Game Theory: An Introduction by Steven TadelisGame Theory: An Introduction by Steven Tadelis

Game Theory: An Introduction

bySteven Tadelis

Hardcover | January 6, 2013

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This comprehensive textbook introduces readers to the principal ideas and applications of game theory, in a style that combines rigor with accessibility. Steven Tadelis begins with a concise description of rational decision making, and goes on to discuss strategic and extensive form games with complete information, Bayesian games, and extensive form games with imperfect information. He covers a host of topics, including multistage and repeated games, bargaining theory, auctions, rent-seeking games, mechanism design, signaling games, reputation building, and information transmission games. Unlike other books on game theory, this one begins with the idea of rationality and explores its implications for multiperson decision problems through concepts like dominated strategies and rationalizability. Only then does it present the subject of Nash equilibrium and its derivatives.



Game Theoryis the ideal textbook for advanced undergraduate and beginning graduate students. Throughout, concepts and methods are explained using real-world examples backed by precise analytic material. The book features many important applications to economics and political science, as well as numerous exercises that focus on how to formalize informal situations and then analyze them.


  • Introduces the core ideas and applications of game theory

  • Covers static and dynamic games, with complete and incomplete information

  • Features a variety of examples, applications, and exercises

  • Topics include repeated games, bargaining, auctions, signaling, reputation, and information transmission

  • Ideal for advanced undergraduate and beginning graduate students

  • Complete solutions available to teachers and selected solutions available to students

Steven Tadelisis associate professor and Barbara and Gerson Bakar Faculty Fellow at the Haas School of Business at the University of California, Berkeley, and a Distinguished Economist at eBay Research Labs.
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Title:Game Theory: An IntroductionFormat:HardcoverDimensions:416 pagesPublished:January 6, 2013Publisher:Princeton University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0691129088

ISBN - 13:9780691129082

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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 Relations5

  • 1.1.2 Payoff Functions7

  • 1.2 The Rational Choice Paradigm 9

  • 1.3 Summary 11

  • 1.4 Exercises 11






Chapter 2 Introducing Uncertainty and Time 14


  • 2.1 Risk, Nature, and Random Outcomes 14
    2.1.1 Finite Outcomes and Simple Lotteries 15
    2.1.2 Simple versus Compound Lotteries 16
    2.1.3 Lotteries over Continuous Outcomes 17

  • 2.2 Evaluating Random Outcomes 18
    2.2.1 Expected Payoff: The Finite Case19
    2.2.2 Expected Payoff: The Continuous Case20
    2.2.3 Caveat: It's Not Just the Order Anymore21
    2.2.4 Risk Attitudes22
    2.2.5 The St. Petersburg Paradox23

  • 2.3 Rational Decision Making with Uncertainty 24
    2.3.1 Rationality Revisited24
    2.3.2 Maximizing Expected Payoffs24

  • 2.4 Decisions over Time 26
    2.4.1 Backward Induction26
    2.4.2 Discounting Future Payoffs28

  • 2.5 Applications 29
    2.5.1 The Value of Information29
    2.5.2 Discounted Future Consumption31

  • 2.6 Theory versus Practice 32

  • 2.7 Summary 33

  • 2.8 Exercises 33





PART II Static Games of Complete Information

Chapter 3 Preliminaries 43


  • 3.1 Normal-Form Games with Pure Strategies 46
    3.1.1 Example: The Prisoner's Dilemma48
    3.1.2 Example: Cournot Duopoly49
    3.1.3 Example: Voting on a New Agenda49

  • 3.2 Matrix Representation: Two-Player Finite Game 50
    3.2.1 Example: The Prisoner's Dilemma51
    3.2.2 Example: Rock-Paper-Scissors52

  • 3.3 Solution Concepts 52
    3.3.1 Assumptions and Setup54
    3.3.2 Evaluating Solution Concepts55
    3.3.3 Evaluating Outcomes56

  • 3.4 Summary 57

  • 3.5 Exercises 58






Chapter 4 Rationality and Common Knowledge 59


  • 4.1 Dominance in Pure Strategies 59
    4.1.1 Dominated Strategies59
    4.1.2 Dominant Strategy Equilibrium61
    4.1.3 Evaluating Dominant Strategy Equilibrium62

  • 4.2 Iterated Elimination of Strictly Dominated Pure Strategies 63
    4.2.1 Iterated Elimination and Common Knowledge of Rationality63
    4.2.2 Example: Cournot Duopoly65
    4.2.3 Evaluating IESDS67

