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GAMES and INFORMATION, FOURTH EDITION an Introduction to Game Theory GAMES AND INFORMATION, FOURTH EDITION An Introduction to Game Theory Eric Rasmusen Basil Blackwell 23 November 2005. Eric Rasmusen, [email protected]. http: //www.rasmusen.org/GI xiv Contents (starred sections are less important) List of Figures List of Tables List of Games Preface Contents and Purpose Changes in the Second Edition (1994) Changes in the Third Edition (2001) Changes in the Fourth Edition (2006) Using the Book The Level of Mathematics Other Books Contact Information Acknowledgements Introduction History Game Theory’s Method Exemplifying Theory This Book’s Style Notes PART 1: GAME THEORY 1 The Rules of the Game 1.1 Definitions 1.2 Dominated and Dominant Strategies: The Prisoners Dilemma 1.3 Iterated Dominance: The Battle of the Bismarck Sea 1.4 Nash Equilibrium: Boxed Pigs, The Battle of the Sexes, and Ranked Coordina- tion 1.5 Focal Points Notes Problems Classroom Game xv 2 Information 2.1 The Strategic and Extensive Forms 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 Classroom Game 3 Mixed and Continuous Strategies 3.1 Mixed Strategies: The Welfare Game 3.2 The Payoff-Equating Method and Games of Timing *3.3 Mixed Strategies with General Parameters and N Players: The Civic Duty Game *3.4 Randomizing Is Not Always Mixing: The Auditing Game 3.5 Continuous Strategies: The Cournot Game 3.6 Continuous Strategies: The Bertrand Game, Strategic Complements, and Strate- gic Substitutes (newly moved here) *3.7 Existence of Equilibrium (new) Notes Problems Classroom Game 4 Dynamic Games with Symmetric Information 4.1 Subgame Perfectness 4.2 An Example of Perfectness: Entry Deterrence I 4.3 Credible Threats, Sunk Costs, and the Open-Set Problem in the Game of Nui- sance Suits *4.4 Recoordination to Pareto-Dominant Equilibria in Subgames: Pareto Perfection Notes Problems Classroom Game 5 Reputation and Repeated Games with Symmetric Information 5.1 Finitely Repeated Games and the Chainstore Paradox xvi 5.2 Infinitely Repeated Games, Minimax Punishments, and the Folk Theorem 5.3 Reputation: The One-sided Prisoner’s Dilemma 5.4 Product Quality in an Infinitely Repeated Game *5.5 Markov Equilibria and Overlapping Generations: Customer Switching Costs *5.6 Evolutionary Equilibrium: The Hawk-Dove Game Notes Problems Classroom Game 6 Dynamic Games with Incomplete Information 6.1 Perfect Bayesian Equilibrium: Entry Deterrence II and III 6.2 Refining Perfect Bayesian Equilibrium: The PhD Admissions Game 6.3 The Importance of Common Knowledge: Entry Deterrence IV and V 6.4 Incomplete Information in the Repeated Prisoner’s Dilemma: The Gang of Four Model 6.5 The Axelrod Tournament *6.6 Credit and the Age of the Firm: The Diamond Model Notes Problems Classroom Game PART 2: 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 The Incentive Compatibility and Participation Constraints 7.4 Optimal Contracts: The Broadway Game Notes Problems Classroom Game 8 Further Topics in Moral Hazard 8.1 Efficiency Wages 8.2 Tournaments *8.3 Institutions and Agency Problems *8.4 Renegotiation: the Repossession Game xvii *8.5 State-space Diagrams: Insurance Games I and II *8.6 Joint Production by Many Agents: The Holmstrom Teams Model *8.7 The Multitask Agency Problem (new) Notes Problems Classroom Game 9 Adverse Selection 9.1 Introduction: Production Game VI 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 *9.5 Market Microstructure *9.6 A Variety of Applications 9.7 Adverse Selection and Moral Hazard Combined: Production Game VII (new) Notes Problems Classroom Game 10 Mechanism Design and Post-Contractual Hidden Knowledge 10.1 Mechanisms, Unravelling, the Maskin Matching Scheme, and the Revelation Principle (new model) 10.2 Myerson Mechanism Design 10.3 An Example of Post-Contractual Hidden Knowledge: The Salesman Game *10.4 The Groves Mechanism *10.5 Price Discrimination *10.6 Rate-of-Return Regulation and Government Procurement Notes Problems Classroom Game 11 Signalling 11.1 The Informed Player Moves First: Signalling 11.2 Variants on the Signalling Model of Education 11.3 General Comments on Signalling in Education 11.4 The Informed Player Moves Second: Screening *11.5 Two Signals: The Game of Underpricing New Stock Issues xviii *11.6 Signal Jamming and Limit Pricing (new model) *11.7 Countersignalling (new) Notes Problems Classroom Game PART 3: APPLICATIONS 12 Bargaining 12.1 The Basic Bargaining Problem: Splitting a Pie 12.2 The Nash Bargaining Solution 12.3 Alternating Offers over Finite Time 12.4 Alternating Offers over Infinite Time 12.5 Incomplete Information *12.6 Setting up a Way to Bargain: The Myerson-Satterthwaite