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Watson_FM_i-xvi_hr.indd THIRD EDITION STRATEGY Joel Watson STRATEGY Third Edition Watson_FM_i-xvi_hr.indd 1 4/9/13 12:55 PM Third Edition B W. W. NORTON & COMPANY new york • london STRATEGY AN INTRODUCTION TO GAME THEORY JOEL WATSON University of California, San Diego Watson_FM_i-xvi_hr.indd 3 4/9/13 12:55 PM W. W. Norton & Company has been independent since its founding in 1923, when William Warder Norton and Mary D. Herter Norton first published lectures delivered at the People’s Institute, the adult education division of New York City’s Cooper Union. The firm soon expanded its program beyond the Institute, publishing books by celebrated academics from America and abroad. By midcentury, the two major pillars of Norton’s publishing program—trade books and college texts—were firmly established. In the 1950s, the Norton family transferred control of the company to its employees, and today—with a staff of four hundred and a comparable number of trade, college, and professional titles published each year—W. W. Norton & Company stands as the largest and oldest publishing house owned wholly by its employees. Editor: Jack Repcheck Assistant Editor: Hannah Bachman Manuscript Editor: Christopher Curioli Project Editor: Rachel Mayer Electronic Media Editor: Cassie del Pilar Marketing Manager: John Kresse Production Manager: Ashley Horna Text Design: Joan Greenfield Art Director: Rubina Yeh Composition: cMPreparé Manufacturing: Sheridan Books, Inc. Copyright © 2013, 2008, 2002 by Joel Watson All rights reserved. Printed in the United States of America. Library of Congress Cataloging-in-Publication Data has been applied for. ISBN 978-0-393-91838-0 W. W. Norton & Company, Inc., 500 Fifth Avenue, New York, NY 10110-0017 wwnorton.com W. W. Norton & Company Ltd., Castle House, 75/76 Wells Street, London W1T 3QT 1 2 3 4 5 6 7 8 9 0 Watson_FM_i-xvi_hr2.indd 4 4/19/13 10:50 AM This book is dedicated, with thanks, to Rosemary Watson. Watson_FM_i-xvi_hr.indd 5 4/9/13 12:56 PM Watson_FM_i-xvi_hr.indd 6 4/9/13 12:56 PM vii PREFACE xiii 1 INTRODUCTION 1 Noncooperative Game Theory 3 Contract and Cooperative Game Theory 4 The Meaning of “Game” 5 PART I: REPRESENTATIONS AND BASIC ASSUMPTIONS 7 2 THE EXTENSIVE FORM 9 Other Examples and Conventions 15 Guided Exercise 17 Exercises 18 3 STRATEgIES AND THE NORMAL FORM 22 Terminology and Notation for Strategies 23 The Normal Form 26 Classic Normal-Form Games 28 Interpretation of the Normal Form 30 Guided Exercise 31 Exercises 33 4 BELIEFS, MIXED STRATEgIES, AND EXPECTED PAYOFFS 37 Guided Exercise 39 Exercises 40 CONTENTS* * Chapters in italics are applications chapters. Watson_FM_i-xvi_hr.indd 7 4/9/13 12:56 PM viii Contents 5 gENERAL ASSUMPTIONS AND METHODOLOgY 42 Rationality 43 Common Knowledge 44 Overview of Solution Concepts 45 The Issue of Realism 46 PART II: ANALYZING BEHAVIOR IN STATIC SETTINGS 47 6 DOMINANCE AND BEST RESPONSE 49 Dominance 49 The First Strategic Tension and the Prisoners’ Dilemma 52 The Concept of Efficiency 53 Best Response 54 Dominance and Best Response Compared 57 Weak Dominance 60 Guided Exercise 61 Exercises 63 7 RATIONALIZABILITY AND ITERATED DOMINANCE 67 The Second Strategic Tension 71 Guided Exercise 73 Exercises 74 8 LOCATION, PARTNERSHIP, AND SOCIAL UNREST 78 A Location Game 78 A Partnership Game: Strategic Complementarities 81 Social Unrest 87 Guided Exercise 90 Exercises 91 9 NASH EQUILIBRIUM 95 Nash Equilibrium 97 Equilibrium of the Partnership Game 100 Coordination and Social Welfare 101 Watson_FM_i-xvi_hr.indd 8 4/9/13 12:56 PM ixContents The Third Strategic Tension 104 Congruous Sets 104 Aside: Experimental Game Theory 106 Guided Exercise 107 Exercises 108 10 OLIGOPOLY, TARIFFS, CRIME, AND VOTING 113 