Introduction To Game Theory In Business And Economics

425 Pages·2009·9.293 MB·English

by  Webster, Thomas J

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T INTRODUCTION to
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INTRODUCTION TO GAME THEORY IN BUSINESS AND ECONOMICS
This innovative textbook introduces students to the rudimentary principles of GAME THEORY
game theory—move and countermove—with an emphasis on real-world business
and economic applications. Students with a background in principles of economics I
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and business mathematics will find the material in this text comprehensive and
accommodating. inT in BUSINESS and
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Demonstration Problems throughout each chapter are designed to enhance the BO
student’s understanding of the concepts presented. Many chapters include non- U
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technical applications designed to further the student’s intuitive understanding of S ECONOMICS
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strategic behavior. Case Studies help underscore the usefulness of game theory for I
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analyzing real-world situations. Each chapter concludes with a Review, as well as C
Questions and Exercises. An online Instructor’s Manual with test bank is available E
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to professors who adopt this text. S
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Thomas J. WebsTer is a professor in the Department of Finance
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and Economics of the Lubin School of Business at Pace University in New dt
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York City. Professor Webster received his B.A. from the American
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University School of International Service in Washington, D.C., and his G
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M.A., M.Phil. and Ph.D. from The City University of New York.
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Armonk, New York h THOMAS J. WEB STER
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London, England
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COVER DESIGN BY JESSE M. SANCHEZ e
IntroductIon to
Game theory
in BusIness and
economIcs
thomas J. WeB ster
M.E.Sharpe
Armonk, New York
London, England
To my sons, Andrew Nicholas and Adam Thomas—two beautiful minds.
Copyright © 2009 by M.E. Sharpe, Inc.
Corrected Edition
All rights reserved. No part of this book may be reproduced in any form
without written permission from the publisher, M.E. Sharpe, Inc.,
80 Business Park Drive, Armonk, New York 10504.
Library of Congress Cataloging-in-Publication Data
Webster, Thomas J.
An introduction to game theory in business and economics / Thomas J. Webster.
p. cm.
Includes bibliographical references and index.
ISBN 978-0-7656-2237-2 (pbk. : alk. paper)
1. Game theory. 2. Economics--Psychological aspects. 3. Strategic planning. I. Title.
HB144.W43 2007
330.01’5193--dc22 2007043943
Printed in the United States of America
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 Z 39.48-1984.
~
BM (p) 10 9 8 7 6 5 4 3 2
Contents
Acknowledgments ........................................................................................................................vii
A Note to Students and Instructors ..............................................................................................ix
1. Introduction to Game Theory ..........................................................................................1
Introduction .........................................................................................................................1
A Short History of Game Theory ........................................................................................2
Strategic Behavior ...............................................................................................................3
Case Study 1.1: Glaxo and Zantac ......................................................................................3
What Is Game Theory? ........................................................................................................5
The Prisoner’s Dilemma ......................................................................................................7
Shortcut for Finding Pure-Strategy Nash Equilibria .........................................................11
Appendix: Mathematics Review .......................................................................................16
2. Noncooperative, One-Time, Static Games with Complete Information .....................34
Introduction .......................................................................................................................34
Strictly Dominant Strategies .............................................................................................35
Application 2.1: Run with the Pitch ..................................................................................36
Application 2.2: Indiana Jones and the Last Crusade .......................................................36
Application 2.3: The Good, the Bad and the Ugly ............................................................37
Nash Equilibrium ..............................................................................................................38
Strictly Dominant Strategy Equilibrium ............................................................................41
Weakly Dominant Strategies .............................................................................................43
Iterated Elimination of Strictly Dominated Strategies ......................................................46
Three-Player Games ..........................................................................................................49
Nondominant Strategies ....................................................................................................50
Application 2.4: A Beautiful Mind ....................................................................................52
Maximin Decision Rule ....................................................................................................53
Minimax Regret Decision Rule .........................................................................................58
3. Focal-Point and Evolutionary Equilibria ......................................................................69
Introduction .......................................................................................................................69
Multiple Nash Equilibria ...................................................................................................69
Focal-Point Equilibrium ....................................................................................................71
Developing a Theory of Focal-Point Equilibria ................................................................76
Framing .............................................................................................................................77
Case Study 3.1: AZT Versus Videx ...................................................................................78
Evolutionary Game Theory ...............................................................................................79
Case Study 3.2: Evolutionary Equilibrium in Broadband Technology? ...........................82
4. Infi nitely Repeated, Static Games with Complete Information ..................................86
Introduction .......................................................................................................................86
Case Study 4.1: Extra-Credit Game Part I ........................................................................87
