Game Theory

The definitive introduction to game theory

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 Theory is 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

Auteur

Steven Tadelis

Résumé
The definitive introduction to game theoryThis 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 Theory is 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 theoryCovers static and dynamic games, with complete and incomplete informationFeatures a variety of examples, applications, and exercisesTopics include repeated games, bargaining, auctions, signaling, reputation, and information transmissionIdeal for advanced undergraduate and beginning graduate studentsComplete solutions available to teachers and selected solutions available to students

Contenu

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 7
• 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 Case 19
  2.2.2 Expected Payoff: The Continuous Case 20
  2.2.3 Caveat: It's Not Just the Order Anymore 21
  2.2.4 Risk Attitudes 22
  2.2.5 The St. Petersburg Paradox 23
• 2.3 Rational Decision Making with Uncertainty 24
  2.3.1 Rationality Revisited 24
  2.3.2 Maximizing Expected Payoffs 24
• 2.4 Decisions over Time 26
  2.4.1 Backward Induction 26
  2.4.2 Discounting Future Payoffs 28
• 2.5 Applications 29
  2.5.1 The Value of Information 29
  2.5.2 Discounted Future Consumption 31
• 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 Dilemma 48
  3.1.2 Example: Cournot Duopoly 49
  3.1.3 Example: Voting on a New Agenda 49
• 3.2 Matrix Representation: Two-Player Finite Game 50
  3.2.1 Example: The Prisoner's Dilemma 51
  3.2.2 Example: Rock-Paper-Scissors 52
• 3.3 Solution Concepts 52
  3.3.1 Assumptions and Setup 54
  3.3.2 Evaluating Solution Concepts 55
  3.3.3 Evaluating Outcomes 56
• 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 Strategies 59
  4.1.2 Dominant Strategy Equilibrium 61
  4.1.3 Evaluating Dominant Strategy Equilibrium 62
• 4.2 Iterated Elimination of Strictly Dominated Pure Strategies 63
  4.2.1 Iterated Elimination and Common Knowledge of Rationality 63
  4.2.2 Example: Cournot Duopoly 65
  4.2.3 Evaluating IESDS 67
• 4.3 Beliefs, Best Response, and Rationalizability 69
  4.3.1 The Best Response 69
  4.3.2 Beliefs and Best-Response Correspondences 71
  4.3.3 Rationalizability 73
  4.3.4 The Cournot Duopoly Revisited 73
  4.3.5 The "p-Beauty Contest" 74
  4.3.6 Evaluating Rationalizability 76
• 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 Matrix 81
  5.1.2 Evaluating the Nash Equilibria Solution 83
• 5.2 Nash Equilibrium: Some Classic Applications 83
  5.2.1 Two Kinds of Societies 83
  5.2.2 The Tragedy of the Commons 84
  5.2.3 Cournot Duopoly 87
  5.2.4 Bertrand Duopoly 88
  5.2.5 Political Ideology and Electoral Competition 93
• 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 Sets 102
  6.1.2 Continuous Strategy Sets 104
  6.1.3 Beliefs and Mixed Strategies 105
  6.1.4 Expected Payoffs 105
• 6.2 Mixed-Strategy Nash Equilibrium 107
  6.2.1 Example: Matching Pennies 108
  6.2.2 Example: Rock-Paper-Scissors 111
  6.2.3 Multiple Equilibria: Pure and Mixed 113
• 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 Trees 132
  7.1.2 Imperfect versus Perfect Information 136
• 7.2 Strategies and Nash Equilibrium 137
  7.2.1 Pure Strategies 137
  7.2.2 Mixed versus Behavioral Strategies 139
  7.2.3 Normal-Form Representation of Extensive-Form Games 143
• 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 Sequentia…