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# Game Theory:An IntroductionSteven Tadelis

 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 71.2 The Rational Choice Paradigm 91.3 Summary 111.4 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 172.2 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 232.3 Rational Decision Making with Uncertainty 242.3.1 Rationality Revisited 242.3.2 Maximizing Expected Payoffs 242.4 Decisions over Time 262.4.1 Backward Induction 262.4.2 Discounting Future Payoffs 282.5 Applications 292.5.1 The Value of Information 292.5.2 Discounted Future Consumption 312.6 Theory versus Practice 322.7 Summary 332.8 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 493.2 Matrix Representation: Two-Player Finite Game 503.2.1 Example: The Prisoner's Dilemma 513.2.2 Example: Rock-Paper-Scissors 523.3 Solution Concepts 523.3.1 Assumptions and Setup 543.3.2 Evaluating Solution Concepts 553.3.3 Evaluating Outcomes 563.4 Summary 573.5 Exercises 58Chapter 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 624.2 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 674.3 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 764.4 Summary 764.5 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 835.2 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 935.3 Summary 955.4 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 1056.2 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 1136.3 IESDS and Rationalizability Revisited 1146.4 Nash's Existence Theorem 1176.5 Summary 1236.6 Exercises 123PART 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 1367.2 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 1437.3 Nash Equilibrium and Paths of Play 1457.4 Summary 1477.5 Exercises 147Chapter 8 Credibility and Sequential Rationality 151 8.1 Sequential Rationality and Backward Induction 1528.2 Subgame-Perfect Nash Equilibrium: Concept 1538.3 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 1668.4 Summary 1698.5 Exercises 170Chapter 9 Multistage Games 175 9.1 Preliminaries 1769.2 Payoffs 1779.3 Strategies and Conditional Play 1789.4 Subgame-Perfect Equilibria 1809.5 The One-Stage Deviation Principle 1849.6 Summary 1869.7 Exercises 186Chapter 10 Repeated Games 190 10.1 Finitely Repeated Games 19010.2 Infinitely Repeated Games 19210.2.1 Payoffs 19310.2.2 Strategies 19510.3 Subgame-Perfect Equilibria 19610.4 Application: Tacit Collusion 20110.5 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 20710.6 The Folk Theorem: Almost Anything Goes 20910.7 Summary 21410.8 Exercises 215Chapter 11 Strategic Bargaining 220 11.1 One Round of Bargaining: The Ultimatum Game 22211.2 Finitely Many Rounds of Bargaining 22411.3 The Infinite-Horizon Game 22811.4 Application: Legislative Bargaining 22911.4.1 Closed-Rule Bargaining 23011.4.2 Open-Rule Bargaining 23211.5 Summary 23511.6 Exercises 236PART 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 24912.2 Examples 25212.2.1 Teenagers and the Game of Chicken 25212.2.2 Study Groups 25512.3 Inefficient Trade and Adverse Selection 25812.4 Committee Voting 26112.5 Mixed Strategies Revisited: Harsanyi's Interpretation 26412.6 Summary 26612.7 Exercises 266Chapter 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 27913.2 Common Values and the Winner's Curse 28213.3 Summary 28513.4 Exercises 285Chapter 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 29014.2 The Revelation Principle 29214.3 Dominant Strategies and Vickrey-Clarke-Groves Mechanisms 29514.3.1 Dominant Strategy Implementation 29514.3.2 Vickrey-Clarke-Groves Mechanisms 29514.4 Summary 29914.5 Exercises 299PART V Dynamic Games of Incomplete Information Chapter 15 Sequential Rationality with Incomplete Information 303 15.1 The Problem with Subgame Perfection 30315.2 Perfect Bayesian Equilibrium 30715.3 Sequential Equilibrium 31215.4 Summary 31415.5 Exercises 314Chapter 16 Signaling Games 318 16.1 Education Signaling: The MBA Game 31916.2 Limit Pricing and Entry Deterrence 32316.2.1 Separating Equilibria 32416.2.2 Pooling Equilibria 33016.3 Refinements of Perfect Bayesian Equilibrium in Signaling Games 33216.4 Summary 33516.5 Exercises 335Chapter 17 Building a Reputation 339 17.1 Cooperation in a Finitely Repeated Prisoner's Dilemma 33917.2 Driving a Tough Bargain 34217.3 A Reputation for Being "Nice" 34917.4 Summary 35417.5 Exercises 354Chapter 18 Information Transmission and Cheap Talk 357 18.1 Information Transmission: A Finite Example 35818.2 Information Transmission: The Continuous Case 36118.3 Application: Information and Legislative Organization 36518.4 Summary 36718.5 Exercises 367Chapter 19 Mathematical Appendix 369 19.1 Sets and Sequences 36919.1.1 Basic Definitions 36919.1.2 Basic Set Operations 37019.2 Functions 37119.2.1 Basic Definitions 37119.2.2 Continuity 37219.3 Calculus and Optimization 37319.3.1 Basic Definitions 37319.3.2 Differentiation and Optimization 37419.3.3 Integration 37719.4 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 Return to Book DescriptionFile created: 4/21/2017 Questions and comments to: webmaster@press.princeton.eduPrinceton University Press