{},[1927,4460,4253],{},[1931,4462,1944],{},[1931,4464,2530],{"stretchy":2520},[1950,4466,4242],{},[1931,4468,1933],{},[1950,4470,4258],{},[1931,4472,2552],{"stretchy":2520},[1950,4474,4258],{},[1931,4476,1944],{},[1950,4478,4479],{},"400.",[1967,4481,4482],{"encoding":1969},"\\pi_L=(40-20)40=800,\n\\qquad\n\\pi_F=(40-20)20=400.",[1898,4484,4486,4541,4562,4586,4653,4674,4698],{"className":4485,"ariaHidden":1964},[1974],[1898,4487,4489,4492,4532,4535,4538],{"className":4488},[1978],[1898,4490],{"className":4491,"style":2582},[1982],[1898,4493,4495,4498],{"className":4494},[1987],[1898,4496,2513],{"className":4497,"style":2444},[1987,2024],[1898,4499,4501],{"className":4500},[2144],[1898,4502,4504,4524],{"className":4503},[1999,2000],[1898,4505,4507,4521],{"className":4506},[2004],[1898,4508,4510],{"className":4509,"style":2154},[2008],[1898,4511,4512,4515],{"style":2460},[1898,4513],{"className":4514,"style":2161},[2016],[1898,4516,4518],{"className":4517},[2165,2166,2167,2168],[1898,4519,4237],{"className":4520},[1987,2024,2168],[1898,4522,2073],{"className":4523},[2072],[1898,4525,4527],{"className":4526},[2004],[1898,4528,4530],{"className":4529,"style":2182},[2008],[1898,4531],{},[1898,4533],{"className":4534,"style":2090},[2052],[1898,4536,1944],{"className":4537},[2094],[1898,4539],{"className":4540,"style":2090},[2052],[1898,4542,4544,4547,4550,4553,4556,4559],{"className":4543},[1978],[1898,4545],{"className":4546,"style":2638},[1982],[1898,4548,2530],{"className":4549},[1991],[1898,4551,4242],{"className":4552},[1987],[1898,4554],{"className":4555,"style":2053},[2052],[1898,4557,1933],{"className":4558},[2057],[1898,4560],{"className":4561,"style":2053},[2052],[1898,4563,4565,4568,4571,4574,4577,4580,4583],{"className":4564},[1978],[1898,4566],{"className":4567,"style":2638},[1982],[1898,4569,4258],{"className":4570},[1987],[1898,4572,2552],{"className":4573},[2086],[1898,4575,4242],{"className":4576},[1987],[1898,4578],{"className":4579,"style":2090},[2052],[1898,4581,1944],{"className":4582},[2094],[1898,4584],{"className":4585,"style":2090},[2052],[1898,4587,4589,4592,4595,4598,4601,4604,4644,4647,4650],{"className":4588},[1978],[1898,4590],{"className":4591,"style":3989},[1982],[1898,4593,4450],{"className":4594},[1987],[1898,4596,1965],{"className":4597},[2222],[1898,4599],{"className":4600,"style":2358},[2052],[1898,4602],{"className":4603,"style":2362},[2052],[1898,4605,4607,4610],{"className":4606},[1987],[1898,4608,2513],{"className":4609,"style":2444},[1987,2024],[1898,4611,4613],{"className":4612},[2144],[1898,4614,4616,4636],{"className":4615},[1999,2000],[1898,4617,4619,4633],{"className":4618},[2004],[1898,4620,4622],{"className":4621,"style":2154},[2008],[1898,4623,4624,4627],{"style":2460},[1898,4625],{"className":4626,"style":2161},[2016],[1898,4628,4630],{"className":4629},[2165,2166,2167,2168],[1898,4631,4253],{"className":4632,"style":2025},[1987,2024,2168],[1898,4634,2073],{"className":4635},[2072],[1898,4637,4639],{"className":4638},[2004],[1898,4640,4642],{"className":4641,"style":2182},[2008],[1898,4643],{},[1898,4645],{"className":4646,"style":2090},[2052],[1898,4648,1944],{"className":4649},[2094],[1898,4651],{"className":4652,"style":2090},[2052],[1898,4654,4656,4659,4662,4665,4668,4671],{"className":4655},[1978],[1898,4657],{"className":4658