The Art of Strategy A GAME THEORIST’S GUIDE TO SUCCESS IN BUSINESS & LIFE Also by AVINASH K DIXIT & BARRY J NALEBUFF Lawlessness and Economics: Alternative Modes of Governance (Gorman Lectures in Economics, University College London) by Avinash K Dixit Investment Under Uncertainty by Avinash K Dixit & Robert S Pindyck Thinking Strategically by Avinash Dixit & Barry J Nalebuff Co-opetition by Adam Brandenburger & Barry J Nalebuff Why Not? by Ian Ayres & Barry J Nalebuff The Art of Strategy A GAME THEORIST’S GUIDE TO SUCCESS IN BUSINESS & LIFE Avinash K Dixit Barry J Nalebuff W W NORTON & COMPANY New York London Copyright â 2008 by Avinash K Dixit and Barry J Nalebuff All rights reserved Doonesbury cartoon: © 1993 G B Trudeau Reprinted with permission of Universal Press Syndicate All rights reserved Peanuts cartoon: © United Features Syndicate, Inc For information about permission to reproduce selections from this book, write to Permissions, W W Norton & Company, Inc 500 Fifth Avenue, New York, NY 10110 Library of Congress Cataloging-in-Publication Data Dixit, Avinash K The art of strategy : a game theorist's guide to success in business & life / Avinash K Dixit, Barry J Nalebuff.—1st ed p cm Includes bibliographical references and index ISBN: 978-0-393-06995-2 Strategic planning Strategy Game theory Decision making I Nalebuff, Barry, 1958–II Title HD30.28.D587 2008 658.4'012—dc22 2008021347 W W Norton & Company, Inc 500 Fifth Avenue, New York, N.Y 10110 www.wwnorton.com W W Norton & Company Ltd Castle House, 75/76 Wells Street, London W1T 3QT To all our students, from whom we have learned so much (especially Seth—BJN) CONTENTS Preface Introduction: How Should People Behave in Society? PART I Ten Tales of Strategy Games Solvable by Backward Reasoning Prisoners’ Dilemmas and How to Resolve Them A Beautiful Equilibrium Epilogue to Part I PART II Choice and Chance Strategic Moves Making Strategies Credible Epilogue to Part II: A Nobel History PART III Interpreting and Manipulating Information Cooperation and Coordination 10 Auctions, Bidding, and Contests 11 Bargaining 12 Voting 13 Incentives 14 Case Studies Further Reading Workouts Notes Preface WE DIDN’T SET out to write a new book The plan was simply to revise our 1991 book, Thinking Strategically But it didn’t quite turn out that way One model for writing a revision comes from Borges’s character Pierre Menard, who decides to rewrite Cervantes’s Don Quixote After great effort, Menard’s revision ends up being word-for-word identical to the original However, 300 years of history and literature have passed since Quixote, including Quixote itself Although Menard’s words are the same, his meaning is now entirely different Alas, our original text wasn’t Don Quixote, and so the revision did require changing a few words In fact, most of the book is entirely new There are new applications, new developments in the theory, and a new perspective So much is new that we decided a new title was called for as well Although the words are new, our meaning remains the same We intend to change the way you see the world, to help you think strategically by introducing the concepts and logic of game theory Like Menard, we have a new perspective When we wrote Thinking Strategically, we were younger, and the zeitgeist was one of self-centered competition We have since come to the full realization of the important part that cooperation plays in strategic situations, and how good strategy must appropriately mix competition and cooperation.* We started the original preface with: “Strategic thinking is the art of outdoing an adversary, knowing that the adversary is trying to the same to you.” To this we now add: It is also the art of finding ways to cooperate, even when others are motivated by self-interest, not benevolence It is the art of convincing others, and even yourself, to what you say It is the art of interpreting and revealing information It is the art of putting yourself in others’ shoes so as to predict and influence what they will We like to think that The Art of Strategy includes this older, wiser perspective But there is also continuity Even though we offer more real-life stories, our purpose remains to help you develop your own ways of thinking about the strategic situations you will face; this is not an airport book offering “seven steps for sure strategic success.” The situations you face will be so diverse that you will succeed better by knowing some general principles and adapting them to the strategic games you are playing Businessmen and corporations must develop good competitive strategies to survive, and find cooperative opportunities to grow the pie Politicians have to devise campaign strategies to get elected and legislative strategies to implement their visions Football