A Course in Game Theory

A Course in Game Theory presents the main ideas of game theory at a level suitable for graduate students and advanced undergraduates, emphasizing the theory's foundations and interpretations of its basic concepts. The authors provide precise definitions and full proofs of results, sacrificing generalities and limiting the scope of the material in order to do so. The text is organized in four parts: strategic games, extensive games with perfect information, extensive games with imperfect information, and coalitional games. It includes over 100 exercises.

Martin J. Osborne is Professor of Economics at the University of Toronto.

Ariel Rubinstein is Professor of Economics at Tel Aviv University and New York University.

Preface

xi

Introduction

1

(8)

Game Theory

1

(1)

Games and Solutions

2

(1)

Game Theory and the Theory of Competitive Equilibrium

3

(1)

Rational Behavior

4

(1)

The Steady State and Deductive Interpretations

5

(1)

Bounded Rationality

6

(1)

Terminology and Notation

6

(3)

Notes

8

(1)

I Strategic Games

9

(78)

Nash Equilibrium

11

(20)

Strategic Games

11

(3)

Nash Equilibrium

14

(1)

Examples

15

(4)

Existence of a Nash Equilibrium

19

(2)

Strictly Competitive Games

21

(3)

Bayesian Games: Strategic Games with Imperfect Information

24

(7)

Notes

29

(2)

Mixed, Correlated, and Evolutionary Equilibrium

31

(22)

Mixed Strategy Nash Equilibrium

31

(6)

Interpretations of Mixed Strategy Nash Equilibrium

37

(7)

Correlated Equilibrium

44

(4)

Evolutionary Equilibrium

48

(5)

Notes

51

(2)

Rationalizability and Iterated Elimination of Dominated Actions

53

(14)

Rationalizability

53

(5)

Iterated Elimination of Strictly Dominated Actions

58

(4)

Iterated Elimination of Weakly Dominated Actions

62

(5)

Notes

64

(3)

Knowledge and Equilibrium

67

(20)

A Model of Knowledge

67

(6)

Common Knowledge

73

(2)

Can People Agree to Disagree?

75

(1)

Knowledge and Solution Concepts

76

(5)

The Electronic Mail Game

81

(6)

Notes

84

(3)

II Extensive Games with Perfect Information

87

(110)

Extensive Games with Perfect Information

89

(28)

Extensive Games with Perfect Information

89

(8)

Subgame Perfect Equilibrium

97

(4)

Two Extensions of the Definition of a Game

101

(2)

The Interpreation of a Strategy

103

(2)

Two Notable Finite Horizon Games

105

(3)

Iterated Elimination of Weakly Dominated Strategies

108

(9)

Notes

114

(3)

Bargaining Games

117

(16)

Bargaining and Game Theory

117

(1)

A Bargaining Game of Alternating Offers

118

(3)

Subgame Perfect Equilibrium

121

(6)

Variations and Extensions

127

(6)

Notes

131

(2)

Repeated Games

133

(30)

The Basic Idea

133

(1)

Infinitely Repeated Games vs. Finitely Repeated Games

134

(2)

Infinitely Repeated Games: Definitions

136

(4)

Strategies as Machines

140

(3)

Trigger Strategies: Nash Folk Theorems

143

(3)

Punishing for a Limited Length of Time: A Perfect Folk Theorem for the Limit of Means Criterion

146

(3)

Punishing the Punisher: A Perfect Folk Theorem for the Overtaking Criterion

149

(1)

Rewarding Players Who Punish: A Perfect Folk Theorem for the Discounting Criterion

150

(3)

The Structure of Subgame Perfect Equilibria Under the Discounting Criterion

153

(2)

Finitely Repeated Games

155

(8)

Notes

160

(3)

Complexity Considerations in Repeated Games

163

(14)

Introduction

163

(1)

Complexity and the Machine Game

164

(4)

The Structure of the Equilibria of a Machine Game

168

(4)

The Case of Lexicographic Preferences

172

(5)

Notes

175

(2)

Implementation Theory

177

(20)

Introduction

177

(1)

The Implementation Problem

178

(2)

Implementation in Dominant Strategies

180

(5)

Nash Implementation

185

(6)

Subgame Perfect Equilibrium Implementation

191

(6)

Notes

195

(2)

III Extensive Games with Imperfect Information

197

(58)

Extensive Games with Imperfect Information

199

(20)

Extensive Games with Imperfect Information

199

(5)

Principles for the Equivalence of Extensive Games

204

(5)

Framing Effects and the Equivalence of Extensive Games

209

(3)

Mixed and Behavioral Strategies

212

(4)

Nash Equilibrium

216

(3)

Notes

217

(2)

Sequential Equilibrium

219

(36)

Strategies and Beliefs

219

(3)

Sequential Equilibrium

222

(9)

Games with Observable Actions: Perfect Bayesian Equilibrium

231

(12)

Refinements of Sequential Equilibrium

243

(3)

Trembling Hand Perfect Equilibrium

246

(9)

Notes

254

(1)

IV Coalitional Games

255

(58)

The Core

257

(20)

Coalitional Games with Transferable Payoff

257

(1)

The Core

258

(4)

Nonemptiness of the Core

262

(1)

Markets with Transferable Payoff

263

(5)

Coalitional Games without Transferable Payoff

268

(1)

Exchange Economies

269

(8)

Notes

274

(3)

Stable Sets, the Bargaining Set, and the Shapley Value

277

(22)

Two Approaches

277

(1)

The Stable Sets of von Neumann and Morgenstern

278

(3)

The Bargaining Set, Kernel, and Nucleolus

281

(8)

The Shapley Value

289

(10)

Notes

297

(2)

The Nash Solution

299

(14)

Bargaining Problems

299

(2)

The Nash Solution: Definition and Characterization

301

(4)

An Axiomatic Definition

305

(5)

The Nash Solution and the Bargaining Game of Alternating Offers

310

(1)

An Exact Implementation of the Nash Solution

311

(2)

Notes

312

(1)

List of Results

313

(8)

References

321

(20)

Index

341

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A Course in Game Theory

Summary

Author Biography

Table of Contents

Supplemental Materials