Watson_FM_i-xvi_hr.indd
THIRD EDITION
XXXXXXXXXXSTRATEGY
XXXXXXXXXXJoel Watson
STRATEGY
Third Edition
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Third Edition
B
W. W. NORTON & COMPANY
new york • london
STRATEGY
AN INTRODUCTION TO GAME THEORY
JOEL WATSON
University of California, San Diego
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W. W. Norton & Company has been independent since its founding in 1923, when William Warder Norton and Mary D. Herter
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Copyright © 2013, 2008, 2002 by Joel Watson
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This book is dedicated, with thanks, to
Rosemary Watson.
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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.
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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 Equili
ium 97
Equili
ium of the Partnership Game 100
Coordination and Social Welfare 101
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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
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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
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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 Equili
ium 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 Equili
ium 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
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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
Equili
ium 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
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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
eadable 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
asic concepts and insights of game-theoretic reasoning, along with classic
examples and applications, without being ove
lown. The entire book can
e digested in a semester course. Thus, instructors will not have to wo
y
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
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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
epresenting 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