Gibbons - A Primer In Game Theory 1992

A Primer in Game Theory
Robert Gibbons

Contents
Preface 1 Static Games of Complete Information 1.1 Basic Theory: Normal-Form Games and Nash Equilibrium 1.1. A Normal-Form Representation of Games . . . . 1.1.B Iterated Elimination of Strictly Dominated Strategies 1.1 .C Motivation and Definition of Nash Equilibrium 1.2 Applications 1.2. A Cournot Model of Duopoly 1.2.B Bertrand Model ofDuopoly 1.2.C Final-Offer Arbitration 1.2.D The Problem of the Commons 1.3 Advanced Theory: Mixed Strategies and Existence of Equilibrium 1.3.A Mixed Strategies 1.3.B Existence of Nash Equilibrium 1.4 Further Reading 1.5 Problems 1.6 References
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1 2 2 4 8 14 14 21 22 27 29 29 33 48 48 51

2 Dynamic Games of Complete Information 55 2.1 Dynamic Games of Complete and Perfect Information 57 2.1.ATheory: Backwards Induction 57 2.1.B Stackelberg Model of Duopoly 61 2.1.C Wages and Employment in a Unionized Firm 64 2.1.D Sequential Bargaining 68 2.2 Two-Stage Games of Complete but Imperfect Information ^ vn

Contents 12.A "Theory: Subgame Perfection 71 I B Bank Runs 73 - C Tariffs and Imperfect International Competition 75 2.2.D Tournaments 79 Repeated Games 82 "A Theory: Two-StageRepeated Games 82 2.3.B Theory: Infinitely Repeated Games 88 : .C Collusion between Coumot Duopolists . . . . 1 0 2 23-D Efficiency Wages 107 • E Time-Consistent Monetary Policy 112 Dynamic Games of Complete but Imperfect Information 115 - ;.A Extensive-Form Representation of Games . .115 2.4.B Subgame-Perfect Nash Equilibrium 122 Further Reading 129 Problems 130 References 138

be 4.2.B job-MarketSignaling 190 4.2.C Corporate Investment and Capital Structure . 205 4.2.D Monetary Policy 208 Other Applications of Perfect Bayesian Equilibrium . 210 4.3.A Cheap-Talk Games 210 4.3.B Sequential Bargaining under Asymmetric Information 218 4.3.C Reputation in the Finitely Repeated Prisoners' Dilemma 224 Refinements of Perfect Bayesian Equilibrium 233 Further Reading 244 Problems 245 References 253•7^7

4.3

2.3

2.4

4.4 4.5 4.6 4.7

2.5 16 17

Index

Static Games of Incomplete Information 143 3.1 Theory: Static Bayesian Games and Bayesian N a s h Equilibrium 144 3.1.A An Example: Cournot Competition u n d e r Asymmetric Information 144 3.1.B Normal-Form Representation of Static Bayesian Games 146 3.1.C Definition of Bayesian Nash Equilibrium . . . 149 3 1 Applications 1523.2.A Mixed Strategies Revisited 152 3.2.B An Auction 155 3.2.C A Double Auction 158 3.3 The Revelation Principle 164 3.4 Further Reading 168 3.5 Problems 169 3.6 References 172 1 Dynamic Games of Incomplete Information Introduction to Perfect Bayesian Equilibrium Signaling Games Perfect Bayesian Equilibrium in Signaling Games 173 175 183 183

Preface
Game theory is the study of multipersondecision problems. Such problems arise frequently in economics. As is widely appreciated, for example, oligopolies present multiperson problems — each firm must consider what the others will do. But many other applications of game theory arise in fields of economics other than industrial organization. At the micro level, models of trading processes (such as bargaining and auction models) involve gametheory. At an intermediate level of aggregation, labor and financial economics include game-theoretic models of the behavior of a firm in its input markets (rather than its output market, as in an oligopoly). There also are multiperson problems within a firm: many workers may vie for one promotion; several divisions may compete for the corporation's investment capital. Finally, at a high level ofaggregation, international economics includes models in which countries compete (or collude) in choosing tariffs and other trade policies, and macroeconomics includes models in which the monetary authority and wage or price setters interact strategically to determine the effects of monetary policy. This book is designed to introduce game theory to those who will later construct (or at least...