An introduction to game theory  by Martin J. Osborne
Table of contents

1Introduction   1
1.1What is game theory?   1
1.2The theory of rational choice   4
1.3Coming attractions: interacting decision-makers   7
Notes   9
Part I:Games with Perfect Information   11
2Nash Equilibrium: Theory   13
2.1Strategic games   13
2.2Example: the Prisoner's Dilemma   14
2.3Example: Bach or Stravinsky?   18
2.4Example: Matching Pennies   19
2.5Example: the Stag Hunt   20
2.6Nash equilibrium   21
2.7Examples of Nash equilibrium   26
2.8Best response functions   35
2.9Dominated actions   45
2.10Equilibrium in a single population: symmetric games and symmetric equilibria   50
Notes   53
3Nash Equilibrium: Illustrations   55
3.1Cournot's model of oligopoly   55
3.2Bertrand's model of oligopoly   63
3.3Electoral competition   70
3.4The War of Attrition   77
3.5Auctions   80
3.6Accident law   91
Notes   97
4Mixed Strategy Equilibrium   99
4.1Introduction   99
4.2Strategic games in which players may randomize   106
4.3Mixed strategy Nash equilibrium   107
4.4Dominated actions   120
4.5Pure equilibria when randomization is allowed   122
4.6Illustration: expert diagnosis   123
4.7Equilibrium in a single population   128
4.8Illustration: reporting a crime   131
4.9The formation of players' beliefs   134
4.10Extension: finding all mixed strategy Nash equilibria   137
4.11Extension: games in which each player has a continuum of actions   142
4.12Appendix: representing preferences by expected payoffs   146
Notes   150
5Extensive Games with Perfect Information: Theory   153
5.1Extensive games with perfect information   153
5.2Strategies and outcomes   159
5.3Nash equilibrium   161
5.4Subgame perfect equilibrium   164
5.5Finding subgame perfect equilibria of finite horizon games: backward induction   169
Notes   179
6Extensive Games with Perfect Information: Illustrations   181
6.1The ultimatum game, the holdup game, and agenda control   181
6.2Stackelberg's model of duopoly   187
6.3Buying votes   192
6.4A race   197
Notes   203
7Extensive Games with Perfect Information: Extensions and Discussion   205
7.1Allowing for simultaneous moves   205
7.2Illustration: entry into a monopolized industry   213
7.3Illustration: electoral competition with strategic voters   215
7.4Illustration: committee decision-making   217
7.5Illustration: exit from a declining industry   221
7.6Allowing for exogenous uncertainty   225
7.7Discussion: subgame perfect equilibrium and backward induction   231
Notes   236
8Coalitional Games and the Core   239
8.1Coalitional games   239
8.2The core   243
8.3Illustration: ownership and the distribution of wealth   247
8.4Illustration: exchanging homogeneous horses   251
8.5Illustration: exchanging heterogeneous houses   256
8.6Illustration: voting   260
8.7Illustration: matching   263
8.8Discussion: other solution concepts   269
Notes   270
Part II:Games with Imperfect Information   271
9Bayesian Games   273
9.1Motivational examples   273
9.2General definitions   278
9.3Two examples concerning information   282
9.4Illustration: Cournot's duopoly game with imperfect information   285
9.5Illustration: providing a public good   289
9.6Illustration: auctions   291
9.7Illustration: juries   301
9.8Appendix: auctions with an arbitrary distribution of valuations   307
Notes   311
10Extensive Games with Imperfect Information   313
10.1Extensive games with imperfect information   313
10.2Strategies   317
10.3Nash equilibrium   318
10.4Beliefs and sequential equilibrium   323
10.5Signaling games   331
10.6Illustration: conspicuous expenditure as a signal of quality   336
10.7Illustration: education as a signal of ability   340
10.8Illustration: strategic information transmission   343
10.9Illustration: agenda control with imperfect information   351
Notes   357
Part III:Variants and Extensions   359
11Strictly Competitive Games and Maxminimization   361
11.1Maxminimization   361
11.2Maxminimization and Nash equilibrium   364
11.3Strictly competitive games   365
11.4Maxminimization and Nash equilibrium in strictly competitive games   367
Notes   375
12Rationalizability   377
12.1Rationalizability   377
12.2Iterated elimination of strictly dominated actions   385
12.3Iterated elimination of weakly dominated actions   388
12.4Dominance solvability   391
Notes   392
13Evolutionary Equilibrium   393
13.1Monomorphic pure strategy equilibrium   394
13.2Mixed strategies and polymorphic equilibrium   400
13.3Asymmetric contests   406
13.4Variation on a theme: sibling behavior   411
13.5Variation on a theme: the nesting behavior of wasps   414
13.6Variation on a theme: the evolution of the sex ratio   416
Notes   417
14Repeated Games: The Prisoner's Dilemma   419
14.1The main idea   419
14.2Preferences   421
14.3Repeated games   423
14.4Finitely repeated Prisoner's Dilemma   424
14.5Infinitely repeated Prisoner's Dilemma   426
14.6Strategies in an infinitely repeated Prisoner's Dilemma   426
14.7Some Nash equilibria of an infinitely repeated Prisoner's Dilemma   428
14.8Nash equilibrium payoffs of an infinitely repeated Prisoner's Dilemma   431
14.9Subgame perfect equilibria and the one-deviation property   437
14.10Some subgame perfect equilibria of an infinitely repeated Prisoner's Dilemma   441
14.11Subgame perfect equilibrium payoffs of an infinitely repeated Prisoner's Dilemma   446
14.12Concluding remarks   449
Notes   449
15Repeated Games: General Results   451
15.1Nash equilibria of general infinitely repeated games   451
15.2Subgame perfect equilibria of general infinitely repeated games   455
15.3Finitely repeated games   460
15.4Variation on a theme: imperfect observability   461
Notes   463
16Bargaining   465
16.1Bargaining as an extensive game   465
16.2Illustration: trade in a market   477
16.3Nash's axiomatic model   481
16.4Relation between strategic and axiomatic models   489
Notes   491
17Appendix: Mathematics   493
17.1Numbers   493
17.2Sets   494
17.3Functions   495
17.4Profiles   498
17.5Sequences   499
17.6Probability   499
17.7Proofs   505
References   507
Index   525