Table of Contents
Preface xi
PART I Rational Decision Making
Chapter 1 The Single-Person Decision Problem 3
- 1.1 Actions, Outcomes, and Preferences 4
- 1.1.1 Preference Relations 5
- 1.1.2 Payoff Functions 7
- 1.2 The Rational Choice Paradigm 9
- 1.3 Summary 11
- 1.4 Exercises 11
Chapter 2 Introducing Uncertainty and Time 14
- 2.1 Risk, Nature, and Random Outcomes 142.1.1 Finite Outcomes and Simple Lotteries 152.1.2 Simple versus Compound Lotteries 162.1.3 Lotteries over Continuous Outcomes 17
- 2.2 Evaluating Random Outcomes 182.2.1 Expected Payoff: The Finite Case 192.2.2 Expected Payoff: The Continuous Case 202.2.3 Caveat: It's Not Just the Order Anymore 212.2.4 Risk Attitudes 222.2.5 The St. Petersburg Paradox 23
- 2.3 Rational Decision Making with Uncertainty 242.3.1 Rationality Revisited 242.3.2 Maximizing Expected Payoffs 24
- 2.4 Decisions over Time 262.4.1 Backward Induction 262.4.2 Discounting Future Payoffs 28
- 2.5 Applications 292.5.1 The Value of Information 292.5.2 Discounted Future Consumption 31
- 2.6 Theory versus Practice 32
- 2.7 Summary 33
- 2.8 Exercises 33
PART II Static Games of Complete Information
Chapter 3 Preliminaries 43
- 3.1 Normal-Form Games with Pure Strategies 463.1.1 Example: The Prisoner's Dilemma 483.1.2 Example: Cournot Duopoly 493.1.3 Example: Voting on a New Agenda 49
- 3.2 Matrix Representation: Two-Player Finite Game 503.2.1 Example: The Prisoner's Dilemma 513.2.2 Example: Rock-Paper-Scissors 52
- 3.3 Solution Concepts 523.3.1 Assumptions and Setup 543.3.2 Evaluating Solution Concepts 553.3.3 Evaluating Outcomes 56
- 3.4 Summary 57
- 3.5 Exercises 58
Chapter 4 Rationality and Common Knowledge 59
- 4.1 Dominance in Pure Strategies 594.1.1 Dominated Strategies 594.1.2 Dominant Strategy Equilibrium 614.1.3 Evaluating Dominant Strategy Equilibrium 62
- 4.2 Iterated Elimination of Strictly Dominated Pure Strategies 634.2.1 Iterated Elimination and Common Knowledge of Rationality 634.2.2 Example: Cournot Duopoly 654.2.3 Evaluating IESDS 67
- 4.3 Beliefs, Best Response, and Rationalizability 694.3.1 The Best Response 694.3.2 Beliefs and Best-Response Correspondences 714.3.3 Rationalizability 734.3.4 The Cournot Duopoly Revisited 734.3.5 The "p-Beauty Contest" 744.3.6 Evaluating Rationalizability 76
- 4.4 Summary 76
- 4.5 Exercises 76
Chapter 5 Pinning Down Beliefs: Nash Equilibrium 79
- 5.1 Nash Equilibrium in Pure Strategies 805.1.1 Pure-Strategy Nash Equilibrium in a Matrix 815.1.2 Evaluating the Nash Equilibria Solution 83
- 5.2 Nash Equilibrium: Some Classic Applications 835.2.1 Two Kinds of Societies 835.2.2 The Tragedy of the Commons 845.2.3 Cournot Duopoly 875.2.4 Bertrand Duopoly 885.2.5 Political Ideology and Electoral Competition 93
- 5.3 Summary 95
- 5.4 Exercises 95
Chapter 6 Mixed Strategies 101
- 6.1 Strategies, Beliefs, and Expected Payoffs 1026.1.1 Finite Strategy Sets 1026.1.2 Continuous Strategy Sets 1046.1.3 Beliefs and Mixed Strategies 1056.1.4 Expected Payoffs 105
- 6.2 Mixed-Strategy Nash Equilibrium 1076.2.1 Example: Matching Pennies 1086.2.2 Example: Rock-Paper-Scissors 1116.2.3 Multiple Equilibria: Pure and Mixed 113
- 6.3 IESDS and Rationalizability Revisited 114
- 6.4 Nash's Existence Theorem 117
- 6.5 Summary 123
- 6.6 Exercises 123
PART III Dynamic Games of Complete Information
Chapter 7 Preliminaries 129
- 7.1 The Extensive-Form Game 1307.1.1 Game Trees 1327.1.2 Imperfect versus Perfect Information 136
- 7.2 Strategies and Nash Equilibrium 1377.2.1 Pure Strategies 1377.2.2 Mixed versus Behavioral Strategies 1397.2.3 Normal-Form Representation of Extensive-Form Games 143
- 7.3 Nash Equilibrium and Paths of Play 145
- 7.4 Summary 147
- 7.5 Exercises 147
Chapter 8 Credibility and Sequential Rationality 151
- 8.1 Sequential Rationality and Backward Induction 152
- 8.2 Subgame-Perfect Nash Equilibrium: Concept 153
- 8.3 Subgame-Perfect Nash Equilibrium: Examples 1598.3.1 The Centipede Game 1598.3.2 Stackelberg Competition 1608.3.3 Mutually Assured Destruction 1638.3.4 Time-Inconsistent Preferences 166