coaches plan strategies for players to execute on the field Parents trying to elicit good behavior from children must become amateur strategists—the children are pros Good strategic thinking in such numerous diverse contexts remains an art But its foundations consist of some simple basic principles—an emerging science of strategy, namely game theory Our premise is that readers from a variety of backgrounds and occupations can become better strategists if they know these principles Some people question how we can apply logic and science to a world where people act irrationally It turns out that there is often method to the madness Indeed, some of the most exciting new insights have come from recent advances in behavioral game theory, which incorporates human psychology and biases into the mix and thus adds a social element to the theory As a result, game theory now does a much better job dealing with people as they are, rather than as we might like them to be We incorporate these insights into our discussions While game theory is a relatively young science—just over seventy years old—it has already provided many useful insights for practical strategists But, like all sciences, it has become shrouded in jargon and mathematics These are essential research tools, but they prevent all but the specialists from understanding the basic ideas Our main motive for writing Thinking Strategically was the belief that game theory is too interesting and important to leave to the academic journals The insights prove useful in many endeavors—business, politics, sports, and everyday social interactions Thus we translated the important insights back into English and replaced theoretical arguments with illustrative examples and case studies We are delighted to find our view becoming mainstream Game theory courses are some of the most popular electives at Princeton and Yale, and most other schools where they are offered Game theory permeates strategy courses in MBA programs, and a Google search for game theory produces more than million pages You’ll find game theory in newspaper stories, op-eds, and public policy debates Of course, much of the credit for these developments belongs to others: to the Economics Nobel Prize Committee, which has awarded two prizes in game theory—in 1994, to John Harsanyi, John Nash, and Reinhard Selten and in 2005, to Robert Aumann and Thomas Schelling;* to Sylvia Nasar, who wrote A Beautiful Mind, the best-selling biography of John Nash; to those who made the awardwinning movie of the same name; and to all those who have written books popularizing the subject We might even share a bit of the credit Since publication, Thinking Strategically has sold 250,000 copies It has been translated into numerous languages, and the Japanese and Hebrew translations have been best sellers We owe a special debt to Tom Schelling His writings on nuclear strategies, particularly The Strategy of Conflict and Arms and Influence, are justly famous In fact, Schelling pioneered a lot of game theory in the process of applying it to nuclear conflict Michael Porter’s Competitive Strategy, drawing on the lessons of game theory for business strategy, is equally important and influential An annotated guide to the works of Schelling, Porter, and many others is provided in our Further Reading section In this book we not confine the ideas to any particular context Instead, we offer a wide range of illustrations for each basic principle Thus readers from different backgrounds will all find something familiar here They will also see how the same principles bear on strategies in less familiar circumstances; we hope this will give them a new perspective on many events in news as well as history We also draw on the shared experience of our readers, with illustrations from, for example, literature, movies, and sports Serious scientists may think this trivializes strategy, but we believe that familiar examples are an effective vehicle for conveying the important ideas * Nixon is tied with Thomas R Marshall (under Woodrow Wilson) and Alben Barkley (under Harry Truman) † Or senators on opposite sides of the issue will try to pair off their absences If the 100 senators are split 51:49 or more lopsidedly, then the outcome is the same no matter which way the vice president votes * Adverse selection may also exist; a student who is willing to work for the wages the professor offers may be of too low a quality to command better offers elsewhere But professors have other ways of finding out the quality of a student: how well the student performed in the professor’s courses, recommendations from colleagues, and so on * You think that is too many errors in all? Try writing a long and complicated book yourself † Perhaps it would have been better to pay $2 per