GAMES AND INFORMATION, THIRD EDITION An Introduction to Game Theory Eric Rasmusen Basil Blackwell 1 Contents1 (starred sections are less important) Preface Contents and Purpose Changes in the Second Edition Changes in the Third Edition Using the Book The Level of Mathematics Other Books Acknowledgements Introduction History Game Theory's Method Exemplifying Theory This Book's Style Notes PART I GAME THEORY 1 The Rules of the Game 1.1 De¯nitions 1.2 Dominant Strategies: The Prisoner's Dilemma 1.3 Iterated Dominance: The Battle of the Bismarck Sea 1.4 Nash Equilibrium: Boxed Pigs, The Battle of the Sexes, and Ranked Coordination 1xxx February 2, 2000. Eric Rasmusen, [email protected]. Footnotes starting with xxx are the author's notes to himself. Comments are welcomed. 2 1.5 Focal Points Notes Problems 2 Information 2.1 The Extensive Form of a Game 2.2 Information Sets 2.3 Perfect, Certain, Symmetric, and Complete Information 2.4 The Harsanyi Transformation and Bayesian Games *2.5 Example: The Png Settlement Game Notes Problems 3 Continuous and Mixed Strategies 3.1 Mixed Strategies: The Welfare Game 3.2 Chicken, The War of Attrition, and Correlated Strategies 3.3 Mixed Strategies with General Parameters and N Players: The Civic Duty Game 3.4 Randomizing versus Mixing: The Auditing Game 3.5 Continuous Strategies: The Cournot Game Notes Problems 4 Dynamic Games with Symmetric Information 4.1 Subgame Perfectness 4.2 An Example of Perfectness: Entry Deterrence I 3 4.3 Credible Threats, Sunk Costs, and the Open-Set Problem in Nui- sance Suits 4.4 RecoordinationtoParetoDominantEquilibriainSubgames: Pareto Perfection Notes Problems 5 Reputation and Repeated Games 5.1 Finitely Repeated Games and the Chainstore Paradox 5.2 In¯nitely Repeated Games, Minimax Punishments, and the Folk Theorem 5.3 Reputation: The One-Sided Prisoner's Dilemma 5.4 Product Quality in an In¯nitely Repeated Game *5.5 MarkovEquilibriaandOverlappingGenerationsinCustomerSwitch- ing Costs *5.6 Evolutionary Equilibrium: The Hawk-Dove Game (formerly Sec- tion 4.6) Notes Problems 6 Dynamic Games with Incomplete Information 6.1 Perfect Bayesian Equilibrium: Entry Deterrence II and III 6.2 Re¯ning Perfect Bayesian Equilibrium: PhD Admissions 6.3 TheImportanceofCommonKnowledge: EntryDeterrenceIVand V 6.4 IncompleteInformation in the Repeated Prisoner's Dilemma: The Gang of Four Model 6.5 The Axelrod Tournament *6.6 WhyEstablishedFirmsPayLessforCapital: TheDiamondModel (formerly Section 15.1) Notes 4 Problems PART II ASYMMETRIC INFORMATION 7 Moral Hazard: Hidden Actions 7.1 Categories of Asymmetric Information Models 7.2 A Principal-Agent Model: The Production Game 7.3 TheIncentiveCompatibility,Participation,andCompetitionCon- straints 7.4 Optimal Contracts: The Broadway Game Notes Problems 8 Further Topics in Moral Hazard 8.1 E±ciency Wages (formerly Section 8.4) 8.2 Tournaments (formerly Section 8.5) 8.3 Institutions and Agency Problems (formerly Section 8.6) *8.4 Renegotiation: The Repossession Game *8.5 State-Space Diagrams: Insurance Games I' and II' (formerly Sec- tion 7.5) *8.6 Joint Production by Many Agents: The Holmstrom Teams Model (formerly Section 8.7) Notes Problems 9 Adverse Selection 9.1 Introduction: Production Game V 9.2 Adverse Selection under Certainty: Lemons I and II 9.3 Heterogeneous Tastes: Lemons III and IV 9.4 Adverse Selection under Uncertainty: Insurance Game III 5 *9.5 MarketMicrostructureandtheKyleModel(formerlySection15.3) *9.6 A Variety of Applications Notes Problems 9a MechanismDesign in AdverseSelection andin Moral Hazard with Hid- den Information 9a.1 The Revelation Principle and Moral Hazard with Hidden Knowl- edge (formerly Section 8.1) 9a.2 An Example of MoralHazard with Hidden Knowledge: The Sales- man Game (formerly Section 8.2) *9a.3 Price Discrimination (new) 9a.4 Rate of Return Regulation and Government Procurement (for- merly Section 15.4) *9a.5 The Groves Mechanism (formerly Section 9.6) Notes Problems 10 Signalling 10.1 The Informed Player Moves First: Signalling 10.2 Variants on the Signalling Model of Education 10.3 General Comments on Signalling in Education 10.4 The Informed Player Moves Second: Screening *10.5 Two Signals: Underpricing of Stock *10.6 Signal Jamming and Limit Pricing (formerly Section 14.2) Notes Problems PART III APPLICATIONS 11 Bargaining 6 11.1 The Basic Bargaining Problem: Splitting a Pie 11.2 The Nash Bargaining Solution 11.3 Alternating O®ers over Finite Time 11.4 Alternating O®ers over In¯nite Time 11.5 Incomplete Information 11.6 Setting up a Way to Bargain: The Myerson-Satterthwaite Mech- anism (new) Notes Problems 12 Auctions 12.1 Auction Classi¯cation and Private-Value Strategies 12.2 Comparing Auction Rules 12.3 Risk and Uncertainty over Values 12.4 Common-Value Auctions and the Winner's Curse 12.5 Information in Common-Value Auctions Notes Problems 13 Pricing 13.1 Quantities as Strategies: Cournot Equilibrium Revisited 13.2 Prices as Strategies 13.3 Location Models *13.4 Comparative Statics and Supermodular Games *13.5 Durable Monopoly Notes Problems *14 Entry *14.1 Innovation and Patent Races 7 *14.2 Takeovers and Greenmail (formerly Section 15.2) *14.3 Predatory Pricing: The Kreps-Wilson Model *14.4 Entry for Buyout Notes Problems *A Mathematical Appendix *A.1 Notation *A.2 Glossary *A.3 Formulas and Functions *A.4 Probability Distributions *A.5 Supermodularity *A.6 Fixed-Point Theorems *A.7 Genericity (new) *A.8 Discounting (formerly Section 4.5) *A.9 Risk (new) References and Name Index Subject Index 8 Preface 1 Contents and Purpose This book is about noncooperative game theory and asymmetric information. In the Introduction, I will say why I think these subjects are important, but here in the Preface I will try to help you decide whether this is the appropriate book to read if they do interest you. I write as an applied theoretical economist, not as a game theorist, and readers in anthropology, law, physics, accounting, and management science have helped me to be aware of the provincialisms of economics and game theory. My aim is to present the game theory and information economics that currently exists in journal articles and oral tradition in a way that shows how to build simple models using a standard format. Journal articles are more complicated and less clear than seems necessary in retrospect; precisely because it is original, even the discoverer rarely understands a trulynovelidea. Afterafewdozensuccessorarticleshaveappeared,weallunderstand itand marvelat its simplicity. Butjournaleditorsareunreceptiveto new articles that admit to containing exactly the same idea as old articles, just presented more clearly. At best, the clari¯cation is hidden in some new article's introduction or condensed to a paragraph in a survey. Students, who ¯nd every idea as complex as the originators of the ideas did when they were new, must learn either from the confused original articles or the oral tradition of a top economics department. This book tries to help. Changes in the Second Edition, 1994 By now, just a few years later after my First Edition, those trying to learn game theoryhavemoretohelpthemthanjustthisbook,andIwilllistanumberofexcellent books below. I have also thoroughly revised Games and Information. George Stigler used to say that it was a great pity Alfred Marshall spent so much time on the eight editions of Principles of Economics that appeared between 1890 and 1920, given the opportunity cost of the other books he might have written. I am no Marshall, so I have been willing to sacri¯ce a Rasmusen article or two for this new edition, though I doubt I will keep it up till 2019. What I have done for the Second Edition is to add a number of new topics, in- crease the number of exercises (and provide detailed answers), update the references, change the terminology here and there, and rework the entire book for clarity. A 1xxx September 6, 1999; February 2, 2000. 1999. Eric Rasmusen, [email protected] Foot- notes starting with xxx are the author's notes to himself. Comments are welcomed. This section is 9 pages long. 9 book, like a poem, is never ¯nished, only abandoned (which is itself a good example of a fundamental economic principle). The one section I have dropped is the some- what obtrusive discussion of existence theorems; I recommend Fudenberg & Tirole (1991) on that subject. The new topics include auditing games, nuisance suits, reco- ordination in equilibria, renegotiation in contracts, supermodularity, signal jamming, market microstructure, and government procurement. The discussion of moral haz- ard has been reorganized. The total number of chapters has increased by two, the topics of repeated games and entry having been given their own chapters. Changes in the Third Edition, 2001 Besides numerous minor changes in wording, I have added new material and reorganized some sections of the book. The new topics are 9a.3 \Price Discrimination"; 11.6 \Setting up a Way to Bargain: The Myerson- Satterthwaite Mechanism"; 12.3 \Risk and Uncertainty over Values" for private-value auctions" ; A.6 \Fixed-Point Theorems"; and A.7 \Gener- icity". Toaccommodatetheadditions,Ihavedropped9.5\OtherEquilibriumConcepts: Wilson Equilibrium and Reactive Equilibrium" (which is still available on the book's website), and Appendix A, \Answers to Odd-Numbered Problems". These answers are very important, but I have moved them to the website because most readers who care to look at them will have web access and problem answers are peculiarly in need of updating. Ideally, I would like to discuss all likely wrong answers as well as the right answers, but I learn the wrong answers only slowly, with the help of new generations of students. Chapter 9a, \Mechanism Design in Adverse Selection and in Moral Hazard with Hidden Information", is new. I have labelled it \9a" so as to preserve the old num- bering of the later chapters, for the convenience of those familiar with the Second Edition. It includes two sections from chapter 8 ( 8.1 \Pooling versus Separating Equilibrium and the Revelation Principle" is now section 9a.1; 8.2 \An Example of Moral Hazard with Hidden Knowledge: The Salesman Game" is now section 9a.2) and one from chapter 9 (9.6 \The Groves Mechanism" is now section 9a.5). Chapter 15 \The New Industrial Organization" has been eliminated and its sec- tions reallocated. Section 15.1 \Why Established Firms Pay Less for Capital: The Diamond Model" is now section 6.6; Section 15.2 \Takeovers and Greenmail" is now section 14.2; section 15.3 \Market Microstructure and theKyle Model" is now section 9.5; and section 15.4 \Rate of Return Regulation and Government Procurement" is now section 9a.4. Topics that have been extensively reorganized or rewritten include 13.2 \Prices as Strategies"; 13.3 \Location Models"; the Mathematical Appendix, and the Bibli- 10