Games and information: an introduction to game theory/ Eric Rasmusen

List of Figures x
List of Tables xiii
List of Games xv
Preface xviii
Contents and Purpose xviii
Changes in the Second Edition, 1994 xviii
Changes in the Third Edition, 2001 xix
Changes in the Fourth Edition, 2006 xx
Using the Book xxii
The Level of Mathematics xxii
Other Books xxiii
Contact Information xxviii
Acknowledgements xxviii
Introduction 1
History 1
Game Theory¿s Method 2
Exemplifying Theory 2
This Book¿s Style 4
Notes 6
Part 1: Game Theory 9
1 The Rules of the Game 11
1.1 Definitions 11
1.2 Dominated and Dominant Strategies: The Prisoner¿s Dilemma 19
1.3 Iterated Dominance: The Battle of the Bismarck Sea 22
1.4 Nash Equilibrium: Boxed Pigs, the Battle of the Sexes and
Ranked Coordination 26
1.5 Focal Points 32
Notes 33
Problems 36
Classroom Game 38
2 Information 40
2.1 The Strategic and Extensive Forms of a Game 40
2.2 Information Sets 45
2.3 Perfect, Certain, Symmetric, and Complete Information 49
2.4 The Harsanyi Transformation and Bayesian Games 52
2.5 An Example: The Png Settlement Game 61
Notes 64
Problems 66
Classroom Game 68
3 Mixed and Continuous Strategies 69
3.1 Mixed Strategies: The Welfare Game 69
3.2 The Payoff-equating Method and Games of Timing 74
*3.3 Mixed Strategies with General Parameters and N Players:
The Civic Duty Game 81
*3.4 Randomizing is not Always Mixing: The Auditing Game 85
3.5 Continuous Strategies: The Cournot Game 87
3.6 Continuous Strategies: The Bertrand Game, Strategic Complements,
and
Strategic Substitutes 90
*3.7 Existence of Equilibrium 95
Notes 98
Problems 103
Classroom Game 107
4 Dynamic Games with Symmetric Information 108
4.1 Subgame Perfectness 108
4.2 An Example of Perfectness: Entry Deterrence I 111
4.3 Credible Threats, Sunks Costs, and the Open-set Problem in the Game
of
Nuisance Suits 113
4.4 Recoordination to Pareto-dominant Equilibria in Subgames:
Pareto Perfection 120
Notes 122
Problems 123
Classroom Game 126
5 Reputation and Repeated Games with Symmetric Information 128
5.1 Finitely Repeated Games and the Chainstore Paradox 128
5.2 Infinitely Repeated Games, Minimax Punishments, and the Folk
Theorem 130
5.3 Reputation: The One-sided Prisoner¿s Dilemma 136
5.4 Product Quality in an Infinitely Repeated Game 137
*5.5 Markov Equilibria and Overlapping Generations: Customer Switching
Costs 141
*5.6 Evolutionary Equilibrium: The Hawk-Dove Game 143
Notes 147
Problems 151
Classroom Game 155
6 Dynamic Games with Incomplete Information 156
6.1 Perfect Bayesian Equilibrium: Entry Deterrence II and III 156
6.2 Refining Perfect Bayesian Equilibrium in the Entry Deterrence and
PhD
Admissions Games 160
6.3 The Importance of Common Knowledge: Entry Deterrence IV and V 164
6.4 Incomplete Information in the Repeated Prisoner¿s Dilemma: The Gang
of
Four Model 166
6.5 The Axelrod Tournament 169
6.6 Credit and the Age of the Firm: The Diamond Model 170
Notes 172
Problems 175
Classroom Game 177
Part 2: Asymmetric Information 179
7 Moral Hazard: Hidden Actions 181
7.1 Categories of Asymmetric Information Models 181
7.2 A Principal-agent Model: The Production Game 184
7.3 The Incentive Compatibility and Participation Constraints 194
7.4 Optimal Contracts: The Broadway Game 195
Notes 201
Problems 204
Classroom Game 209
8 Further Topics in Moral Hazard 211
8.1 Efficiency Wages 211
8.2 Tournaments 214
*8.3 Institutions and Agency Problems 216
*8.4 Renegotiation: The Repossession Game 219
*8.5 State-space Diagrams: Insurance Games I and II 222
*8.6 Joint Production by Many Agents: The Holmstrom Teams Model 227
*8.7 The Multitask Agency Problem 230
Notes 236
Problems 239
Classroom Game 242
9 Adverse Selection 243
9.1 Introduction: Production Game VI 243
9.2 Adverse Selection under Certainty: Lemons I and II 249
9.3 Heterogeneous Tastes: Lemons III and IV 252
9.4 Adverse Selection under Uncertainty: Insurance Game III 255
*9.5 Market Microstructure 259
*9.6 A Variety of Applications 263
9.7 Adverse Selection and Moral Hazard Combined: Production Game VII
266
Notes 269
Problems 272
Classroom Game 274
10 Mechanism Design and Postcontractual Hidden Knowledge 276
10.1 Mechanisms, Unravelling, Cross Checking, and the Revelation
Principle 276
10.2 Myerson Mechanism Design 287
10.3 An Example of Postcontractual Hidden Knowledge: The Salesman Game
289
*10.4 The Groves Mechanism 293
10.5 Price Discrimination 296
*10.6 Rate-of-return Regulation and Government Procurement 304
Notes 314
Problems 316
Classroom Game 319
11 Signalling 320
11.1 The Informed Player Moves First: Signalling 320
11.2 Variants on the Signalling Model of Education 324
11.3 General Comments on Signalling in Education 329
11.4 The Informed Player Moves Second: Screening 330
*11.5 Two Signals: The Game of Underpricing New Stock Issues 338
*11.6 Signal Jamming and Limit Pricing 341
*11.7 Countersignalling 345
Notes 348
Problems 349
Classroom Game 352
Part 3: Applications 355
12 Bargaining 357
12.1 The Basic Bargaining Problem: Splitting a Pie 357
12.2 The Nash Bargaining Solution 359
12.3 Alternating Offers over Finite Time 361
12.4 Alternating Offers over Infinite Time 362
12.5 Incomplete Information 365
*12.6 Setting Up a Way to Bargain: The Myerson¿Satterthwaite Model 369
Notes 380
Problems 381
Classroom Game 384
13 Auctions 385
13.1 Values Private and Common, Continuous and Discrete 385
13.2 Optimal Strategies under Different Rules in Private-value Auctions
390
13.3 Revenue Equivalence, Risk Aversion, and Uncertainty 403
13.4 Reserve Prices and the Marginal Revenue Approach 409
13.5 Common-value Auctions and the Winner¿s Curse 414
13.6 Asymmetric Equilibria, Affiliation, and Linkage: The Wallet Game
423
Notes 428
Problems 430
Classroom Game 432
14 Pricing 433
14.1 Quantities as Strategies: Cournot Equilibrium Revisited 433
14.2 Capacity Constraints: The Edgeworth Paradox 436
14.3 Location Models 441
14.4 Comparative Statics and Supermodular Games 449
*14.5 Vertical Differentiation 454
*14.6 Durable Monopoly 461
Notes 467
Problems 469
Classroom Game 471
Mathematical Appendix 473
*A.1 Notation 473
*A.2 The Greek Alphabet 475
*A.3 Glossary 475
*A.4 Formulas and Functions 479
*A.5 Probability Distributions 480
A.6 Supermodularity 482
A.7 Fixed Point Theorems 484
*A.8 Genericity 485
*A.9 Discounting 486
*A.10 Risk 487
References and Name Index 493
Subject Index 521