- 8.4 Summary 169
- 8.5 Exercises 170
Chapter 9 Multistage Games 175
- 9.1 Preliminaries 176
- 9.2 Payoffs 177
- 9.3 Strategies and Conditional Play 178
- 9.4 Subgame-Perfect Equilibria 180
- 9.5 The One-Stage Deviation Principle 184
- 9.6 Summary 186
- 9.7 Exercises 186
Chapter 10 Repeated Games 190
- 10.1 Finitely Repeated Games 190
- 10.2 Infinitely Repeated Games 19210.2.1 Payoffs 19310.2.2 Strategies 195
- 10.3 Subgame-Perfect Equilibria 196
- 10.4 Application: Tacit Collusion 201
- 10.5 Sequential Interaction and Reputation 20410.5.1 Cooperation as Reputation 20410.5.2 Third-Party Institutions as Reputation Mechanisms 20510.5.3 Reputation Transfers without Third Parties 207
- 10.6 The Folk Theorem: Almost Anything Goes 209
- 10.7 Summary 214
- 10.8 Exercises 215
Chapter 11 Strategic Bargaining 220
- 11.1 One Round of Bargaining: The Ultimatum Game 222
- 11.2 Finitely Many Rounds of Bargaining 224
- 11.3 The Infinite-Horizon Game 228
- 11.4 Application: Legislative Bargaining 22911.4.1 Closed-Rule Bargaining 23011.4.2 Open-Rule Bargaining 232
- 11.5 Summary 235
- 11.6 Exercises 236
PART IV Static Games of Incomplete Information
Chapter 12 Bayesian Games 241
- 12.1 Strategic Representation of Bayesian Games 24612.1.1 Players, Actions, Information, and Preferences 24612.1.2 Deriving Posteriors from a Common Prior: A Player's Beliefs 24712.1.3 Strategies and Bayesian Nash Equilibrium 249
- 12.2 Examples 25212.2.1 Teenagers and the Game of Chicken 25212.2.2 Study Groups 255
- 12.3 Inefficient Trade and Adverse Selection 258
- 12.4 Committee Voting 261
- 12.5 Mixed Strategies Revisited: Harsanyi's Interpretation 264
- 12.6 Summary 266
- 12.7 Exercises 266
Chapter 13 Auctions and Competitive Bidding 270
- 13.1 Independent Private Values 27213.1.1 Second-Price Sealed-Bid Auctions 27213.1.2 English Auctions 27513.1.3 First-Price Sealed-Bid and Dutch Auctions 27613.1.4 Revenue Equivalence 279
- 13.2 Common Values and the Winner's Curse 282
- 13.3 Summary 285
- 13.4 Exercises 285
Chapter 14 Mechanism Design 288
- 14.1 Setup: Mechanisms as Bayesian Games 28814.1.1 The Players 28814.1.2 The Mechanism Designer 28914.1.3 The Mechanism Game 290
- 14.2 The Revelation Principle 292
- 14.3 Dominant Strategies and Vickrey-Clarke-Groves Mechanisms 29514.3.1 Dominant Strategy Implementation 29514.3.2 Vickrey-Clarke-Groves Mechanisms 295
- 14.4 Summary 299
- 14.5 Exercises 299
PART V Dynamic Games of Incomplete Information
Chapter 15 Sequential Rationality with Incomplete Information 303
- 15.1 The Problem with Subgame Perfection 303
- 15.2 Perfect Bayesian Equilibrium 307
- 15.3 Sequential Equilibrium 312
- 15.4 Summary 314
- 15.5 Exercises 314
Chapter 16 Signaling Games 318
- 16.1 Education Signaling: The MBA Game 319
- 16.2 Limit Pricing and Entry Deterrence 32316.2.1 Separating Equilibria 32416.2.2 Pooling Equilibria 330
- 16.3 Refinements of Perfect Bayesian Equilibrium in Signaling Games 332
- 16.4 Summary 335
- 16.5 Exercises 335
Chapter 17 Building a Reputation 339
- 17.1 Cooperation in a Finitely Repeated Prisoner's Dilemma 339
- 17.2 Driving a Tough Bargain 342
- 17.3 A Reputation for Being "Nice" 349
- 17.4 Summary 354
- 17.5 Exercises 354
Chapter 18 Information Transmission and Cheap Talk 357
- 18.1 Information Transmission: A Finite Example 358
- 18.2 Information Transmission: The Continuous Case 361
- 18.3 Application: Information and Legislative Organization 365
- 18.4 Summary 367
- 18.5 Exercises 367
Chapter 19 Mathematical Appendix 369
- 19.1 Sets and Sequences 36919.1.1 Basic Definitions 36919.1.2 Basic Set Operations 370
- 19.2 Functions 37119.2.1 Basic Definitions 37119.2.2 Continuity 372
- 19.3 Calculus and Optimization 37319.3.1 Basic Definitions 37319.3.2 Differentiation and Optimization 37419.3.3 Integration 377
- 19.4 Probability and Random Variables 378 19.4.1 Basic Definitions 37819.4.2 Cumulative Distribution and Density Functions 37919.4.3 Independence, Conditional Probability, and Bayes' Rule 38019.4.4 Expected Values 382
References 385Index 389