Game Theory

Roger B. Myerson is Harold L. Stuart Professor of Decision Sciences at the J. L. Kellogg Graduate School of Management, Northwestern University. He is a Fellow of the Econometric Society.

• Preface 1. Decision-Theoretic Foundations 1.1 Game Theory, Rationality, and Intelligence 1.2 Basic Concepts of Decision Theory 1.3 Axioms 1.4 The Expected-Utility Maximization Theorem 1.5 Equivalent Representations 1.6 Bayesian Conditional-Probability Systems 1.7 Limitations of the Bayesian Model 1.8 Domination 1.9 Proofs of the Domination Theorems Exercises 2. Basic Models 2.1 Games in Extensive Form 2.2 Strategic Form and the Normal Representation 2.3 Equivalence of Strategic-Form Games 2.4 Reduced Normal Representations 2.5 Elimination of Dominated Strategies 2.6 Multiagent Representations 2.7 Common Knowledge 2.8 Bayesian Games 2.9 Modeling Games with Incomplete Information Exercises 3. Equilibria of Strategic-Form Games 3.1 Domination and Ratonalizability 3.2 Nash Equilibrium 3.3Computing Nash Equilibria 3.4Significance of Nash Equilibria 3.5The Focal-Point Effect 3.6The Decision-Analytic Approach to Games 3.7Evolution. Resistance. and Risk Dominance 3.8Two-Person Zero-Sum Games 3.9Bayesian Equilibria 3.10 Purification of Randomized Strategies in Equilibria 3.11 Auctions 3.12 Proof of Existence of Equilibrium 3.13 Infinite Strategy Sets Exercises 4. Sequential Equilibria of Extensive-Form Games 4.1Mixed Strategies and Behavioral Strategies 4.2Equilibria in Behavioral Strategies 4.3Sequential Rationality at Information States with Positive Probability 4.4Consistent Beliefs and Sequential Rationality at All Information States 4.5Computing Sequential Equilibria 4.6Subgame-Perfect Equilibria 4.7 Games with Perfect Information 4.8Adding Chance Events with Small Probability 4.9Forward Induction 4.10 Voting and Binary Agendas 4.11 Technical Proofs Exercises 5. Refinements of Equilibrium in Strategic Form 5.1Introduction 5.2Perfect Equilibria 5.3Existence of Perfect and Sequential Equilibria 5.4Proper Equilibria 5.5Persistent Equilibria 5.6Stable Sets 01 Equilibria 5.7Generic Properties 5.8Conclusions Exercises 6. Games with Communication 6.1Contracts and Correlated Strategies 6.2 Correlated Equilibria 6.3 Bayesian Games with Communication 6.4Bayesian Collective-Choice Problems and Bayesian Bargaining Problems 6.5Trading Problems with Linear Utility 6.6General Participation Constraints for Bayesian Games with Contracts 6.7Sender-Receiver Games 6.8Acceptable and Predominant Correlated Equilibria 6.9Communication in Extensive-Form and Multistage Games Exercises Bibliographic Note 7. Repeated Games 7.1The Repeated Prisoners Dilemma 7.2A General Model of Repeated Garnet 7.3Stationary Equilibria of Repeated Games with Complete State Information and Discounting 7.4Repeated Games with Standard Information: Examples 7.5General Feasibility Theorems for Standard Repeated Games 7.6Finitely Repeated Games and the Role of Initial Doubt 7.7Imperfect Observability of Moves 7.8Repeated Wines in Large Decentralized Groups 7.9Repeated Games with Incomplete Information 7.10 Continuous Time 7.11 Evolutionary Simulation of Repeated Games Exercises 8. Bargaining and Cooperation in Two-Person Games 8.1Noncooperative Foundations of Cooperative Game Theory 8.2Two-Person Bargaining Problems and the Nash Bargaining Solution 8.3Interpersonal Comparisons of Weighted Utility 8.4Transferable Utility 8.5Rational Threats 8.6Other Bargaining Solutions 8.7An Alternating-Offer Bargaining Game 8.8An Alternating-Offer Game with Incomplete Information 8.9A Discrete Alternating-Offer Game 8.10 Renegotiation Exercises 9. Coalitions in Cooperative Games 9.1Introduction to Coalitional Analysis 9.2Characteristic Functions with Transferable Utility 9.3The Core 9.4The Shapkey Value 9.5Values with Cooperation Structures 9.6Other Solution Concepts 9.7Colational Games with Nontransferable Utility 9.8Cores without Transferable Utility 9.9Values without Transferable Utility Exercises Bibliographic Note 10. Cooperation under Uncertainty 10.1 Introduction 10.2 Concepts of Efficiency 10.3 An Example 10.4 Ex Post Inefficiency and Subsequent Oilers 10.5 Computing Incentive-Efficient Mechanisms 10.6 Inscrutability and Durability 10.7 Mechanism Selection by an Informed Principal 10.8 Neutral Bargaining Solutions 10.9 Dynamic Matching Processes with Incomplete Information Exercises Bibliography Index

In a clear, Myersonian writing style, this book systematically describes our state-of-the-art knowledge of game theory. Written as an introductory text, it looks at the subject from the viewpoint of a newcomer to the field, beginning with utility theory and arriving at the most sophisticated ideas discussed today. Myerson not only gives complete mathematical statements and proofs, but also supplies the intuitive arguments that motivate them...Because of its comprehensiveness, researchers and users of game theory can find descriptions of almost all special game theoretic topics and issues presented in "user friendly" style...It is very likely that Myerson's Game Theory will remain the main introductory text for many years to come.