Collusion ...........................................................................................................................89
The Prisoner’s Dilemma Revisited ....................................................................................90
Trigger Strategies ..............................................................................................................91
Evaluating Payoffs in Infi nitely Repeated Games .............................................................92
iii
iv CONTENTS
Cheating Rule for Infi nitely Repeated Games ...................................................................96
Making Threats Credible ...................................................................................................98
Application 4.1: The Hunt for Red October ....................................................................102
Application 4.2: Fail-Safe ...............................................................................................103
Determinants of Business Collusion ...............................................................................103
5. Finitely Repeated, Static Games with Complete Information ..................................112
Introduction .....................................................................................................................112
Finitely Repeated Games with a Certain End .................................................................112
End-of-Game Problem ....................................................................................................114
Case Study 5.1: Extra-Credit Game Part II .....................................................................117
Finitely Repeated Games with an Uncertain End ...........................................................118
Application 5.1: Groundhog Day ....................................................................................119
Cheating Rule for Finitely Repeated Games with an Uncertain End ..............................120
Common Enforcement Mechanisms ...............................................................................123
Case Study 5.2: Philip Morris Versus BAT .....................................................................126
6. Mixing Pure Strategies ..................................................................................................132
Introduction .....................................................................................................................132
Zero-Sum Games .............................................................................................................132
Minimax Theorem ...........................................................................................................136
Mixed Strategies ..............................................................................................................139
Optimal Mixing Rules .....................................................................................................141
Computing Optimal Mixing Rules ..................................................................................144
When to Use Optimal Mixing Rules ...............................................................................148
Randomizing Pure Strategies ..........................................................................................149
Bluffi ng ............................................................................................................................150
7. Static Games with Continuous Strategies ...................................................................157
Introduction .....................................................................................................................157
Continuous Strategies ......................................................................................................157
Reaction (Best Response) Functions ...............................................................................160
Tragedy of the Commons ................................................................................................162
The Coase Theorem .........................................................................................................165
Case Study 7.1: The Global Carbon Tax .........................................................................168
Shifting Reaction Functions ............................................................................................170
8. Imperfect Competition ..................................................................................................175
Introduction .....................................................................................................................175
Market Structure ..............................................................................................................175
Oligopoly .........................................................................................................................176
Models of Oligopoly .......................................................................................................177
Case Study 8.1: Cournot-Nash Equilibrium in the Corn Wet Milling Industry ..............189
Case Study 8.2: The OPEC Price-Fixing Cartel ..............................................................198
Case Study 8.3: Blood Diamonds ...................................................................................199
9. Perfect Competition and Monopoly .............................................................................206
Introduction .....................................................................................................................206
Standard Model of Perfect Competition ..........................................................................206
Perfect Competition and Game Theory ...........................................................................212
Perfect Competition and the Cournot Model ..................................................................213
How Many Firms Are Necessary for Perfect Competition? ............................................216
Standard Model of Monopoly .........................................................................................216
Sources of Monopoly Power ...........................................................................................218
CONTENTS v
Monopoly and Game Theory ..........................................................................................220
Contestable Monopoly ....................................................................................................220
10. Strategic Trade Policy ...................................................................................................227
Introduction .....................................................................................................................227
Case Study 10.1: Boeing Versus Airbus ..........................................................................228
Strategic Trade Policy with Discrete Pure Strategies ......................................................229
Strategic Trade Policy with Continuous Pure Strategies .................................................233
National Welfare ..............................................................................................................234
Intraindustry Trade ..........................................................................................................236
Imperfect Competition and International Trade ..............................................................237
To Trade or Not to Trade? ...............................................................................................239
Export Subsidies ..............................................................................................................242
Reciprocity ......................................................................................................................243