error but then dock the student $10 for each one missed Since the missed errors are only discovered over time, that would require holding part of the payment in escrow, which might be more complicated than it is worth When is the escrow released? Is there a maximum amount docked? Simplicity is a third constraint on incentive schemes The people being incentivized need to understand how the system works * To fill out the analogy, imagine that the mechanic can “invent” a problem that brings him $1,000 of extra profits, which at a 10% interest rate is like an extra $100 per year However, there is a 25 percent chance that you will catch him, in which case you will never return to this garage If your future business will bring in more than $400 of profit every year, then he would rather play it straight than risk losing your future business and the profits that go with it * Recall that a successful project is worth $200,000 Since the employee is paid a bonus of $100,000 for success, it is just as if the employee owns half the business * Actually, this is what Barry wished he had done It was 3:00 in the morning and much too much champagne had been drunk for him to have been thinking this clearly He bet £200 on the even numbers, figuring that he would end up in second place only in the event that he lost and she won, the odds of which were approximately 5:1 in his favor Of course 5:1 events sometimes happen, and this was one of those cases She won * Unfortunately, it is not an equilibrium for Macy’s bid to succeed either, for in that case, the two-tiered bid would attract less than 50 percent of the shares and so the price per share offered would be above the bid by Macy’s Alas, this is one of those cases with no equilibrium Finding a solution requires the use of randomized strategies, as discussed in chapter * Others have used the same ploy Roald Amundsen started his journey of exploration to the South Pole using a trick; those who signed up did so in the belief that they were going on a long but much less risky voyage to the Arctic He revealed his true objective only at the last possible point of return, and offered a passage-paid return to Norway to anyone who did not want to continue No one took him up on this, even though later there was much muttering: “Why did you say yes? If only you had answered no, I would have done the same” (Roland Huntford, The Last Place on Earth [New York: Modern Library, 1999], 289) Like Henry V, Amundsen was victorious and became the first man to stand on the geographic South Pole * AT&T (Cingular) is the exception to this practice * The empirical evidence suggests that allowing the public to carry a concealed gun does not reduce the probability of crime, but it does not increase it, either See Ian Ayres and John Donohue, “Shooting Down the ‘More Guns, Less Crime’ Hypothesis,” Stanford Law Review 55 (2003): 1193–1312 * Could the criminals have done even better? No Their best outcome is the homeowners’ worst Since homeowners can guarantee themselves or better by owning guns, no strategic move by criminals can leave homeowners at Hence a commitment to go unarmed is the best strategic move for criminals What about a commitment by the criminals to carry arms? This is their dominant strategy Homeowners would anticipate this move anyway It has no strategic value As with warnings and assurances, a commitment to a dominant strategy could be called a “declaration”: it is informational rather than strategic † What happens if homeowners preempt and let the criminals respond? Homeowners can predict that for any unconditional choice of action on their part, criminals will respond by going armed Hence homeowners will want to go armed, and the result is no better than with simultaneous moves * In an information escrow, each side makes an offer and then a neutral party evaluates whether the offers cross or not In the legal environment, the DA offers a plea bargain, say three years The defendant offers to accept anything under five Since the defendant is willing to accept the DA’s offer, a deal is done But if the offers don’t overlap—if, say, the DA asks for six years—then neither party learns what the other has put on the table ... That brings us to one last point You may be thinking you are playing one game, but it is only part of a larger game There is always a larger game THE SHAPE OF THINGS TO COME These examples have... game to your advantage, and how to manipulate information in strategic interaction Finally, we take up several broad classes of strategic situations—bargaining, auctions, voting, and the design of. .. understanding the basic ideas Our main motive for writing Thinking Strategically was the belief that game theory is too interesting and important to leave to the academic journals The insights