Game theory : an introduction

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. -- From Back Cover. Part I: Rational Decision Making. The Single-person Decision Problem -- Introducing Uncertainty And Time -- Part Ii: Static Games Of Complete Information. Preliminaries -- Rationality And Common Knowledge -- Pinning Down Beliefs: Nash Equilibrium -- Mixed Strategies -- Part Iii: Dynamic Games Of Complete Information. Preliminaries -- Credibility And Sequential Rationality -- Multistage Games -- Repeated Games -- Strategic Bargaining -- Part Iv: Static Games Of Incomplete Information. Bayesian Games -- Auctions And Competitive Bidding -- Mechanism Design -- Part V: Dynamic Games Of Incomplete Information. Sequential Rationality With Incomplete Information -- Signaling Games -- Building A Reputation -- Information Transmission And Cheap Talk -- Mathematical Appendix. Steven Tadelis. Includes Bibliographical References (p. 385-388) And Index. Cover......Page 1 GAME THEORY......Page 4 Title......Page 6 Copyright......Page 7 Contents......Page 8 Preface......Page 14 PART I Rational Decision Making......Page 20 Chapter 1 The Single-Person Decision Problem......Page 22 1.1 Actions, Outcomes, and Preferences......Page 23 1.1.1 Preference Relations......Page 24 1.1.2 Payoff Functions......Page 26 1.2 The Rational Choice Paradigm......Page 28 1.3 Summary......Page 30 2.1 Risk, Nature, and Random Outcomes......Page 33 2.1.1 Finite Outcomes and Simple Lotteries......Page 34 2.1.2 Simple versus Compound Lotteries......Page 35 2.1.3 Lotteries over Continuous Outcomes......Page 36 2.2 Evaluating Random Outcomes......Page 37 2.2.1 Expected Payoff: The Finite Case......Page 38 2.2.2 Expected Payoff: The Continuous Case......Page 39 2.2.3 Caveat: It’s Not Just the Order Anymore......Page 40 2.2.4 Risk Attitudes......Page 41 2.2.5 The St. Petersburg Paradox......Page 42 2.3.2 Maximizing Expected Payoffs......Page 43 2.4.1 Backward Induction......Page 45 2.4.2 Discounting Future Payoffs......Page 47 2.5.1 The Value of Information......Page 48 2.5.2 Discounted Future Consumption......Page 50 2.6 Theory versus Practice......Page 51 2.8 Exercises......Page 52 PART II Static Games of Complete Information......Page 60 Chapter 3 Preliminaries......Page 62 3.1 Normal-Form Games with Pure Strategies......Page 65 3.1.1 Example: The Prisoner’s Dilemma......Page 67 3.1.3 Example: Voting on a New Agenda......Page 68 3.2 Matrix Representation: Two-Player Finite Game......Page 69 3.2.1 Example: The Prisoner’s Dilemma......Page 70 3.3 Solution Concepts......Page 71 3.3.1 Assumptions and Setup......Page 73 3.3.2 Evaluating Solution Concepts......Page 74 3.3.3 Evaluating Outcomes......Page 75 3.4 Summary......Page 76 3.5 Exercises......Page 77 4.1.1 Dominated Strategies......Page 78 4.1.2 Dominant Strategy Equilibrium......Page 80 4.1.3 Evaluating Dominant Strategy Equilibrium......Page 81 4.2.1 Iterated Elimination and Common Knowledge of Rationality......Page 82 4.2.2 Example: Cournot Duopoly......Page 84 4.2.3 Evaluating IESDS......Page 86 4.3.1 The Best Response......Page 88 4.3.2 Beliefs and Best-Response Correspondences......Page 90 4.3.4 The Cournot Duopoly Revisited......Page 92 4.3.5 The “p-Beauty Contest”......Page 93 4.5 Exercises......Page 95 Chapter 5 Pinning Down Beliefs: Nash Equilibrium......Page 98 5.1 Nash Equilibrium in Pure Strategies......Page 99 5.1.1 Pure-Strategy Nash Equilibrium in a Matrix......Page 100 5.2.1 Two Kinds of Societies......Page 102 5.2.2 The Tragedy of the Commons......Page 103 5.2.3 Cournot Duopoly......Page 106 5.2.4 Bertrand Duopoly......Page 107 5.2.5 Political Ideology and Electoral Competition......Page 112 5.4 Exercises......Page 114 Chapter 6 Mixed Strategies......Page 120 6.1.1 Finite Strategy Sets......Page 121 6.1.2 Continuous Strategy Sets......Page 123 6.1.4 Expected Payoffs......Page 124 6.2 Mixed-Strategy Nash Equilibrium......Page 126 6.2.1 Example: Matching Pennies......Page 127 6.2.2 Example: Rock-Paper-Scissors......Page 130 6.2.3 Multiple Equilibria: Pure and Mixed......Page 132 6.3 IESDS and Rationalizability Revisited......Page 133 6.4 Nash’s Existence Theorem......Page 136 6.6 Exercises......Page 142 PART III Dynamic Games of Complete Information......Page 146 Chapter 7 Preliminaries......Page 148 7.1 The Extensive-Form Game......Page 149 7.1.1 Game Trees......Page 151 7.1.2 Imperfect versus Perfect Information......Page 155 7.2.1 Pure Strategies......Page 156 7.2.2 Mixed versus Behavioral Strategies......Page 158 7.2.3 Normal-Form Representation of Extensive-Form Games......Page 162 7.3 Nash Equilibrium and Paths of Play......Page 164 7.5 Exercises......Page 166 Chapter 8 Credibility and Sequential Rationality......Page 170 8.1 Sequential Rationality and Backward Induction......Page 171 8.2 Subgame-Perfect Nash Equilibrium: Concept......Page 172 8.3.1 The Centipede Game......Page 178 8.3.2 Stackelberg Competition......Page 179 8.3.3 Mutually Assured Destruction......Page 