Cournot Duopoly Model 113 Bertrand Duopoly Model 115 Tariff Setting by Two Countries 117 A Model of Crime and Police 118 The Median Voter Theorem 118 Strategic Voting 120 Guided Exercise 123 Exercises 124 11 MIXED-STRATEgY NASH EQUILIBRIUM 132 Randomization in Sports 135 Technical Notes 136 Example: Duopoly with Capacity Constraints 137 Guided Exercise 140 Exercises 140 12 STRICTLY COMPETITIVE gAMES AND SECURITY STRATEgIES 148 Guided Exercise 151 Exercises 152 13 CONTRACT, LAW, AND ENFORCEMENT IN STATIC SETTINgS 154 Complete Contracting in Discretionary Environments 158 Contracting with Court-Imposed Breach Remedies 161 Guided Exercise 166 Exercises 167 Watson_FM_i-xvi_hr.indd 9 4/9/13 12:56 PM x Contents PART III: ANALYZING BEHAVIOR IN DYNAMIC SETTINGS 173 14 DETAILS OF THE EXTENSIVE FORM 175 Recalling the Strategy Definition 179 Guided Exercise 180 Exercises 181 15 SEQUENTIAL RATIONALITY AND SUBgAME PERFECTION 183 Incredible Threats in the Stackelberg Duopoly Game 184 Sequential Rationality 185 Backward Induction 186 Subgame Perfection 188 The SPE of the Stackelberg Duopoly Game 191 Technical Notes 192 Conditional Dominance and Forward Induction 195 Guided Exercise 198 Exercises 199 16 TOPICS IN INDUSTRIAL ORGANIZATION 204 Advertising and Competition 204 A Model of Limit Capacity 206 Dynamic Monopoly 209 Price Guarantees as a Commitment to High Prices 213 Dynamic Price Competition with Capacity Constraints 215 Guided Exercise 217 Exercises 219 17 PARLOR gAMES 224 Guided Exercise 226 Exercises 226 18 BARgAININg PROBLEMS 230 Bargaining: Value Creation and Division 230 An Abstract Representation of Bargaining Problems 232 An Example 234 The Standard Bargaining Solution 236 A Note About Legal Default Rules 238 Guided Exercise 240 Exercises 241 Watson_FM_i-xvi_hr.indd 10 4/9/13 12:56 PM xiContents 19 ANALYSIS OF SIMPLE BARGAINING GAMES 244 Ultimatum Games: Power to the Proposer 244 Two-Period, Alternating-Offer Games: Power to the Patient 246 Infinite-Period, Alternating-Offer Game 250 Multilateral Bargaining 251 Guided Exercise 254 Exercises 255 20 GAMES WITH JOINT DECISIONS; NEGOTIATION EQUILIBRIUM 259 Joint Decisions 260 Negotiation Equilibrium 262 Example: Contracting for High-Powered Incentives 263 Guided Exercise 265 Exercises 267 21 UNVERIFIABLE INVESTMENT, HOLD UP, OPTIONS, AND OWNERSHIP 274 Hold-Up Example 275 Up-Front Contracting and Option Contracts 278 Asset Ownership 281 Guided Exercise 283 Exercises 285 22 REPEATED GAMES AND REPUTATION 291 A Two-Period Repeated Game 292 An Infinitely Repeated Game 297 The Equilibrium Payoff Set with Low Discounting 302 Guided Exercise 306 Exercises 307 23 COLLUSION, TRADE AGREEMENTS, AND GOODWILL 311 Dynamic Oligopoly and Collusion 311 Enforcing International Trade Agreements 313 Goodwill and Trading a Reputation 314 Guided Exercise 317 Exercises 318 Watson_FM_i-xvi_hr2.indd 11 4/19/13 10:51 AM xii Contents PART IV: INFORMATION 325 24 RANDOM EVENTS AND INCOMPLETE INFORMATION 327 Guided Exercise 331 Exercises 332 25 RISK AND INCENTIVES IN CONTRACTING 336 Risk Aversion 336 A Principal–Agent Game 340 Guided Exercise 345 Exercises 346 26 BAYESIAN NASH EQUILIBRIUM AND RATIONALIZABILITY 350 Guided Exercise 353 Exercises 354 27 LEMONS, AUCTIONS, AND INFORMATION AGGREGATION 360 Markets and Lemons 360 Auctions 363 Information Aggregation 368 Guided Exercise 373 Exercises 374 28 PERFECT BAYESIAN EQUILIBRIUM 378 Conditional Beliefs about Types 379 Sequential Rationality 380 Consistency of Beliefs 381 Equilibrium Definition 382 Guided Exercise 384 Exercises 386 29 JOB-MARKET SIGNALING AND REPUTATION 392 Jobs and School 392 Reputation and Incomplete Information 395 Guided Exercise 398 Exercises 400 APPENDICES 407 INDEX 477 Watson_FM_i-xvi_hr.indd 12 4/9/13 12:56 PM Game theory has become