,"style":2638},[1982],[1898,4660,2530],{"className":4661},[1991],[1898,4663,4242],{"className":4664},[1987],[1898,4666],{"className":4667,"style":2053},[2052],[1898,4669,1933],{"className":4670},[2057],[1898,4672],{"className":4673,"style":2053},[2052],[1898,4675,4677,4680,4683,4686,4689,4692,4695],{"className":4676},[1978],[1898,4678],{"className":4679,"style":2638},[1982],[1898,4681,4258],{"className":4682},[1987],[1898,4684,2552],{"className":4685},[2086],[1898,4687,4258],{"className":4688},[1987],[1898,4690],{"className":4691,"style":2090},[2052],[1898,4693,1944],{"className":4694},[2094],[1898,4696],{"className":4697,"style":2090},[2052],[1898,4699,4701,4705],{"className":4700},[1978],[1898,4702],{"className":4703,"style":4704},[1982],"height:0.6444em;",[1898,4706,4479],{"className":4707},[1987],[1832,4709,4710,4727],{},[1835,4711,4712],{},[1838,4713,4714,4717,4721,4724],{},[1841,4715,4716],{},"Model",[1841,4718,4720],{"align":4719},"right","Total output",[1841,4722,4723],{"align":4719},"Price",[1841,4725,4726],{},"Strategic advantage",[1848,4728,4729,4742,4756,4768],{},[1838,4730,4731,4734,4736,4739],{},[1853,4732,4733],{},"monopoly",[1853,4735,4242],{"align":4719},[1853,4737,4738],{"align":4719},"60",[1853,4740,4741],{},"coordinated quantity restriction",[1838,4743,4744,4747,4750,4753],{},[1853,4745,4746],{},"Cournot duopoly",[1853,4748,4749],{"align":4719},"53.33",[1853,4751,4752],{"align":4719},"46.67",[1853,4754,4755],{},"neither moves first",[1838,4757,4758,4761,4763,4765],{},[1853,4759,4760],{},"Stackelberg",[1853,4762,4738],{"align":4719},[1853,4764,4242],{"align":4719},[1853,4766,4767],{},"leader commits to output",[1838,4769,4770,4773,4775,4777],{},[1853,4771,4772],{},"competitive benchmark",[1853,4774,3776],{"align":4719},[1853,4776,4258],{"align":4719},[1853,4778,4779],{},"price equals marginal cost",[1798,4781,4782],{},"First-mover advantage requires credible commitment. If capacity can be reversed costlessly before rivals react, the Stackelberg logic weakens.",[1793,4784,4786],{"id":4785},"_5-collusion-is-an-incentive-problem","5. Collusion is an incentive problem",[1798,4788,4789],{},"A cartel tries to reproduce monopoly output, but each member benefits from secretly expanding while others restrict. Repetition can deter deviation when future punishment is valuable, monitoring is informative, and entry is limited.",[1798,4791,4792],{},"Facilitating conditions include:",[1809,4794,4795,4798,4801,4804],{},[1812,4796,4797],{},"few symmetric firms and frequent interaction;",[1812,4799,4800],{},"transparent prices or quantities;",[1812,4802,4803],{},"stable demand and costs;",[1812,4805,4806],{},"credible punishment and high entry barriers.",[1798,4808,4809],{},"Transparency can help consumers search yet also help firms monitor one another. Its effect is an empirical institutional question.",[1793,4811,4813],{"id":4812},"_6-entry-and-contestability","6. Entry and contestability",[1798,4815,4816],{},"Entry occurs when expected post-entry profit covers sunk entry cost. An incumbent may invest in capacity, compatibility, product proliferation, or long contracts before entry.",[1798,4818,4819],{},"To distinguish competition from exclusion, ask:",[4821,4822,4823,4826,4829,4832,4835],"ol",{},[1812,4824,4825],{},"Would the action be profitable without deterring a