Table of Contents
Preface v
1 Introduction 1
1 What is game theory? 1
2 Definition of a game 2
3 Games in extensive form 5
4 Utility and payoff 9
5 Games and their solutions 12
6 Problems 16
Non-Co operative Game Theory 19
2 Two Person Zero-Sum Games 21
1 Introduction 21
2 Strategy choices: Domination and maximin 22
3 Equilibria 26
4 Mixed strategies and mixed extensions of games 27
5 Proof of the main theorem 31
6 Problems 35
3 Applications of Minimax Theory 37
1 Introduction 37
2 Linear programming 38
3 Comparing 'information services 41
4 Approachability 44
5 Problems 48
4 Solutions for General Non-Cooperative Games 51
1 Introduction 51
2 Dominance and elimination of dominated strategies 53
3 Rationalizable strategies 58
4 Evolutionary stability 60
5 Correlated equilibria 63
6 Problems 66
5 More About Nash Equilibria 69
1 Existence of Nash equilibria 69
2 Economic applications of Nash equilibrium 71
3 Extensive form games with perfect information 75
4 Behavior strategies and perfect recall 76
5 Subgame perfectness in extensive form games 80
6 Problems 83
6 Games with Incomplete Information 85
1 Bayesian Nash equilibria 85
2 States, beliefs and information 89
3 Auctions 93
4 Mechanisms and the revelation principle 99
5 Sequential equilibria 102
6 Global games 105
7 Problems 109
7 Choosing Among Nash Equilibria 111
1 Introduction 111
2 Some Nash equilibria are better than others 112
3 Perfect and proper equilibria 113
4 Strategic stability 119
5 Cheap talk and signaling games 124
6 Problems 130
8 Repeated Games 133
1 Introduction: Repetition enhances cooperation 133
2 Nash equilibria in repeated games 137
3 Payoffs in subgame perfect Nash equilibria 140
4 Repeated games with limited rationality 144
5 Problems 152
9 Selected Topics in Non-Cooperative Games 153
1 Introduction 153
2 Games and logic 153
3 Ehrenfeucht-Fraïssé games 154
4 Combinatorial games 158
5 Differential games 164
6 Problems 171
Cooperative Game Theory 173
10 Introduction to Cooperative Games 175
1 Introduction 175
2 Cooperative solution concepts for normal form games 175
3 Characteristic function 180
4 Simple games 185
5 Problems 189
11 Bargaining 191
1 Introduction 191
2 Axiomatic bargaining theory 192
3 Bargaining solutions as result of a process 196
4 The Nash program: Bargaining as a non-cooperative game 198
5 Bargaining with incomplete information 202
6 Problems 204
12 TU Games: Classical Solutions 207
1 Introduction 207
2 The von Neumann-Morgenstern solution 209
3 The core 212
4 The Shapley value 220
5 Problems 226
13 TU Games: Other Solutions 229
1 The bargaining set and the kernel 229
2 The nucleolus 233
3 The reduced game property 236
4 The τ-value 239
5 Problems 243
14 Solutions of NTU Games: The Core 247
1 Introduction 247
2 The core, convex games 248
3 Balanced games 250
4 Extensions of Scarf's theorem 253
5 The partnered core 254
6 Axiomatic characterization of the core 257
7 Problems 261
15 Values of NTU Games 263
1 The Shapley NTU value 263
2 Axiomatic characterization of the Shapley NTU value 265
3 The Harsanyi NTU value 269
4 Axiomatic characterization of the Harsanyi NTU value 276
5 Problems 280
16 The Theory of Game Forms 283
1 Introduction 283
2 Game forms and effectivity functions 287
3 Solvability of game forms 290
4 Stable matching 294
5 Problems 297
Bibliography 299
Index 305