an enormously important field of study. It is now a vital methodology for researchers and teachers in many disciplines, includ- ing economics, political science, biology, and law. This book provides a thor- ough introduction to the subject and its applications, at the intermediate level of instruction. It is designed for the upper-division game theory courses that are offered in most undergraduate economics programs and also serves graduate students in economics, political science, law, and business who seek a solid and readable introduction to the theory. The book can be a primary or secondary source for graduate courses that have a significant game-theoretic component. I have designed this book in pursuit of the following three ideals: 1. Coverage of the Essential Topics, without Excess. This book covers the basic concepts and insights of game-theoretic reasoning, along with classic examples and applications, without being overblown. The entire book can be digested in a semester course. Thus, instructors will not have to worry about having their students skipping or bouncing between chapters as much as is the case with most other textbooks. In terms of content, the book’s major innovation is that it integrates an analysis of contract in the devel- opment of the theory. Research on contract has blossomed in the past few decades and, in my experience, students are keenly interested in this impor- tant game-theoretic topic. This book offers one of the first substantive treat- ments of contract at the intermediate level, without bending too far from standard game theory coverage. 2. Proper Mathematics without Complication. This book does not skimp on mathematical precision. However, each concept and application presented here is developed using the simplest, most straightforward model that I could find. In other words, the book emphasizes mathematically rigorous analysis of simple examples rather than complicated or incomplete analysis of general models. This facilitates the reader’s understanding of key ideas without getting bogged down in unnecessary mathematical formalism. 3. Relaxed Style. This book is written in a style that is lively and not overly formal. PREFACE Watson_FM_i-xvi_hr.indd 13 4/9/13 12:56 PM xiv Preface The book is also class-tested. It grew out of the undergraduate game theory course that I teach and has been developed and fine-tuned over the past decade. I used preliminary versions of the book for my game theory courses at the University of California, San Diego, and at Yale University. It was class-tested at Stanford University by Steven Tadelis, at the University of Michigan by Ennio Stacchetti, and at New York University by Charles Wilson. The first edition of the book was adopted for courses at numerous universities. I also have made it available as a supplemental textbook for my graduate game theory courses, including courses in the core microeconomics sequence. The journey to final, published book was carefully guided by comments from professors, reviewers, colleagues, and—to a significant extent—students. I am proud to report that the comments from students have been overwhelmingly positive. The text is organized into four parts. Part I introduces the standard ways of representing games and carefully defines and illustrates the concepts of strategy and belief. Because the concept of strategy is so important, and because students who fail to grasp it inevitably sink deeper into confusion later on, I begin the formal part of the book with a nontechnical discussion of the extensive form. The material in Part I can be covered in just a couple of lectures, and it is an investment that pays great dividends later. Part II presents the concepts used to analyze static settings. Part III surveys