rival?",[1812,4827,4828],{},"Does it lower the incumbent's cost or improve quality?",[1812,4830,4831],{},"Does it raise rivals' costs or deny a necessary input?",[1812,4833,4834],{},"Is the commitment credible and observable?",[1812,4836,4837],{},"What happens to consumers in the short and long run?",[1798,4839,4840],{},"Low current prices can reflect competition, predation, penetration pricing, learning, or cross-subsidy. One observation does not identify the mechanism.",[1793,4842,4844],{"id":4843},"_7-platforms-and-ai-foundation-models","7. Platforms and AI foundation models",[1798,4846,4847],{},"Platform markets add indirect network effects, multi-homing, data feedback, default placement, interoperability, and often zero monetary prices on one side. Relevant bottlenecks may include compute, chips, cloud distribution, data, app stores, or access to users.",[1798,4849,4850,4851,4857],{},"The UK Competition and Markets Authority's 2024 foundation-model update mapped an interconnected set of more than 90 partnerships and investments involving major technology firms and highlighted risks around control of critical inputs and routes to market (",[2259,4852,4856],{"href":4853,"rel":4854},"https:\u002F\u002Fwww.gov.uk\u002Fgovernment\u002Fpublications\u002Fai-foundation-models-update-paper",[4855],"nofollow","CMA, 2024",").",[1798,4859,4860],{},"This is a forward-looking competition assessment, not a finding that every partnership harms competition. A proper analysis compares efficiencies—funding, compute access, distribution—with foreclosure, dependency, and reduced independent entry.",[1793,4862,4864],{"id":4863},"_8-field-evidence-on-pricing-software","8. Field evidence on pricing software",[1798,4866,4867,4868,4857],{},"Assad, Clark, Ershov, and Xu study Germany's retail gasoline market, where algorithmic-pricing software became widely available. They infer adoption from changes in pricing patterns and instrument with headquarters adoption. Adoption increased margins for non-monopoly stations; in duopoly and triopoly markets, margins rose when all stations adopted (",[2259,4869,4872],{"href":4870,"rel":4871},"https:\u002F\u002Fdoi.org\u002F10.1086\u002F726906",[4855],"2024",[1798,4874,4875],{},"The evidence is consistent with altered strategic interaction. It does not show that every algorithm autonomously colludes: adoption is inferred, the setting is gasoline retail, and software, market transparency, ownership, and local rivalry matter.",[1793,4877,4879],{"id":4878},"_9-welfare-and-policy-diagnosis","9. Welfare and policy diagnosis",[1798,4881,4882],{},"Market power can raise price, reduce quantity, distort quality or innovation, and redistribute surplus. But intervention can also reduce investment or destroy integration efficiencies.",[1832,4884,4885,4898],{},[1835,4886,4887],{},[1838,4888,4889,4892,4895],{},[1841,4890,4891],{},"Diagnosis",[1841,4893,4894],{},"Candidate response",[1841,4896,4897],{},"Main design risk",[1848,4899,4900,4911,4922,4933,4944],{},[1838,4901,4902,4905,4908],{},[1853,4903,4904],{},"merger removes close rival",[1853,4906,4907],{},"merger control\u002Fremedy",[1853,4909,4910],{},"wrong counterfactual entry",[1838,4912,4913,4916,4919],{},[1853,4914,4915],{},"bottleneck foreclosure",[1853,4917,4918],{},"access\u002Finteroperability rule",[1853,4920,4921],{},"weak