Preface xi
1Introduction 1
1.3
Game Theory and the Theory of Competitive Equilibrium 3
1.4
Rational Behavior 4
1.5
The Steady State and Deductive Interpretations 5
1.6
Bounded Rationality 6
1.7
Terminology and Notation 6
Notes 8
IStrategic Games 9
2Nash Equilibrium 11
2.1
Strategic Games 11
2.2
Nash Equilibrium 14
2.3
Examples 15
2.4
Existence of a Nash Equilibrium 19
2.5
Strictly Competitive Games 21
2.6
Bayesian Games: Strategic Games with Imperfect Information 24
Notes 29
3Mixed, Correlated, and Evolutionary Equilibrium 31
3.1
Mixed Strategy Nash Equilibrium 31
3.2
Interpretations of Mixed Strategy Nash Equilibrium 37
3.3
Correlated Equilibrium 44
3.4
Evolutionary Equilibrium 48
Notes 51
4Rationalizability and Iterated Elimination of Dominated Actions 53
4.1
Rationalizability 53
4.2
Iterated Elimination of Strictly Dominated Actions 58
4.3
Iterated Elimination of Weakly Dominated Actions 62
Notes 64
5Knowledge and Equilibrium 67
5.1
A Model of Knowledge 67
5.2
Common Knowledge 73
5.3
Can People Agree to Disagree? 75
5.4
Knowledge and Solution Concepts 76
5.5
The Electronic Mail Game 81
Notes 84
IIExtensive Games with Perfect Information 9
6Extensive Games with Perfect Information 89
6.1
Extensive Games with Perfect Information 89
6.2
Subgame Perfect Equilibrium 97
6.3
Two Extensions of the Definition of a Game 101
6.4
The Interpretation of a Strategy 103
6.5
Two Notable Finite Horizon Games 105
6.6
Iterated Elimination of Weakly Dominated Strategies 108
Notes 114
7Bargaining Games 117
7.1
Bargaining and Game Theory 117
7.2
A Bargaining Game of Alternating Offers 118
7.3
Subgame Perfect Equilibrium 121
7.4Variations and Extensions 127
Notes 131
8Repeated Games 133
8.1
The Basic Idea 133
8.2
Infinitely Repeated Games vs. Finitely Repeated Games 134
8.3
Infinitely Repeated Games: Definitions 136
8.4
Strategies as Machines 140
8.5
Trigger Strategies: Nash Folk Theorems 143
8.6
Punishing for a Limited Length of Time: A Perfect Folk Theorem for the Limit of Means Criterion 146
8.7
Punishing the Punisher: A Perfect Folk Theorem for the Overtaking Criterion 149
8.2
Rewarding Players Who Punish: A Perfect Folk Theorem for the Discounting Criterion 150
8.9
The Structure of Subgame Perfect Equilibria Under the Discounting Criterion 153
8.10
Finitely Repeated Games 155
Notes 160
9Complexity Considerations in Repeated Games 163
9.1
Introduction 163
9.2
Complexity and the Machine Game 164
9.3
The Structure of the Equilibria of a Machine Game 168
9.4
The Case of Lexicographic Preferences 172
Notes 175
10Implementation Theory 177
10.1
Introduction 177
10.2
The Implementation Problem 178
10.3
Implementation in Dominant Strategies 180
10.4
Nash Implementation 185
10.5
Subgame Perfect Equilibrium Implementation 191
Notes 195
IIIExtensive Games with Imperfect Information 9
11Extensive Games with Imperfect Information 199
11.2
Principles for the Equivalence of Extensive Games 204
11.3
Framing Effects and the Equivalence of Extensive Games 209
11.4
Mixed and Behavioral Strategies 212
11.5
Nash Equilibrium 216
Notes 217
12Sequential Equilibrium 219
12.1
Strategies and Beliefs 219
12.2
Sequential Equilibrium 222
12.3
Games with Observable Actions: Perfect Bayesian Equilibrium 231
12.4
Refinements of Sequential Equilibrium 243
12.5
Trembling Hand Perfect Equilibrium 246
Notes 254
IVCoalitional Games 9
13The Core 257
13.1
Coalitional Games with Transferable Payoff 257
13.2
The Core 258
13.3
Nonemptiness of the Core 262
13.4
Markets with Transferable Payoff 263
13.5
Coalitional Games without Transferable Payoff 268
13.6
Exchange Economies 269
Notes 274
14Stable Sets, the Bargaining Set, and the Shapley Value 277
14.1
Two Approaches 277
14.1
The Stable Sets of von Neumann and Morgenstern 278
14.1
The Bargaining Set, Kernel, and Nucleolus 281
14.1
The Shapley Value 289
Notes 297
15The Nash Solution 299
15.1
Bargaining Problems 299
15.3
The Nash Solution: Definition and Characterization 301
15.3
An Axiomatic Definition 305
15.4
The Nash Solution and the Bargaining Game of Alternating Offers 310
15.5
An Exact Implementation of the Nash Solution 311
Notes 312
List of Results 313
References 321
Index 341