Table Of ContentAnalyzing Strategic Behavior
in Business and Economics
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Analyzing Strategic Behavior
in Business and Economics
A Game Theory Primer
Thomas J. Webster
Lexington Books
Lanham • Boulder • New York • Toronto • Plymouth, UK
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Published by Lexington Books
A wholly owned subsidiary of Rowman & Littlefield
4501 Forbes Boulevard, Suite 200, Lanham, Maryland 20706
www.rowman.com
10 Thornbury Road, Plymouth PL6 7PP, United Kingdom
Copyright © 2014 by Lexington Books
All rights reserved. No part of this book may be reproduced in any form or by any electronic
or mechanical means, including information storage and retrieval systems, without written
permission from the publisher, except by a reviewer who may quote passages in a review.
British Library Cataloguing in Publication Information Available
Library of Congress Cataloging-in-Publication Data
Webster, Thomas J.
Analyzing strategic behavior in business and economics : a game theory primer / Thomas J.
Webster.
pages cm
Includes bibliographical references and index.
ISBN 978-0-7391-8604-6 (cloth) — ISBN 978-0-7391-8605-3 (electronic) 1. Game theory.
2. Decision making. 3. Management. I. Title.
HB144.W33 2014
658.4'033—dc23
2013043736
™
The paper used in this publication meets the minimum requirements of
American National Standard for Information Sciences—Permanence of Paper
for Printed Library Materials, ANSI/NISO Z39.48-1992.
Printed in the United States of America
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Contents
Preface xi
Chapter 1 Introduction to Game Theory 1
Introduction 1
Strategic Behavior 1
Short History of Game Theory 2
Lexicon of Game Theory 3
Rational Versus Actual Behavior 4
Practice Exercises 5
PART I: STATIC GAMES WITH COMPLETE INFORMATION
Chapter 2 Coalition Games 9
Introduction 9
Prisoner’s Dilemma 9
The Extensive Form 10
The Normal Form 11
Nash Equilibrium 12
Shortcut for Finding Pure-Strategy Nash Equilibria 13
Determinants of Business Collusion 14
Number of Firms with Similar Interests 14
Firm Size Relative to the Industry 14
Visibility 15
Practice Exercises 16
v
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vi • Contents
Chapter 3 Strategic Moves and Deterring Defection 19
Introduction 19
Strategic Moves 19
Deterring Defection 20
Contracts 20
Reputation 20
Cutting Off Communications 21
Preventing Retreat 21
Brinksmanship 22
Incrementalism 23
Teamwork 23
Agents 24
Practice Exercises 24
Chapter 4 Competition Games 27
Introduction 27
Strictly-Dominant Strategies 27
Weakly-Dominant Strategies 28
Iterated Elimination of Dominated Strategies 29
Three-Player Games 31
Non-Dominant Strategies 32
Maximin (Secure) Strategy 33
Practice Exercises 34
Chapter 5 Coordination Games 39
Introduction 39
Battle-of-the-Sexes Game 39
Focal-Point Equilibrium 41
Developing a Theory of Focal-Point Equilibria 43
Framing 43
Practice Exercises 44
Chapter 6 Infinitely-Repeated Games 47
Introduction 47
Coalitions 47
Repeated Static Games 48
Trigger Strategies 49
Evaluating Payoffs in Infinitely-Repeated Games 50
Practice Exercises 52
Chapter 7 Finitely-Repeated Games 55
Introduction 55
Finitely-Repeated Games with a Certain End 55
End-of-Game Problem 56
Finitely-Repeated Games with an Uncertain End 57
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Contents • vii
A Word of Caution 59
Practice Exercises 60
Chapter 8 Evolution Games 63
Introduction 63
Evolutionary Game Theory 63
Reproductive Success 63
Evolutionary Equilibrium 64
Networks 64
Positive Feedback Effects 66
Network Game 67
Implications 68
Practice Exercises 69
Chapter 9 Tit-for-Tat 71
Introduction 71
Tit-for-Tat 71
End-of-Game Problem 73
Practice Exercises 75
Chapter 10 Mixing Pure Strategies 77
Introduction 77
Zero-Sum Games 77
Matching Pennies 78
Minimax Theorem 78
Mixed Strategies 79
Optimal Mixing Rules 80
Calculating Optimal Mixing Rules 83
When to Use Optimal Mixing Rules 86
How to Use Optimal Mixing Rules 86
Bluffing 87
Practice Exercises 88
Chapter 11 Continuous Strategies 91
Introduction 91
Continuous Strategies 91
Best-Response (Reaction) Functions 92
Tragedy of the Commons 94
Shifting Best-Response Functions 96
Practice Exercises 98
Chapter 12 Static Oligopoly Games 101
Introduction 101
Cournot Model 102
Advertising in a Cournot Setting 104
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viii • Contents
Bertrand Model 105
Bertrand Paradox 106
Practice Exercises 108
Chapter 13 Strategic Trade Policy 111
Introduction 111
Discrete Pure Strategies 111
Continuous Pure Strategies 114
National Welfare 115
Intraindustry Trade 116
Imperfect Competition 116
Intraindustry Coalitions 118
Export Subsidies 120
Reciprocity 121
Practice Exercises 123
Chapter 14 Product Differentiation 127
Introduction 127
Horizontal Differentiation 127
Vertical Differentiation 127
Location 128
Product Differences 130
Practice Exercises 130
Chapter 15 Strategic Complements 133
Introduction 133
Double Marginalization 134
Practice Exercises 137
PART II: DYNAMIC GAMES WITH COMPLETE
AND PERFECT INFORMATION
Chapter 16 Game Trees 141
Introduction 141
Game Trees 141
Subgame Perfection 142
Backward Induction 143
Credible Threats 145
First-Mover Advantage 146
Entry Deterrence 148
Practice Exercises 150
Chapter 17 A Dynamic Oligopoly Game 153
Introduction 153
Stackelberg Model 153
Practice Exercises 155
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Contents • ix
Chapter 18 Bargaining 157
Introduction 157
The Bargaining Problem 157
Ultimatum Bargaining 158
Ultimatum Paradox 160
Nash Bargaining 161
Rubenstein Bargaining 162
Last-Mover Advantage 163
Symmetric Impatience 164
Asymmetric Impatience 165
Practice Exercises 167
PART III: GAMES WITH INCOMPLETE INFORMATION
Chapter 19 Decision Making and Uncertainty 171
Introduction 171
Risk and Uncertainty 171
Static Games with Uncertain Payoffs 172
Static Games in Extensive Form 174
Dynamic Games with Uncertain Payoffs 175
Attitudes Toward Risk 178
Risk Aversion 179
Understanding Risk-Averse Behavior 182
Practice Exercises 185
Chapter 20 Adverse Selection 189
Introduction 189
The Market for Lemons 190
Practice Exercises 192
Chapter 21 Incentive Contracts 193
Introduction 193
Principal-Agent Problem 193
Incentive Contracts 194
Principal-Agent Problem with Moral Hazard 194
Practice Exercises 199
PART IV: GAMES WITH IMPERFECT INFORMATION
Chapter 22 Information Sets 203
Introduction 203
Information Sets 203
Bayesian Updating 206
Practice Exercises 209
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