Mechanism Notes Problems Classroom Game 13 Auctions 13.1 Values Private and Common, Continuous and Discrete 13.2 Optimal Strategies under Different Rules in Private-Value Auctions 13.3 Revenue Equivalence, Risk Aversion, and Uncertainty *13.4 Reserve Prices and the Marginal Revenue Approach (new) 13.5 Common-Value Auctions and the Winner’s Curse (new model) *13.6 Asymmetric Equilibria, Affiliation, and Linkage: The Wallet Game (new) Notes Problems Classroom Game 14 Pricing 14.1 Quantities as Strategies: Cournot Equilibrium Revisited 14.2 Capacity Constraints: The Edgeworth Paradox 14.3 Location Models *14.4 Comparative Statics and Supermodular Games *14.5 Vertical Differentiation (new) *14.6 Durable Monopoly xix Notes Problems Classroom Game *A Mathematical Appendix *A.1 Notation *A.2 The Greek Alphabet *A.3 Glossary *A.4 Formulas and Functions *A.5 Probability Distributions *A.6 Supermodularity *A.7 Fixed Point Theorems *A.8 Genericity *A.9 Discounting *A.10 Risk References and Name Index Subject Index xx List of Figures 1 The Rules of the Game 1 : The Dry Cleaners Game as a Decision Tree 2 : The Dry Cleaners Game as a Game Tree 2 Information 1 : Follow-the-Leader I in Extensive Form 2 : Ranked Coordination in Extensive Form 3 : The Time Line for Stock Underpricing: (a) A Good Time Line; (b) A Bad Time Line 4 : Information Sets and Information Partitions. 5 : Follow-the-Leader II 6 : Follow-the-Leader III: Original 7 : Follow-the-Leader III: After the Harsanyi Transformation 8 : Bayess Rule 9 : The Game Tree for the Png Settlement Game 3 Mixed and Continuous Strategies 1 : The Payoffs in Patent Race for a New Market 2 : Reaction Curves in The Cournot Game 3 : Stackelberg Equilibrium 4 : Bertrand Reaction Functions with Differentiated Products 5 : Cournot vs. Differentiated Bertrand Reaction Functions (Strategic Substitutes vs. Strategic Complements) 6 : Continuous and Discontinuous Reaction Functions 4 Dynamic Games with Symmetric Information 1 : Follow the Leader I 2 : The Tremble Game: Trembling Hand Versus Subgame Perfectness 3 : Entry Deterrence I 4 : The Extensive Form for Nuisance Suits 5 : The Pareto Perfection Puzzle 5 Reputation and Repeated Games with Symmetric Information 1 : The Dimensionality Condition 2 : Evolutionary Dynamics in the Hawk-Dove- Bourgeois Game xxi 6 Dynamic Games with Incomplete Information 1 : Entry Deterrence II, III, and IV 2 : The PhD Admissions Game 3 : Entry Deterrence V 4 : The Interest Rate over Time 5 : The Beer-Quiche Game 7 Moral Hazard: Hidden Actions 1 : Categories of Asymmetric Information Models 2 : The Efficient Effort Level in Production Game I 3 : Three Contracts that Induce Effort e∗ for wage w∗ 4 : Shifting Supports in an Agency Model 8 Further Topics in Moral Hazard 1 : Insurance Game I 2 : Insurance Game II with Full and Partial Insurance 3 : More on Partial Insurance in Insurance Game II 4 : Contracts in the Holmstrom Teams Model 9 Adverse Selection 1 : An Extensive Form for Lemons I 2 : Lemons II: Identical Tastes 3 : Lemons III: Buyers Value Cars More Than Sellers: 4 : Lemons IV: Sellers Valuations Differ 5 : Insurance Game III: Nonexistence of a Pooling Equilibrium 6 : A Separating Equilibrium for Insurance Game III 7 : Curves for Which There is No Equilibrium in Insurance Game III 8 : Lemons III When Buyers Value Cars More and the Minimum Quality is Zero 10 Mechanism Design in Adverse Selection and Post-Contractual Hidden Information 1 : The Salesman Game with Curves for Pooling Equilibria 2 : Indifference Curves for a Separating Equilibrium 3 : Linear and Nonlinear Pricing 4 : Perfect Price Discrimination 5 : The Varian Nonlinear Pricing Game 6 : Marginal versus Average Demand 7 : Two Depictions of the Single Crossing Property xxii 8 : Why the Expensive Firms Incentive Compatibility Constraint Is Nonbinding 11 Signalling 1 : Education VI: No Pooling Equilibrium in a Screening Game 2 : Education VII: Neither Separating nor Pooling Pure-Strategy Equilibria in a Screening Game 3 : How the Signal Changes with the Variance 4 : Different Ways to Signal a Given Company Value 12 Bargaining 1 : (a) Nash Bargaining Game; (b) Splitting a Pie 2 : Trades in Bilateral Trading II 3 : Trade in the one-price equilibrium 4 : Trade in the linear equilibrium 13 Auctions 1 : Smoothing a Discrete Distribution 2 : The Bid Function in an All-Pay Auction with Identical Buyers 3a : Auctions and Marginal Revenue: Reserve Price Needed 3b : Auctions and Marginal Revenue: No Reserve Price Needed 4 : Extracting Information From Uniformly Distributed Signals 14 Pricing 1 : Different Demand Curves 2 : Multiple Cournot-Nash Equilibria 3 : Rationing Rules when pb
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