Strategy An Intro To Game Theory Joel Watson i541h

STRATEGY

AN INTRODUCTION TO GAME THEORY

JOEL WATSON University of California, San Diego

Third Edition

W. W. NORTON & COMPANY NEW YORK • LONDON

CONTENTS*

PREFACE 1 INTRODUCTION Noncooperative Game Theory Contract and Cooperative Game Theory The Meaning of "Game"

PART I: REPRESENTATIONS AND BASIC ASSUMPTIONS 2 THE EXTENSIVE FORM Other Examples and Conventions Guided Exercise Exercises

xiii 1 3 4 5

7 9 15 17 18

3 STRATEGIES AND THE NORMAL FORM

22

Terminology and Notation for Strategies The Normal Form Classic Normal-Form Games Interpretation of the Normal Form Guided Exercise Exercises

23 26 28 30 31 33

4 BELIEFS, MIXED STRATEGIES, AND EXPECTED PAYOFFS Guided Exercise Exercises

37 39 40

* Chapters in italics are applications chapters. vii

viii

Contents 5 GENERAL ASSUMPTIONS AND METHODOLOGY Rationality Common Knowledge Overview of Solution Concepts The Issue of Realism

PART II: ANALYZING BEHAVIOR IN STATIC SETTINGS 6 DOMINANCE AND BEST RESPONSE Dominance The First Strategic Tension and the Prisoners' Dilemma The Concept of Efficiency Best Response Dominance and Best Response Compared Weak Dominance Guided Exercise Exercises 7 RATIONALIZABILITY AND ITERATED DOMINANCE The Second Strategic Tension Guided Exercise Exercises 8 LOCATION, PARTNERSHIP, AND SOCIAL UNREST A Location Game A Partnership Game: Strategic Complementarities Social Unrest Guided Exercise Exercises 9 NASH EQUILIBRIUM Nash Equilibrium Equilibrium of the Partnership Game Coordination and Social Welfare

42 43 44 45 46

47 49 49 52 53 54 57 60 61 63 67 71 73 74 78 7g 81 gy gQ g -j g5

gy 1 QQ n.

Contents The Third Strategic Tension Congruous Sets Aside: Experimental Game Theory Guided Exercise Exercises 10 OLIGOPOLY, TARIFFS, CRIME, AND VOTING Cournot Duopoly Model Bertrand Duopoly Model Tariff Setting by Two Countries A Model of Crime and Police The Median Voter Theorem Strategic Voting Guided Exercise Exercises

104 104 106 107 108 113 113 115 117 118 118 120 123 124

11 MIXED-STRATEGY NASH EQUILIBRIUM

132

Randomization in Sports Technical Notes Example: Duopoly with Capacity Constraints Guided Exercise Exercises

135 136 137 140 140

12 STRICTLY COMPETITIVE GAMES AND SECURITY STRATEGIES Guided Exercise Exercises 13 CONTRACT, LAW, AND ENFORCEMENT IN STATIC SETTINGS Complete Contracting in Discretionary Environments Contracting with Court-Imposed Breach Remedies Guided Exercise Exercises

148 151 152

154 158 161 166 167

ix

X

Contents PART III: ANALYZING BEHAVIOR IN DYNAMIC SETTINGS

173

14 DETAILS OF THE EXTENSIVE FORM

175

Recalling the Strategy Definition Guided Exercise Exercises 15 SEQUENTIAL RATIONALITY AND SUBGAME PERFECTION Incredible Threats in the Stackelberg Duopoly Game Sequential Rationality Backward Induction Subgame Perfection The SPE of the Stackelberg Duopoly Game Technical Notes Conditional Dominance and Forward Induction Guided Exercise Exercises 16 TOPICS IN INDUSTRIAL ORGANIZATION Advertising and Competition A Model of Limit Capacity Dynamic Monopoly Price Guarantees as a Commitment to High Prices Dynamic Price Competition with Capacity Constraints Guided Exercise Exercises 17 PARLOR GAMES Guided Exercise

18 BARGAINING PROBLEMS Bargaining: Value Creation and Division An Abstract Representation of Bargaining Problems An Example The Standard Bargaining Solution A Note About Legal Default Rules Guided Exercise Exercises

179 180 181 183 184 185 186 188 191 192 195 198 199 204 204 206 209 21 3 21 5 217 21 9 224 226 226 230 230 232 234 236 238 240 241

Contents 19 ANALYSIS OF SIMPLE BARGAINING GAMES Ultimatum Games: Power to the Proposer Two-Period, Alternating-Offer Games: Power to the Patient Infinite-Period, Alternating-Offer Game Multilateral B argaining Guided Exercise Exercises 20 GAMES WITH T DECISIONS; NEGOTIATION EQUILIBRIUM

244 244 246 250 2 51 254 255

259

t Decisions Negotiation Equilibrium Example: Contracting for High-Powered Incentives Guided Exercise Exercises

260 262 263 265 267

21 UNVERIFIABLE INVESTMENT, HOLD UP, OPTIONS, AND OWNERSHIP

274

Hold-Up Example Up-Front Contracting and Option Contracts Asset Ownership Guided Exercise Exercises 22 REPEATED GAMES AND REPUTATION A Two-Period Repeated Game An Infinitely Repeated Game The Equilibrium Payoff Set with Low Discounting Guided Exercise Exercises 23 COLLUSION, TRADE AGREEMENTS, AND GOODWILL Dynamic Oligopoly and Collusion Enforcing International Trade Agreements Goodwill and Trading a Reputation Guided Exercise Exercises

275 278 281 283 285 291 292 297 302 306 307 311 311 313 314 317 318

xi

xii

Contents PART IV: INFORMATION

325

24 RANDOM EVENTS AND INCOMPLETE INFORMATION

327

Guided Exercise Exercises 25 RISK AND INCENTIVES IN CONTRACTING Risk Aversion A Principal-Agent Game Guided Exercise Exercises 26 BAYESIAN NASH EQUILIBRIUM AND RATIONALIZABILITY Guided Exercise Exercises 27 LEMONS, AUCTIONS, AND INFORMATION AGGREGATION Markets and Lemons Auctions Information Aggregation Guided Exercise Exercises 28 PERFECT BAYESIAN EQUILIBRIUM Conditional Beliefs about Types Sequential Rationality Consistency of Beliefs Equilibrium Definition Guided Exercise Exercises 29 JOB-MARKET SIGNALING AND REPUTATION Jobs and School Reputation and Incomplete Information Guided Exercise Exercises

331 332 336 336 340 345 346 350 353 354 360 360 363 368 373 374 378 379 380 381 382 3g4 3gg 392 392 395 3gg 4QQ

APPENDICES

407

INDEX

4?7