AN INTRODUCTION TO GAME THEORY

Transcription

1 AN INTRODUCTION TO GAME THEORY 2008 AGI-Information Management Consultants May be used for personal purporses only or by libraries associated to dandelon.com network. MARTIN J. OSBORNE University of Toronto NEW YORK OXFORD OXFORD UNIVERSITY PRESS 2004

2 Contents Preface xi 1 Introduction What is game theory? 1 An outline of the history of game theory 2 John von Neumann The theory of rational choice Coming attractions: interacting decision-makers 7 Notes 9 1 Games with Perfect Information 11 2 Nash Equilibrium: Theory Strategic games Example: the Prisoner's Dilemma Example: Bach or Stravinsky? Example: Matching Pennies Example: the Stag Hunt Nash equilibrium 21 John F. Nash, Jr. 23 Studying Nash equilibrium experimentally Examples of Nash equilibrium 26 Experimental evidence on the Prisoner's Dilemma 28 Focal points Best response functions Dominated actions Equilibrium in a single population: symmetric games and symmetric equilibria 50 Notes 53 3 Nash Equilibrium: Illustrations Cournot's model of oligopoly Bertrand's model of oligopoly 63 Cournot, Bertrand, and Nash: some historical notes Electoral competition The War of Attrition 77

3 vi Contents 3.5 Auctions 80 Auctions from Babylonia to ebay Accident law 91 Notes 97 4 Mixed Strategy Equilibrium Introduction 99 Some evidence on expected payoff functions Strategic games in which players may randomize Mixed strategy Nash equilibrium Dominated actions Pure equilibria when randomization is allowed Illustration: expert diagnosis Equilibrium in a single population Illustration: reporting a crime 131 Reporting a crime: social psychology and game theory The formation of players' beliefs Extension: finding all mixed strategy Nash equilibria Extension: games in which each player has a continuum of actions Appendix: representing preferences by expected payoffs 146 Notes Extensive Games with Perfect Information: Theory Extensive games with perfect information Strategies and outcomes Nash equilibrium Subgame perfect equilibrium Finding subgame perfect equilibria of finite horizon games: backward induction 169 Ticktacktoe, chess, and related games 178 Notes Extensive Games with Perfect Information: Illustrations The ultimatum game, the holdup game, and agenda control 181 Experiments on the ultimatum game Stackelberg's model of duopoly Buying votes A race 197 Notes Extensive Games with Perfect Information: Extensions and Discussion Allowing for simultaneous moves 205 More experimental evidence on subgame perfect equilibrium Illustration: entry into a monopolized industry Illustration: electoral competition with strategic voters 215

4 Contents vii 7.4 Illustration: committee decision-making Illustration: exit from a declining industry Allowing for exogenous uncertainty Discussion: subgame perfect equilibrium and backward induction 231 Experimental evidence on the centipede game 234 Notes Coalitional Games and the Core Coalitional games The core Illustration: ownership and the distribution of wealth Illustration: exchanging homogeneous horses Illustration: exchanging heterogeneous houses Illustration: voting Illustration: matching 263 Matching doctors with hospitals Discussion: other solution concepts 269 Notes 270 II Games with Imperfect Information Bayesian Games Motivational examples General definitions Two examples concerning information Illustration: Cournot's duopoly game with imperfect information Illustration: providing a public good Illustration: auctions 291 Auctions of the radio spectrum Illustration: juries Appendix: auctions with an arbitrary distribution of valuations 307 Notes Extensive Games with Imperfect Information Extensive games with imperfect information Strategies Nash equilibrium Beliefs and sequential equilibrium Signaling games Illustration: conspicuous expenditure as a signal of quality Illustration: education as a signal of ability Illustration: strategic information transmission Illustration: agenda control with imperfect information 351 Notes 357

5 viii Contents III Variants and Extensions Strictly Competitive Games and Maxminimization Maxminimization Maxminimization and Nash equilibrium Strictly competitive games Maxminimization and Nash equilibrium in strictly competitive games 367 Maxminimization: some history 370 Empirical tests: experiments, tennis, and soccer 373 Notes Rationalizability Rationalizability Iterated elimination of strictly dominated actions Iterated elimination of weakly dominated actions Dominance solvability 391 Notes Evolutionary Equilibrium Monomorphic pure strategy equilibrium 394 Evolutionary game theory: some history Mixed strategies and polymorphic equilibrium Asymmetric contests 406 Side-blotched lizards 407 Explaining the outcomes of contests in nature Variation on a theme: sibling behavior Variation on a theme: the nesting behavior of wasps Variation on a theme: the evolution of the sex ratio 416 Notes Repeated Games: The Prisoner's Dilemma The main idea Preferences Repeated games Finitely repeated Prisoner's Dilemma Infinitely repeated Prisoner's Dilemma Strategies in an infinitely repeated Prisoner's Dilemma Some Nash equilibria of an infinitely repeated Prisoner's Dilemma Nash equilibrium payoffs of an infinitely repeated Prisoner's Dilemma 431 Experimental evidence Subgame perfect equilibria and the one-deviation property 437 Axelrod's tournaments 439

6 Contents Some subgame perfect equilibria of an infinitely repeated Prisoner's Dilemma 441 Reciprocal altruism among sticklebacks Subgame perfect equilibrium payoffs of an infinitely repeated Prisoner's Dilemma 446 Medieval trade fairs Concluding remarks 449 Notes Repeated Games: General Results Nash equilibria of general infinitely repeated games Subgame perfect equilibria of general infinitely repeated games Finitely repeated games Variation on a theme: imperfect observability 461 Notes Bargaining Bargaining as an extensive game Illustration: trade in a market Nash's axiomatic model Relation between strategic and axiomatic models 489 Notes Appendix: Mathematics Numbers Sets Functions Profiles Sequences Probability Proofs 505 References 507 Index 525