Game Theory (ebook)

Argumento de Game Theory (ebook)

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

"The book aims to be precise and rigorous, yet accessible and reader-friendly, and, to a great extent, it does hit these apparently conflicting targets. . . . The depth of the book is intermediate, with a conventional, yet clear, style of writing. It will please mainstream economists. . . . It can help advanced undergraduates and also students at honors or master's levels. It can also be used by PhD students seeking a fast, not so mathematized introduction to the field."--Jose Rodriques-Neto, Economic Record

"Steve Tadelis's Game Theory is an ideal textbook for advanced undergraduates, and great preparation for graduate work. It provides a clear, self-contained, and rigorous treatment of all the key concepts, along with interesting applications; it also introduces key technical tools in a straightforward and intuitive way."--Drew Fudenberg, Harvard University

"Steven Tadelis is a leading scholar in applied game theory, and his expertise shines through in this excellent new text. Aimed at intermediate to advanced undergraduates, it presents and discusses the theory remarkably clearly, at both the intuitive and formal levels. One novel feature I like is its serious consideration of the decision theoretic foundations of game theory. Another is its transparent presentation of relatively recent topics and applications, such as reputations in asymmetric information games, legislative bargaining, and cheap talk communication."--Steve Matthews, University of Pennsylvania

"Steve Tadelis has written an up-to-date, comprehensive, yet reader-friendly introductory textbook to game theory. He explains difficult concepts in an exceptionally clear and simple way, making the book accessible to students with a minimal background in mathematics. The abundance of examples and illustrations, drawing from economics, political science, and business strategy, not only shows the wide range of applications of game theory, but also makes the book attractive and fun to read. Tadelis's book will undoubtedly become a reference textbook for a first course in game theory."--Francis Bloch, école Polytechnique

"These days, game theory plays an essential role not only in economics, but in many other branches of social and engineering science, as well as philosophy, biology, psychology, even law. In all these disciplines, students and instructors alike should welcome this excellent resource for mastering the key tools of modern game theory."--Peter Hammond, University of Warwick

"It's hard to write a game theory textbook that strikes a good balance between precision and accessibility. But Steve Tadelis has accomplished this juggling act, with style and humor besides."--Eric S. Maskin, Nobel Laureate in Economics, Harvard University

"Game theory is a powerful tool for understanding strategic behavior in business, politics, and other settings. Steve Tadelis's text provides an ideal guide, taking you from first principles of decision theory to models of bargaining, auctions, signaling, and reputation building in a style that is both rigorous and reader-friendly."--Jonathan Levin, Stanford University

"Game Theory fills a void in the literature, serving as a text for an advanced undergraduate--or masters-level class. It has more detail than most undergraduate texts, while still being accessible to a broad audience and stopping short of the more technical approach of PhD-level texts. This is a valuable book, written by a meticulous scholar who is an expert in the field."--Matthew O. Jackson, author of Social and Economic Networks

"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 University0Preface 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 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 Game 159
  8.3.2 Stackelberg Competition 160
  8.3.3 Mutually Assured Destruction 163
  8.3.4 Time-Inconsistent Preferences 166
  
• 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 Payoffs 193
  10.2.2 Strategies 195
  
• 10.3 Subgame-Perfect Equilibria 196
  
• 10.4 Application: Tacit Collusion 201
  
• 10.5 Sequential Interaction and Reputation 204
  10.5.1 Cooperation as Reputation 204
  10.5.2 Third-Party Institutions as Reputation Mechanisms 205
  10.5.3 Reputation Transfers without Third Parties 207
  
• 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 Bargaining 230
  11.4.2 Open-Rule Bargaining 232
  
• 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 Preferences 246
  12.1.2 Deriving Posteriors from a Common Prior: A Player's Beliefs 247
  12.1.3 Strategies and Bayesian Nash Equilibrium 249
  
• 12.2 Examples 252
  12.2.1 Teenagers and the Game of Chicken 252
  12.2.2 Study Groups 255
  
• 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 Auctions 272
  13.1.2 English Auctions 275
  13.1.3 First-Price Sealed-Bid and Dutch Auctions 276
  13.1.4 Revenue Equivalence 279
  
• 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 Players 288
  14.1.2 The Mechanism Designer 289
  14.1.3 The Mechanism Game 290
  
• 14.2 The Revelation Principle 292
  
• 14.3 Dominant Strategies and Vickrey-Clarke-Groves Mechanisms 295
  14.3.1 Dominant Strategy Implementation 295
  14.3.2 Vickrey-Clarke-Groves Mechanisms 295
  
• 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 Equilibria 324
  16.2.2 Pooling Equilibria 330
  
• 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 Definitions 369
  19.1.2 Basic Set Operations 370
  
• 19.2 Functions 371
  19.2.1 Basic Definitions 371
  19.2.2 Continuity 372
  
• 19.3 Calculus and Optimization 373
  19.3.1 Basic Definitions 373
  19.3.2 Differentiation and Optimization 374
  19.3.3 Integration 377
  
• 19.4 Probability and Random Variables 378
  19.4.1 Basic Definitions 378
  19.4.2 Cumulative Distribution and Density Functions 379
  19.4.3 Independence, Conditional Probability, and Bayes' Rule 380
  19.4.4 Expected Values 382
  

References 385
Index 389