1 | 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 |
Part I: | Games with Perfect Information 11 |
2 | Nash 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 |
3 | Nash 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 |
4 | Mixed 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 |
5 | Extensive 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 |
6 | Extensive 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 |
7 | Extensive 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 |
8 | Coalitional 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 |
Part II: | Games with Imperfect Information 271 |
9 | Bayesian 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 |
10 | Extensive 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 |
Part III: | Variants and Extensions 359 |
11 | Strictly 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 |
12 | Rationalizability 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 |
13 | Evolutionary 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 |
14 | Repeated 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 |
15 | Repeated 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 |
16 | Bargaining 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 |
17 | Appendix: 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 |