  • 4.3 Beliefs, Best Response, and Rationalizability 69
    4.3.1 The Best Response69
    4.3.2 Beliefs and Best-Response Correspondences71
    4.3.3 Rationalizability73
    4.3.4 The Cournot Duopoly Revisited73
    4.3.5 The "p-Beauty Contest"74
    4.3.6 Evaluating Rationalizability76

  • 4.4 Summary 76

  • 4.5 Exercises 76





Chapter 5 Pinning Down Beliefs: Nash Equilibrium 79


  • 5.1 Nash Equilibrium in Pure Strategies 80
    5.1.1 Pure-Strategy Nash Equilibrium in a Matrix81
    5.1.2 Evaluating the Nash Equilibria Solution83

  • 5.2 Nash Equilibrium: Some Classic Applications 83
    5.2.1 Two Kinds of Societies83
    5.2.2 The Tragedy of the Commons84
    5.2.3 Cournot Duopoly87
    5.2.4 Bertrand Duopoly88
    5.2.5 Political Ideology and Electoral Competition93

  • 5.3 Summary 95

  • 5.4 Exercises 95





Chapter 6 Mixed Strategies 101


  • 6.1 Strategies, Beliefs, and Expected Payoffs 102
    6.1.1 Finite Strategy Sets102
    6.1.2 Continuous Strategy Sets104
    6.1.3 Beliefs and Mixed Strategies105
    6.1.4 Expected Payoffs105

  • 6.2 Mixed-Strategy Nash Equilibrium 107
    6.2.1 Example: Matching Pennies108
    6.2.2 Example: Rock-Paper-Scissors111
    6.2.3 Multiple Equilibria: Pure and Mixed113

  • 6.3 IESDS and Rationalizability Revisited 114

  • 6.4 Nash's Existence Theorem 117

  • 6.5 Summary 123

  • 6.6 Exercises 123






PART III Dynamic Games of Complete Information

Chapter 7 Preliminaries 129


  • 7.1 The Extensive-Form Game 130
    7.1.1 Game Trees132
    7.1.2 Imperfect versus Perfect Information136

  • 7.2 Strategies and Nash Equilibrium 137
    7.2.1 Pure Strategies137
    7.2.2 Mixed versus Behavioral Strategies139
    7.2.3 Normal-Form Representation of Extensive-Form Games143

  • 7.3 Nash Equilibrium and Paths of Play 145

  • 7.4 Summary 147

  • 7.5 Exercises 147






Chapter 8 Credibility and Sequential Rationality 151


  • 8.1 Sequential Rationality and Backward Induction 152

  • 8.2 Subgame-Perfect Nash Equilibrium: Concept 153

  • 8.3 Subgame-Perfect Nash Equilibrium: Examples 159
    8.3.1 The Centipede Game159
    8.3.2 Stackelberg Competition160
    8.3.3 Mutually Assured Destruction163
    8.3.4 Time-Inconsistent Preferences166

  • 8.4 Summary 169

  • 8.5 Exercises 170






Chapter 9 Multistage Games 175


  • 9.1 Preliminaries 176

  • 9.2 Payoffs 177

  • 9.3 Strategies and Conditional Play 178

  • 9.4 Subgame-Perfect Equilibria 180

  • 9.5 The One-Stage Deviation Principle 184

  • 9.6 Summary 186

  • 9.7 Exercises 186






Chapter 10 Repeated Games 190


  • 10.1 Finitely Repeated Games 190

  • 10.2 Infinitely Repeated Games 192
    10.2.1 Payoffs193
    10.2.2 Strategies195

  • 10.3 Subgame-Perfect Equilibria 196

  • 10.4 Application: Tacit Collusion 201

  • 10.5 Sequential Interaction and Reputation 204
    10.5.1 Cooperation as Reputation204
    10.5.2 Third-Party Institutions as Reputation Mechanisms205
    10.5.3 Reputation Transfers without Third Parties207

  • 10.6 The Folk Theorem: Almost Anything Goes 209

  • 10.7 Summary 214

  • 10.8 Exercises 215






Chapter 11 Strategic Bargaining 220


  • 11.1 One Round of Bargaining: The Ultimatum Game 222

  • 11.2 Finitely Many Rounds of Bargaining 224

  • 11.3 The Infinite-Horizon Game 228

  • 11.4 Application: Legislative Bargaining 229
    11.4.1 Closed-Rule Bargaining230
    11.4.2 Open-Rule Bargaining232

