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
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81
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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 JOINT DECISIONS;
NEGOTIATION EQUILIBRIUM
244
244
246
250
2 51
254
255
259
Joint 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