Introduction 1
1.1
What is game theory? 1
1.2
The theory of rational choice 4
1.3
Coming attractions: interacting decision-makers 7
Notes 9
IGames with Perfect Information 11
2Nash Equilibrium: Theory 13
2.1
Strategic games 13
2.2
Example: the Prisoner's Dilemma 14
2.3
Example: Bach or Stravinsky? 18
2.4
Example: Matching Pennies 19
2.5
Example: the Stag Hunt 20
2.6
Nash equilibrium 21
2.7
Examples of Nash equilibrium 26
2.8
Best response functions 35
2.9
Dominated actions 45
2.10
Equilibrium in a single population: symmetric games and symmetric equilibria 50
Notes 53
3Nash Equilibrium: Illustrations 55
3.1
Cournot's model of oligopoly 55
3.2
Bertrand's model of oligopoly 63
3.3
Electoral competition 70
3.4
The War of Attrition 77
3.5
Auctions 80
3.6
Accident law 91
Notes 97
4Mixed Strategy Equilibrium 99
4.1
Introduction 99
4.2
Strategic games in which players may randomize 106
4.3
Mixed strategy Nash equilibrium 107
4.4
Dominated actions 120
4.5
Pure equilibria when randomization is allowed 122
4.6
Illustration: expert diagnosis 123
4.7
Equilibrium in a single population 128
4.8
Illustration: reporting a crime 131
4.9
The formation of players' beliefs 134
4.10
Extension: finding all mixed strategy Nash equilibria 137
4.11
Extension: games in which each player has a continuum of actions 142
4.12
Appendix: representing preferences by expected payoffs 146
Notes 150
5Extensive Games with Perfect Information: Theory 153
5.1
Extensive games with perfect information 153
5.2
Strategies and outcomes 159
5.3
Nash equilibrium 161
5.4
Subgame perfect equilibrium 164
5.5
Finding subgame perfect equilibria of finite horizon games: backward induction 169
Notes 179
6Extensive Games with Perfect Information: Illustrations 181
6.1
The ultimatum game, the holdup game, and agenda control 181
6.2
Stackelberg's model of duopoly 187
6.3
Buying votes 192
6.4
A race 197
Notes 203
7Extensive Games with Perfect Information: Extensions and Discussion 205
7.1
Allowing for simultaneous moves 205
7.2
Illustration: entry into a monopolized industry 213
7.3
Illustration: electoral competition with strategic voters 215
7.4
Illustration: committee decision-making 217
7.5
Illustration: exit from a declining industry 221
7.6
Allowing for exogenous uncertainty 225
7.7
Discussion: subgame perfect equilibrium and backward induction 231
Notes 236
8Coalitional Games and the Core 239
8.1
Coalitional games 239
8.2
The core 243
8.3
Illustration: ownership and the distribution of wealth 247
8.4
Illustration: exchanging homogeneous horses 251
8.5
Illustration: exchanging heterogeneous houses 256
8.6
Illustration: voting 260
8.7
Illustration: matching 263
8.8
Discussion: other solution concepts 269
Notes 270
IIGames with Imperfect Information 271
9Bayesian Games 273
9.1
Motivational examples 273
9.2
General definitions 278
9.3
Two examples concerning information 282
9.4
Illustration: Cournot's duopoly game with imperfect information 285
9.5
Illustration: providing a public good 289
9.6
Illustration: auctions 291
9.7
Illustration: juries 301
9.8
Appendix: auctions with an arbitrary distribution of valuations 307
Notes 311
10Extensive Games with Imperfect Information 313
10.1
Extensive games with imperfect information 313
10.2
Strategies 317
10.3
Nash equilibrium 318
10.4
Beliefs and sequential equilibrium 323
10.5
Signaling games 331
10.6
Illustration: conspicuous expenditure as a signal of quality 336
10.7
Illustration: education as a signal of ability 340
10.8
Illustration: strategic information transmission 343
10.9
Illustration: agenda control with imperfect information 351
Notes 357
IIIVariants and Extensions 271
11Strictly Competitive Games and Maxminimization 361
11.1
Maxminimization 361
11.2
Maxminimization and Nash equilibrium 364
11.3
Strictly competitive games 365
11.4
Maxminimization and Nash equilibrium in strictly competitive games 367
Notes 375
12Rationalizability 377
12.1
Rationalizability 377
12.2
Iterated elimination of strictly dominated actions 385
12.3
Iterated elimination of weakly dominated actions 388
12.4
Dominance solvability 391
Notes 392
13Evolutionary Equilibrium 393
13.1
Monomorphic pure strategy equilibrium 394
13.2
Mixed strategies and polymorphic equilibrium 400
13.3
Asymmetric contests 406
13.4
Variation on a theme: sibling behavior 411
13.5
Variation on a theme: the nesting behavior of wasps 414
13.6
Variation on a theme: the evolution of the sex ratio 416
Notes 417
14Repeated Games: The Prisoner's Dilemma 419
14.1
The main idea 419
14.2
Preferences 421
14.3
Repeated games 423
14.4
Finitely repeated Prisoner's Dilemma 424
14.5
Infinitely repeated Prisoner's Dilemma 426
14.6
Strategies in an infinitely repeated Prisoner's Dilemma 426
14.7
Some Nash equilibria of an infinitely repeated Prisoner's Dilemma 428
14.8
Nash equilibrium payoffs of an infinitely repeated Prisoner's Dilemma 431
14.9
Subgame perfect equilibria and the one-deviation property 437
14.10
Some subgame perfect equilibria of an infinitely repeated Prisoner's Dilemma 441
14.11
Subgame perfect equilibrium payoffs of an infinitely repeated Prisoner's Dilemma 446
14.12
Concluding remarks 449
Notes 449
15Repeated Games: General Results 451
15.1
Nash equilibria of general infinitely repeated games 451
15.2
Subgame perfect equilibria of general infinitely repeated games 455
15.3
Finitely repeated games 460
15.4
Variation on a theme: imperfect observability 461
Notes 463
16Bargaining 465
16.1
Bargaining as an extensive game 465
16.2
Illustration: trade in a market 477
16.3
Nash's axiomatic model 481
16.4
Relation between strategic and axiomatic models 489
Notes 491
17Appendix: Mathematics 493
17.1
Numbers 493
17.2
Sets 494
17.3
Functions 495
17.4
Profiles 498
17.5
Sequences 499
17.6
Probability 499
17.7
Proofs 505
References 507
Index 525