182 8.3.4 Time-Inconsistent Preferences......Page 185 8.4 Summary......Page 188 8.5 Exercises......Page 189 Chapter 9 Multistage Games......Page 194 9.1 Preliminaries......Page 195 9.2 Payoffs......Page 196 9.3 Strategies and Conditional Play......Page 197 9.4 Subgame-Perfect Equilibria......Page 199 9.5 The One-Stage Deviation Principle......Page 203 9.7 Exercises......Page 205 10.1 Finitely Repeated Games......Page 209 10.2 Infinitely Repeated Games......Page 211 10.2.1 Payoffs......Page 212 10.2.2 Strategies......Page 214 10.3 Subgame-Perfect Equilibria......Page 215 10.4 Application: Tacit Collusion......Page 220 10.5.1 Cooperation as Reputation......Page 223 10.5.2 Third-Party Institutions as Reputation Mechanisms......Page 224 10.5.3 Reputation Transfers without Third Parties......Page 226 10.6 The Folk Theorem: Almost Anything Goes......Page 228 10.7 Summary......Page 233 10.8 Exercises......Page 234 Chapter 11 Strategic Bargaining......Page 239 11.1 One Round of Bargaining: The Ultimatum Game......Page 241 11.2 Finitely Many Rounds of Bargaining......Page 243 11.3 The Infinite-Horizon Game......Page 247 11.4 Application: Legislative Bargaining......Page 248 11.4.1 Closed-Rule Bargaining......Page 249 11.4.2 Open-Rule Bargaining......Page 251 11.5 Summary......Page 254 11.6 Exercises......Page 255 PART IV Static Games of Incomplete Information......Page 258 Chapter 12 Bayesian Games......Page 260 12.1.1 Players, Actions, Information, and Preferences......Page 265 12.1.2 Deriving Posteriors from a Common Prior: A Player’s Beliefs......Page 266 12.1.3 Strategies and Bayesian Nash Equilibrium......Page 268 12.2.1 Teenagers and the Game of Chicken......Page 271 12.2.2 Study Groups......Page 274 12.3 Inefficient Trade and Adverse Selection......Page 277 12.4 Committee Voting......Page 280 12.5 Mixed Strategies Revisited: Harsanyi’s Interpretation......Page 283 12.7 Exercises......Page 285 Chapter 13 Auctions and Competitive Bidding......Page 289 13.1.1 Second-Price Sealed-Bid Auctions......Page 291 13.1.2 English Auctions......Page 294 13.1.3 First-Price Sealed-Bid and Dutch Auctions......Page 295 13.1.4 Revenue Equivalence......Page 298 13.2 Common Values and the Winner’s Curse......Page 301 13.4 Exercises......Page 304 14.1.1 The Players......Page 307 14.1.2 The Mechanism Designer......Page 308 14.1.3 The Mechanism Game......Page 309 14.2 The Revelation Principle......Page 311 14.3.2 Vickrey-Clarke-Groves Mechanisms......Page 314 14.5 Exercises......Page 318 PART V Dynamic Games of Incomplete Information......Page 320 15.1 The Problem with Subgame Perfection......Page 322 15.2 Perfect Bayesian Equilibrium......Page 326 15.3 Sequential Equilibrium......Page 331 15.5 Exercises......Page 333 Chapter 16 Signaling Games......Page 337 16.1 Education Signaling: The MBA Game......Page 338 16.2 Limit Pricing and Entry Deterrence......Page 342 16.2.1 Separating Equilibria......Page 343 16.2.2 Pooling Equilibria......Page 349 16.3 Refinements of Perfect Bayesian Equilibrium in Signaling Games......Page 351 16.5 Exercises......Page 354 17.1 Cooperation in a Finitely Repeated Prisoner’s Dilemma......Page 358 17.2 Driving a Tough Bargain......Page 361 17.3 A Reputation for Being “Nice”......Page 368 17.5 Exercises......Page 373 Chapter 18 Information Transmission and Cheap Talk......Page 376 18.1 Information Transmission: A Finite Example......Page 377 18.2 Information Transmission: The Continuous Case......Page 380 18.3 Application: Information and Legislative Organization......Page 384 18.5 Exercises......Page 386 19.1.1 Basic Definitions......Page 388 19.1.2 Basic Set Operations......Page 389 19.2.1 Basic Definitions......Page 390 19.2.2 Continuity......Page 391 19.3.1 Basic Definitions......Page 392 19.3.2 Differentiation and Optimization......Page 393 19.3.3 Integration......Page 396 19.4.1 Basic Definitions......Page 397 19.4.2 Cumulative Distribution and Density Functions......Page 398 19.4.3 Independence, Conditional Probability, and Bayes’ Rule......Page 399 19.4.4 Expected Values......Page 401 References......Page 404 Index......Page 408 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 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. It introduces the core ideas and applications of game theory. It covers static and dynamic games, with complete and incomplete information. It features a variety of examples, applications, and exercises. Topics include repeated games, bargaining, auctions, signaling, reputation, and information transmission. It is ideal for advanced undergraduate and beginning graduate students. Complete solutions available to teachers and selected solutions available to students Suitable for advanced undergraduate and beginning graduate students, this title introduces readers to the principal ideas and applications of game theory. It covers static and dynamic games, with complete and incomplete information and features a variety of examples, applications, and exercises.