  • 11.5 Summary 235

  • 11.6 Exercises 236






PART IV Static Games of Incomplete Information

Chapter 12 Bayesian Games 241


  • 12.1 Strategic Representation of Bayesian Games 246
    12.1.1 Players, Actions, Information, and Preferences246
    12.1.2 Deriving Posteriors from a Common Prior: A Player's Beliefs247
    12.1.3 Strategies and Bayesian Nash Equilibrium249

  • 12.2 Examples 252
    12.2.1 Teenagers and the Game of Chicken252
    12.2.2 Study Groups255

  • 12.3 Inefficient Trade and Adverse Selection 258

  • 12.4 Committee Voting 261

  • 12.5 Mixed Strategies Revisited: Harsanyi's Interpretation 264

  • 12.6 Summary 266

  • 12.7 Exercises 266






Chapter 13 Auctions and Competitive Bidding 270


  • 13.1 Independent Private Values 272
    13.1.1 Second-Price Sealed-Bid Auctions272
    13.1.2 English Auctions275
    13.1.3 First-Price Sealed-Bid and Dutch Auctions276
    13.1.4 Revenue Equivalence279

  • 13.2 Common Values and the Winner's Curse 282

  • 13.3 Summary 285

  • 13.4 Exercises 285






Chapter 14 Mechanism Design 288


  • 14.1 Setup: Mechanisms as Bayesian Games 288
    14.1.1 The Players288
    14.1.2 The Mechanism Designer289
    14.1.3 The Mechanism Game290

  • 14.2 The Revelation Principle 292

  • 14.3 Dominant Strategies and Vickrey-Clarke-Groves Mechanisms 295
    14.3.1 Dominant Strategy Implementation295
    14.3.2 Vickrey-Clarke-Groves Mechanisms295

  • 14.4 Summary 299

  • 14.5 Exercises 299






PART V Dynamic Games of Incomplete Information

Chapter 15 Sequential Rationality with Incomplete Information 303


  • 15.1 The Problem with Subgame Perfection 303

  • 15.2 Perfect Bayesian Equilibrium 307

  • 15.3 Sequential Equilibrium 312

  • 15.4 Summary 314

  • 15.5 Exercises 314






Chapter 16 Signaling Games 318


  • 16.1 Education Signaling: The MBA Game 319

  • 16.2 Limit Pricing and Entry Deterrence 323
    16.2.1 Separating Equilibria324
    16.2.2 Pooling Equilibria330

  • 16.3 Refinements of Perfect Bayesian Equilibrium in Signaling Games 332

  • 16.4 Summary 335

  • 16.5 Exercises 335






Chapter 17 Building a Reputation 339


  • 17.1 Cooperation in a Finitely Repeated Prisoner's Dilemma 339

  • 17.2 Driving a Tough Bargain 342

  • 17.3 A Reputation for Being "Nice" 349

  • 17.4 Summary 354

  • 17.5 Exercises 354






Chapter 18 Information Transmission and Cheap Talk 357


  • 18.1 Information Transmission: A Finite Example 358

  • 18.2 Information Transmission: The Continuous Case 361

  • 18.3 Application: Information and Legislative Organization 365

  • 18.4 Summary 367

  • 18.5 Exercises 367






Chapter 19 Mathematical Appendix 369


  • 19.1 Sets and Sequences 369
    19.1.1 Basic Definitions369
    19.1.2 Basic Set Operations370

  • 19.2 Functions 371
    19.2.1 Basic Definitions371
    19.2.2 Continuity372

  • 19.3 Calculus and Optimization 373
    19.3.1 Basic Definitions373
    19.3.2 Differentiation and Optimization374
    19.3.3 Integration377

  • 19.4 Probability and Random Variables 378
    19.4.1 Basic Definitions378
    19.4.2 Cumulative Distribution and Density Functions379
    19.4.3 Independence, Conditional Probability, and Bayes' Rule380
    19.4.4 Expected Values382






References 385
Index 389

Editorial Reviews

"This is a great text, just at the right level for fourth-year undergraduates. The style is just right and the exercises are of high quality. Flow and organization are major strengths of the book-I can follow the text almost as is for the class I teach."-Luca Anderlini, Georgetown University