security or investment",[1838,4923,4924,4927,4930],{},[1853,4925,4926],{},"collusive communication",[1853,4928,4929],{},"antitrust enforcement",[1853,4931,4932],{},"confusing parallel response with agreement",[1838,4934,4935,4938,4941],{},[1853,4936,4937],{},"algorithmic opacity",[1853,4939,4940],{},"audit, records, monitoring",[1853,4942,4943],{},"box-ticking without causal evidence",[1838,4945,4946,4949,4952],{},[1853,4947,4948],{},"switching\u002Fdata lock-in",[1853,4950,4951],{},"portability and open standards",[1853,4953,4954],{},"low use or privacy leakage",[1793,4956,4958],{"id":4957},"practice","Practice",[4821,4960,4961,4970,4977,4980,4983],{},[1812,4962,4963,4964,4966,4967,2569],{},"Derive the ",[2227,4965,3102],{},"-firm Cournot equilibrium and its limit as ",[2227,4968,4969],{},"n→∞",[1812,4971,4972,4973,4976],{},"Add a capacity of 20 to each Bertrand firm and explain why ",[2227,4974,4975],{},"p=c"," may fail.",[1812,4978,4979],{},"Compare consumer surplus in monopoly, Cournot, and Stackelberg for the worked market.",[1812,4981,4982],{},"Write the one-period deviation condition for cartel cooperation.",[1812,4984,4985],{},"Map one AI service from chips to end users and identify two possible bottlenecks and two efficiencies.",[1793,4987,4989],{"id":4988},"quick-check","Quick check",[1809,4991,4992,4995,4998,5001,5004],{},[1812,4993,4994],{},"Oligopoly predictions depend on the strategic variable and timing.",[1812,4996,4997],{},"Bertrand's result is powerful because its assumptions are transparent.",[1812,4999,5000],{},"Commitment can change equilibrium even when demand and cost do not.",[1812,5002,5003],{},"Collusion requires an incentive-compatible punishment path.",[1812,5005,5006],{},"Algorithmic adoption evidence is market-specific, not a universal verdict.",[1798,5008,5009,5013,5014,2569],{},[5010,5011,5012],"strong",{},"Next:"," ",[2259,5015,5017],{"href":5016},"..\u002F07-information-economics\u002F","analyse hidden types, hidden actions, signals, and contracts",{"title":10,"searchDepth":5019,"depth":5019,"links":5020},2,[5021,5022,5023,5024,5028,5029,5030,5031,5032,5033,5034,5035,5036],{"id":1795,"depth":5019,"text":1796},{"id":1803,"depth":5019,"text":1804},{"id":1829,"depth":5019,"text":1830},{"id":2233,"depth":5019,"text":2234,"children":5025},[5026],{"id":3724,"depth":5027,"text":3725},3,{"id":4017,"depth":5019,"text":4018},{"id":4211,"depth":5019,"text":4212},{"id":4785,"depth":5019,"text":4786},{"id":4812,"depth":5019,"text":4813},{"id":4843,"depth":5019,"text":4844},{"id":4863,"depth":5019,"text":4864},{"id":4878,"depth":5019,"text":4879},{"id":4957,"depth":5019,"text":4958},{"id":4988,"depth":5019,"text":4989},"Cournot, Bertrand, Stackelberg, collusion, entry, platform competition, pricing algorithms, welfare, and competition policy.","md",null,{},true,{"title":757,"description":5037},"h9A7kjS8wIbhyjGcpU0WGXD9Poa4Bxh_9OmUcv4GCEM",[5045,5047],{"title":751,"path":752,"stem":753,"description":5046,"children":-1},"Best responses, Nash equilibrium, mixed strategies, backward induction, credibility, repeated interaction, and Bayesian games.",{"title":763,"path":764,"stem":765,"description":5048,"children":-1},"Adverse selection, signalling, screening, moral hazard, incentive compatibility, and machine-learning credit evidence.",1785754732696]