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Introduction To Game Theory In Business And Economics PDF

425 Pages·2009·9.293 MB·English
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W E B S T INTRODUCTION to E R 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 N and business mathematics will find the material in this text comprehensive and accommodating. inT in BUSINESS and R Demonstration Problems throughout each chapter are designed to enhance the BO student’s understanding of the concepts presented. Many chapters include non- U D technical applications designed to further the student’s intuitive understanding of S ECONOMICS U strategic behavior. Case Studies help underscore the usefulness of game theory for I N 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 T to professors who adopt this text. S I SO aN Thomas J. WebsTer is a professor in the Department of Finance n and Economics of the Lubin School of Business at Pace University in New dt o York City. Professor Webster received his B.A. from the American E University School of International Service in Washington, D.C., and his G C M.A., M.Phil. and Ph.D. from The City University of New York. A O M N E O T M H I CE O S www.mesharpe.com R Y M Ë|xHSKHQFy622372zv*:+:!:+:! . E M.E.Sharpe . S Armonk, New York h THOMAS J. WEB STER a London, England r p 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

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Most books are stored in the elastic cloud where traffic is expensive. For this reason, we have a limit on daily download.