Game Theory: Analysis of Conflict

Eminently suited to classroom use as well as individual study, Roger Myerson's introductory text provides a clear and thorough examination of the models, solution concepts, results, and methodological principles of noncooperative and cooperative game theory. Myerson introduces, clarifies, and synthesizes the extraordinary advances made in the subject over the past fifteen years, presents an overview of decision theory, and comprehensively reviews the development of the fundamental models: games in extensive form and strategic form, and Bayesian games with incomplete information.

Game Theory will be useful for students at the graduate level in economics, political science, operations research, and applied mathematics. Everyone who uses game theory in research will find this book essential.

This introductory text provides an examination of the models, solution concepts, results, and methodological principles of nonco-operative and co-operative game theory. It introduces, clarifies, and synthesizes advances in the field and presents an overview of decision theory.

Eminently suited to classroom use as well as individual study, Roger Myerson's introductory text provides a clear and thorough examination of the models, solution concepts, results, and methodological principles of noncooperative and cooperative game theory. Myerson introduces, clarifies, and synthesizes the extraordinary advances made in the subject over the past fifteen years, presents an overview of decision theory, and comprehensively reviews the development of the fundamental models: games in extensive form and strategic form, and Bayesian games with incomplete information.

Game Theory will be useful for students at the graduate level in economics, political science, operations research, and applied mathematics. Everyone who uses game theory in research will find this book essential.

Includes bibliographical references (p. [539]-551) and index.

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

3.3 Computing Nash Equilibria

3.4 Significance of Nash Equilibria

3.5 The Focal-Point Effect

3.6 The Decision-Analytic Approach to Games

3.7 Evolution. Resistance. and Risk Dominance

3.8 Two-Person Zero-Sum Games

3.9 Bayesian 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

4.1 Mixed Strategies and Behavioral Strategies

4.2 Equilibria in Behavioral Strategies

4.3 Sequential Rationality at Information States with Positive Probability

4.4 Consistent Beliefs and Sequential Rationality at All Information States

4.5 Computing Sequential Equilibria

4.6 Subgame-Perfect Equilibria

4.7 Games with Perfect Information

4.8 Adding Chance Events with Small Probability

4.9 Forward Induction

4.10 Voting and Binary Agendas

4.11 Technical Proofs

Exercises

5. Refinements of Equilibrium in Strategic Form

5.1 Introduction

5.2 Perfect Equilibria

5.3 Existence of Perfect and Sequential Equilibria

5.4 Proper Equilibria

5.5 Persistent Equilibria

5.6 Stable Sets 01 Equilibria

5.7 Generic Properties

5.8 Conclusions

Exercises

6. Games with Communication

6.1 Contracts and Correlated Strategies

6.2 Correlated Equilibria

6.3 Bayesian Games with Communication

6.4 Bayesian Collective-Choice Problems and Bayesian Bargaining Problems

6.5 Trading Problems with Linear Utility

6.6 General Participation Constraints for Bayesian Games with Contracts

6.7 Sender-Receiver Games

6.8 Acceptable and Predominant Correlated Equilibria

6.9 Communication in Extensive-Form and Multistage Games

Exercises

Bibliographic Note

7. Repeated Games

7.1 The Repeated Prisoners Dilemma

7.2 A General Model of Repeated Garnet

7.3 Stationary Equilibria of Repeated Games with Complete State Information and Discounting

7.4 Repeated Games with Standard Information: Examples

7.5 General Feasibility Theorems for Standard Repeated Games

7.6 Finitely Repeated Games and the Role of Initial Doubt

7.7 Imperfect Observability of Moves

7.8 Repeated Wines in Large Decentralized Groups

7.9 Repeated Games with Incomplete Information

7.10 Continuous Time

7.11 Evolutionary Simulation of Repeated Games

Exercises

8. Bargaining and Cooperation in Two-Person Games

8.1 Noncooperative Foundations of Cooperative Game Theory

8.2 Two-Person Bargaining Problems and the Nash Bargaining Solution

8.3 Interpersonal Comparisons of Weighted Utility

8.4 Transferable Utility

8.5 Rational Threats

8.6 Other Bargaining Solutions

8.7 An Alternating-Offer Bargaining Game

8.8 An Alternating-Offer Game with Incomplete Information

8.9 A Discrete Alternating-Offer Game

8.10 Renegotiation

Exercises

9. Coalitions in Cooperative Games

9.1 Introduction to Coalitional Analysis

9.2 Characteristic Functions with Transferable Utility

9.3 The Core

9.4 The Shapkey Value

9.5 Values with Cooperation Structures

9.6 Other Solution Concepts

9.7 Colational Games with Nontransferable Utility

9.8 Cores without Transferable Utility

9.9 Values 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