Case Study 10.2: U.S.–Japanese Voluntary Export Restraints ........................................246
Increasing Returns to Scale .............................................................................................247
11. Dynamic Games with Complete and Perfect Information ........................................252
Introduction .....................................................................................................................252
Game Trees ......................................................................................................................252
Case Study 11.1: Sun Country Versus Northwest Airlines ..............................................254
Subgame Perfect Equilibrium .........................................................................................256
Backward Induction ........................................................................................................258
Simplifying the Notation .................................................................................................266
First-Mover Advantage ....................................................................................................267
Case Study 11.2: Leader of the Pack ...............................................................................267
Credible Threats ..............................................................................................................275
Dynamic Games with Continuous Strategies ..................................................................277
The Stackelberg Model....................................................................................................277
12. Bargaining ......................................................................................................................286
Introduction .....................................................................................................................286
Nash Bargaining ..............................................................................................................287
Dynamic Bargaining and the Last-Mover Advantage .....................................................288
Dynamic Bargaining with Symmetric Impatience ..........................................................290
Dynamic Bargaining with Asymmetric Impatience ........................................................292
13. Pure Strategies with Uncertain Payoffs .......................................................................297
Introduction .....................................................................................................................297
Static Games with Uncertain Payoffs ..............................................................................297
Risk and Uncertainty .......................................................................................................300
Case Study 13.1: Global Warming: Uncertainties, Certainties, and Urgencies ..............302
Attitudes Toward Risk .....................................................................................................303
Risk-Averse Consumer Behavior ....................................................................................309
Risk-Averse Firm Behavior .............................................................................................309
Dynamic Games with Uncertain Payoffs ........................................................................312
Appendix: Measuring Risk ..............................................................................................321
14. Torts and Contracts .......................................................................................................325
Introduction .....................................................................................................................325
Torts .................................................................................................................................325
Nash Equilibrium and Economic Effi ciency ...................................................................333
Contracts ..........................................................................................................................335
Case Study 14.1: Economic Effi ciency and the Common Law.......................................337
vi CONTENTS
15. Auctions ..........................................................................................................................341
Introduction .....................................................................................................................341
Business, Auctions, and the Internet ...............................................................................341
Case Study 15.1: FCC’s Wireless Spectrum Auction ......................................................342
Case Study 15.2: EBay ....................................................................................................343
Types of Auctions ............................................................................................................343
Auctions with Complete and Perfect Information ...........................................................346
Auctions with Independent Private Values ......................................................................350
Case Study 15.3: Google Goes Dutch .............................................................................355
Auctions with Correlated Value Estimates ......................................................................357
Common-Value Auctions and the Winner’s Curse ..........................................................357
Auctions and Risk-Averse Behavior ...............................................................................359
Revelation Principle ........................................................................................................359
16. Dynamic Games with Imperfect Information .............................................................366
Introduction .....................................................................................................................366
Information Sets ..............................................................................................................366
Bayesian Updating ..........................................................................................................370
Adverse Selection and the Market for Lemons ...............................................................373
Signaling ..........................................................................................................................374
Spence Education Game ..................................................................................................375
Case Study 16.1: The U.S. News & World Report College Rankings .............................378
Separating Strategy ..........................................................................................................379
Pooling Strategy ..............................................................................................................381
Screening .........................................................................................................................383
Glossary of Terms and Concepts...............................................................................................389
References and Suggestions for Further Reading .....................................................................399
Index ..........................................................................................................................................407
Acknowledgments
I would like to express my heartfelt appreciation to my colleagues and students at Pace Univer-
sity who provided many invaluable insights and suggestions during the preparation of this text.
