GAME THEORY. Analysis of Conflict ROGER B. MYERSON. HARVARD UNIVERSITY PRESS Cambridge, Massachusetts London, England

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1 GAME THEORY Analysis of Conflict ROGER B. MYERSON HARVARD UNIVERSITY PRESS Cambridge, Massachusetts London, England

2 Contents Preface 1 Decision-Theoretic Foundations 1.1 Game Theory, Rationality, and Intelligence Basic Concepts of Decision Theory Axioms The Expected-Utility Maximization Theorem 1.5 Equivalent Representations Bayesian Conditional-Probability Systems Limitations of the Bayesian Model Domination Proofs of the Domination Theorems 31 Exercises 33 2 Basic Models 2.1 Games in Extensive Form Strategie Form and the Normal Representation 2.3 Equivalence of Strategie-Form Games Reduced Normal Representations Elimination of Dominated Strategies Multiagent Representations Common Knowledge Bayesian Games Modeling Games with Incomplete Information Exercises 83 3 Equilibria of Strategie-Form Games 3.1 Domination and Rationalizability Nash Equilibrium 91

3 viii Contents 3.3 Computing Nash Equilibria Significance of Nash Equilibria The Focal-Point Effect The Decision-Analytic Approach to Games Evolution, Resistance, and Risk Dominance Two-Person Zero-Sum Games Bayesian Equilibria Purification of Randomized Strategies in Equilibria Auctions Proof of Existence of Equilibrium Infinite Strategy Sets 140 Exercises Sequential Equilibria of Extensive-Form Games Mixed Strategies and Behavioral Strategies Equilibria in Behavioral Strategies Sequential Rationality at Information States with Positive Probability Consistent Beliefs and Sequential Rationality at All Information States Computing Sequential Equilibria Subgame-Perfect Equilibria Games with Perfect Information Adding Chance Events with Small Probability Forward Induction Voting and Binary Agendas Technical Proofs 202 Exercises Refinements of Equilibrium in Strategie Form Introduction Perfect Equilibria Existence of Perfect and Sequential Equilibria Proper Equilibria Persistent Equilibria Stable Sets of Equilibria Generic Properties Conclusions 240 Exercises Games with Communication Contracts and Correlated Strategies Correlated Equilibria Bayesian Games with Communication Bayesian Coilective-Choice Problems and Bayesian Bargaining Problems 263

4 Contents ix Trading Problems with Linear Utility 271 General Participation Constraints for Bayesian Games with Contracts 281 Sender-Receiver Games 283 Acceptable and Predominant Correlated Equilibria 288 Communication in Extensive-Form and Multistage Games 294 Exercises 299 Bibliographie Note Repeated Games The Repeated Prisoners'Dilemma A General Model of Repeated Games Stationary Equilibria of Repeated Games with Complete State Information and Discounting Repeated Games with Standard Information: Examples General Feasibility Theorems for Standard Repeated Games Finitely Repeated Games and the Role of Initial Doubt Imperfect Observability of Moves Repeated Games in Large Decentralized Groups Repeated Games with Incomplete Information Continuous Time Evolutionary Simulation of Repeated Games 364 Exercises Bargaining and Cooperation in Two-Person Games Noncooperative Foundations of Cooperative Game Theory Two-Person Bargaining Problems and the Nash Bargaining Solution Interpersonal Comparisons of Weighted Utility Transferable Utility Rational Threats Other Bargaining Solutions An Alternating-Offer Bargaining Game An Alternating-Offer Game with Incomplete Information A Discrete Alternating-Offer Game Renegotiation 408 Exercises Coalitions in Cooperative Games Introduction to Coalitional Analysis Characteristic Functions with Transferable Utility The Core The Shapley Value Values with Cooperation Structures Other Solution Concepts Coalitional Games with Nontransferable Utility 456

5 x Contents 9.8 Cores without Transferable Utility Values without Transferable Utility 468 Exercises 478 Bibliographie Note Cooperation under Uncertainty Introduction Concepts of Efficiency An Example Ex Post Inefficiency and Subsequent Offers Computing Incentive-Efficient Mechanisms Inscrutability and Durability Mechanism Selection by an Informed Principal Neutral Bargaining Solutions Dynamic Matching Processes with Incomplete Information 526 Exercises 534 Bibliography Index

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