Games of Strategy

Cover (Games of Strategy) ... 1
Front Matter ... 2
Title page ... 4
Copyright ... 5
Contents ... 8
Preface ... 21
Part One - Introduction and General Principles ... 24
1 - Basic Ideas and Examples ... 26
1 What is a Game of Strategy? ... 27
2 Some Examples and Stories of Strategic Games ... 29
3 Our Strategy for Studying Games of Strategy ... 37
2 - How to Think about Strategic Games ... 40
1 Decisions Versus Games ... 41
2 Classifying Games ... 43
3 Some Terminology and Background Assumptions ... 50
4 The Uses of Game Theory ... 59
5 The Structure of the Chapters to Follow ... 61
Part Two - Concepts and Techniques ... 68
3 - Games with Sequential Moves ... 70
1 Game Trees ... 71
2 Solving Games by Using Trees ... 75
3 Adding More Players ... 80
4 Order Advantages ... 85
5 Adding More Moves ... 86
6 Evidence Concerning Rollback ... 94
7 Strategies in Survivor ... 98
4 - Simultaneous-Move Games: Discrete Strategies ... 114
1 Depicting Simultaneous-Move Games with Discrete Strategies ... 115
2 Nash Equilibrium ... 117
3 Dominance ... 122
4 Best-Response Analysis ... 129
5 Three Players ... 131
6 Multiple Equilibria in Pure Strategies ... 134
7 No Equilibrium in Pure Strategies ... 141
5 - Simultaneous- Move Games: Continuous Strategies, Discussion, and Evidence ... 156
1 Pure Strategies that are Continuous Variables ... 157
2 Critical Discussion of the Nash Equilibrium Concept ... 166
3 Rationalizability ... 172
4 Empirical Evidence Concerning Nash Equilibrium ... 178
6 - Combining Sequential and Simultaneous Moves ... 203
1 Games with both Simultaneous and Sequential Moves ... 204
2 Changing the Order of Moves in a Game ... 210
3 Change in the Method of Analysis ... 217
4 Three-Player Games ... 223
7 - Simultaneous-Move Games: Mixed Strategies ... 237
1 What is a Mixed Strategy? ... 238
2 Mixing Moves ... 239
3 Nash Equilibrium as a System of Beliefs and Responses ... 244
4 Mixing in Non-Zero-Sum Games ... 245
5 General Discussion of Mixed-Strategy Equilibria ... 250
6 Mixing When One Player has Threeor More Pure Strategies ... 256
7 Mixing When Both Players have Three Strategies ... 260
8 How to Use Mixed Strategies in Practice ... 265
9 Evidence on Mixing ... 267
Part Three - Some Broad Classes of Games and Strategies ... 292
8 - Uncertainty and Information ... 294
1 Imperfect Information: Dealing with Risk ... 296
2 Asymmetric Information: Basic Ideas ... 302
3 Direct Communication, or “Cheap Talk” ... 304
4 Adverse Selection, Signaling, and Screening ... 317
5 Signaling in the Labor Market ... 327
6 Equilibria in Two -Player Signaling Games ... 333
Appendix: Risk Attitudes and Bayes’ Theorem ... 358
1 Attitudes Toward Risk And Expected Utility ... 358
2 Infering Probabilities from observing consequences ... 361
9 - Strategic Moves ... 365
1 A Classification of Strategic Moves ... 366
2 Credibility of Strategic Moves ... 369
3 Commitments ... 371
4 Threats and Promises ... 375
5 Some Additional Topics ... 383
6 Acquiring Credibility ... 385
7 Countering Your Opponent’s Strategic Moves ... 391
10 - The Prisoners’ Dilemma and Repeated Games ... 400
1 The Basic Game (Review) ... 401
2 Solutions I: Repetition ... 402
3 Solutions II: Penalties and Rewards ... 412
4 Solutions III: Leadership ... 415
5 Experimental Evidence ... 418
6 Real-World Dilemmas ... 422
Appendix: Infinite Sums ... 437
11 - Collective-Action Games ... 440
1 Collective-Action Games with Two Players ... 441
2 Collective-Action Problems in Large Groups ... 446
3 Spillovers, or Externalities ... 454
4 A Brief History of Ideas ... 466
5 “Help!”: A Game of Chicken with Mixed Strategies ... 477
12 - Evolutionary Games ... 488
1 The Framework ... 489
2 Prisoners’ Dilemma ... 493
3 Chicken ... 502
4 The Assurance Game ... 505
5 Three Phenotypes in the Population ... 507
6 The Hawk–Dove Game ... 511
7 Interactions by Population and Across Species ... 518
8 Evolution of Cooperation and Altruism ... 522
13 - Mechanism Design ... 538
1 Price Discrimination ... 539
3 Cost-Plus and Fixed-Price Contracts ... 545
4 Evidence Concerning Information Revelation Mechanisms ... 550
5 Incentives for Effort: The Simplest Case ... 552
6 Incentives for Effort: Evidence and Extensions ... 560
Part Four - Applications to Specific Strategic Situations ... 580
14 - Brinkmanship the Cuban Missile Crisis ... 582
1 A Brief Narrative of Events ... 583
2 A Simple Game-Theoretic Explanation ... 590
3 Accounting for additional complexities ... 592
4 A Probabilistic Threat ... 598
5 Practicing Brinkmanship ... 602
15 - Strategy and Voting ... 612
1 Voting Rules and Procedures ... 613
2 Voting Paradoxes ... 617
3 Evaluating voting systems ... 623
4 Strategic Manipulation of Votes ... 627
5 The Median Voter Theorem ... 636
16 - Bidding Strategy and Auction Design ... 655
1 Types of Auctions ... 656
2 The Winner’s Curse ... 659
3 Bidding Strategies ... 662
4 All-Pay Auctions ... 665
5 How to Sell at Auction ... 668
6 Some Added Twists to Consider ... 672
7 aditional reading ... 679
17 - Bargaining ... 686
1 Nash’s Cooperative Solution ... 688
2 Variable-Threat Bar ... 695
3 Alternating-Offers Model I: Total Value Decays ... 697
4 Experimental Evidence ... 700
5 Alternating-Offers Model II: Impatience ... 703
6 Manipulating Information in Bargaining ... 708
7 Bargaining with Many Parties and Issues ... 711
Glossary ... 718
Index ... 735