I would also like to express my appreciation to those individuals who were gracious enough to
review earlier drafts of this text. Although their feedback was not always positive, or fl attering,
it was always constructive and invaluable. In particular, I would like to extend a special thanks
to Professors Walter Antognini, Roy Girasa, and Art Magaldi of Pace University for their legal
expertise, Professor John Teall of Rensselaer Polytechnic Institute for his insights and encourage-
ment, and Assistant Dean Germaine Hodges of Pace University for her friendship, forbearance,
and honesty. I would like to express my appreciation to Professor Udayan Roy of Long Island
University for his painstaking review of early drafts of several chapters of this text. His critical
comments, especially in the area of mixed strategies, were invaluable. I would like to thank my
son, Adam Webster, a student at the University of Arizona, who reviewed early drafts of this text
and contributed a case study on global warming. Finally, I would like to express a very special
thanks to Lynn Taylor, Nicole Cirino, Angela Piliouras, and Eileen Chetti at M.E. Sharpe, who
managed to suffer through my incessant nagging with much grace and aplomb.
vii

A Note to Students and
Instructors
TO THE STUDENT
More than in most disciplines, students of business and economics come to appreciate very early
in their education the importance of thinking strategically. Strategic interaction between and
among rivals is the essence of competition in the marketplace. A business manager who attempts
to anticipate how rivals will react to changes in product pricing, the introduction of a new product
line, an increase in advertising expenditures, expanding into overseas markets, or the naming of a
new chief operating offi cer is thinking strategically. Sometimes this game is played just once, but
more often than not this game is played repeatedly. Rivals’ decisions can be made simultaneously
or sequentially. If I do this, what will you do? And, if you do that, how will I react, and so on and
so forth. The essence of game theory is to make sense of this back-and-forth (circular) reasoning.
By putting ourselves in the shoes of rivals, we turn the game to our advantage. The objective of
the study of game theory is to understand strategic interaction—move and countermove. Indeed,
no graduate or undergraduate program in business and economics is complete without a rudimen-
tary understanding of the principles of game theory that extend beyond the prisoner’s dilemma
paradigm, which can be found in most fundamentals of microeconomics textbooks.
This book is designed to appeal to both graduate and advanced undergraduate students in
business, economics, and other social sciences with varied educational backgrounds. Most of the
material presented in this text can be understood by students with a basic understanding of the
principles of microeconomics. For the most part, mathematical training beyond elementary algebra
is unnecessary, although a one-semester course in differential calculus is necessary to master the
material dealing with continuous strategies and best-response functions. This is especially true
when we discuss models of imperfect competition and strategic trade policy. The appendices to
Chapters 1 and 13 present a review of the basic mathematical and statistical concepts necessary
to master the material presented in this text.
TO THE INSTRUCTOR
This text originated from a series of lectures that were prepared for beginning, part-time MBA
students with diverse backgrounds. The objective was to convey to these students an appreciation
of benefi ts of strategic thinking in a casual and nonthreatening manner. These lectures constitute
the fi rst three chapters of this text. As interest among students developed, these lectures were
extended to include more esoteric topics, which were presented in a dedicated course on basic
strategy. As the topic coverage was expanded, it became necessary to elevate somewhat the level
of mathematical rigor, but not to raise it so high as to alienate most students.
The fi rst three chapters of the text deal with one-time, noncooperative, pure-strategy, static
(simultaneous-move) games with complete information. Chapters 4 and 5 consider repeated, pure-
strategy, static games in which cooperation between and among the players is possible, but not
guaranteed even when it is in their collective best interest to do so. In these chapters, basic rules are
developed to assess the stability of cartel arrangements in static games that are infi nitely repeated,
or are repeated a fi nite number of times where the end of the game is certain and uncertain. These
ix