playing for real a text on game theory mar 2007

www.dbebooks.com - Free Books & magazines Playing for Real This page intentionally left blank Playing for Real A Text on Game Theory Ken Binmore 1 2007 1 Oxford University Press, Inc., publishes works that further Oxford University’s objective of excellence in research, scholarship, and education. Oxford New York Auckland Cape Town Dar es Salaam Hong Kong Karachi Kuala Lumpur Madrid Melbourne Mexico City Nairobi New Delhi Shanghai Taipei Toronto With offices in Argentina Austria Brazil Chile Czech Republic France Greece Guatemala Hungary Italy Japan Poland Portugal Singapore South Korea Switzerland Thailand Turkey Ukraine Vietnam Copyright # 2007 by Oxford University Press, Inc. Published by Oxford University Press, Inc. 198 Madison Avenue, New York, New York 10016 www.oup.com Oxford is a registered trademark of Oxford University Press All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior permission of Oxford University Press. Library of Congress Cataloging-in-Publication Data Binmore, K. G., 1940– Playing for real : a text on game theory / Ken Binmore. p. cm. Includes index. ISBN 978-0-19-530057-4 1. Game theory. 1. Title. QA269.B475 2005 519.3—dc22 2005053938 135798642 Printed in the United States of America on acid-free paper I dedicate Playing for Real to my wife, Josephine This page intentionally left blank Preface There are at least three questions a game theory book might answer: What is game theory about? How do I apply game theory? Why is game theory right? Playing for Real tries to answer all three questions. I think it is the only book that makes a serious attempt to do so without getting heavily mathematical. There are elementary books that offer students the opportunity to admire some game theory concepts. There are cookbooks that run through lots of applied models. There are philosophical works that supposedly address the foundational issues, but none of these address more than two of the questions. However, answering questions is only part of what this book is about. Just as athletes take pleasure in training their bodies, so there is immense satisfaction to be found in training your mind to think in a way that is simultaneously rational and creative. With all of its puzzles and paradoxes, game theory provides a magnificent mental gymnasium for this purpose. I hope that exercising on the equipment will bring you the same kind of pleasure it has brought me. Moving on. Playing for Real isn’t my first textbook on game theory. My earlier book, Fun and Games, was used quite widely for teaching advanced undergraduate and beginning graduate students. I had originally planned a modestly revised second edition, in which the rather severe introduction would be replaced with a new chapter that would ease students into the subject by running through all the angles on the Prisoners’ Dilemma. The remaining chapters were then simply to be broken down into more digestible chunks. But the project ran away with me. I made the improvements I planned to make but somehow ended up with a whole new book. There are two reasons why. The first is that game theory has moved on since I wrote Fun and Games. Some of the decisions on what material to include that seemed a little daring at the time now look totally uncontroversial. So I have tried my luck at guessing which way the subject is going to jump again. The second reason is that I have moved on as well. In particular, I have done a great deal of consulting work, applying game theory to real-world problems in order to raise money for my research center. The biggest project was the design of a telecom auction that raised $35 billion. I always knew that game theory works, but seeing it triumph on such a scale was beyond all expectation! I have also written a book applying game theory to philosophical issues, which taught me a great deal about how and why beginners make mistakes when thinking about strategic issues. Both kinds of experience have contributed to making Playing for Real a better book than its predecessor. My flirtation with philosophy even generated a lot of light- hearted exercises that nevertheless make genuinely serious points. Material. As a text on game theory for undergraduates with some mathematical training, Playing for Real improves on Fun and Games in a number of ways. It continues to be suitable for courses attended by students from a variety of disci- plines. (Some of my very best undergraduates at the University of Michigan were from Classics.) It also continues to provide backup sections on the necessary mathematics, so that students whose skills are rusty can keep up with what’s going on without too much effort. However, the book as a whole covers fewer basic topics in a more relaxed and discursive style, with many more examples and economic applications. I hope the opening chapter, which uses the Prisoners’ Dilemma to provide an undemanding overview of what game theory is all about, will prove to be a par- ticularly attractive feature. Economists will also be pleased to see a whole chapter devoted to the theory of imperfect competition, where I believe I may even have made Bertrand-Edgeworth competition accessible to undergraduates. It is a tragedy that evolutionary game theory had to go, but this important subject has gotten so big that it deserves a whole book to itself. Although fewer topics are covered, some topics are covered in much more detail than in Fun and Games . These include cooperative game theory, Bayesian decision theory, games of incomplete information, mec hanism design, and auction theory, each of which now has its own chapter. However, the theory of bargaining has grown more than anything else, partly because I hope to discourage various mis- understandings of the theory that have become commonplace in applied work, and partly because I wanted to illustrate its potential use in ethics and moral philosophy. Teaching. There is enough material in this book for at least two courses in game theory, even leaving aside the review and other sections that are intended for private reading. I have tried to make things easy for teachers who want to design a course based on a selection of topics from the whole book by including marginal notes to facilitate skipping. For example, the Mad Hatter, who has appeared in the margin, suggests skipping on to the first chapter, on the grounds that there is too much philosophy in this preface. The exercises are similarly labeled with warnings about their content. Nobody will want to attempt all of the enormous number of exercises, but when I teach, I insist on students trying a small number of carefully chosen exercises every week. phil ! 1.1 viii Preface Once they get into the habit, students are often surprised to find that solving prob- lems can be a lot of fun. By the time the book is published, Jernej Copic will have finish ed getting his solutions onto a website. Oxford University Press will provide access details to recognized teacher s. Thanks. So many people have helped me, with both Fun and Games and Playing for Real, that I have lost track of them all. I shall therefore mention only the very special debt of gratitude I owe to my long-tim e coauthor, Larry Samuelson, for both his patience and his encouragement. I also want to thank the California Institute of Technology for giving me the leisure to complete this book as a Gordon Moor e Scholar. I should also acknowledge the Victorian artist John Tenniel, whose mag- nificent illustrations from Lewis Carroll’s Alice books I have shamelessly stolen and messed around with. Apologies. Let me aopolgize in advance for the errors that have doubtless found their way into Playing for Real. If you find an error, please join the many others who have helped me by letting me know about it at k.binmore@ucl.ac.uk. I will be genuinely grateful. Finally, I need to apologize not only for my mistakes but also for my attempts at humor. Oscar Wilde reported that a piano in a Western saloon carried a notice saying, ‘‘Please don’t shoot the pianist. He’s doing his best.’’ The same goes for me, too. It isn’t easy to write in a light-hearted style when presenting mathematical material, but I did my best. Ken Binmore Preface ix [...]... them Adolf Hitler and Josef Stalin played a game that killed off a substantial fraction of the world’s population Kruschev and Kennedy played a game during the Cuban missile crisis that might have wiped us out altogether Drivers maneuvering in heavy traffic are playing a game with the drivers of the other cars Art lovers at an auction are playing a game with the rival bidders for an old master A firm and... and a union negotiating next year’s wage contract are playing a bargaining game When the prosecuting and defending attorneys in a murder trial decide what arguments to put before the jury, they are playing a game A supermarket manager deciding today’s price for frozen pizza is playing a game with all the other storekeepers in the neighborhood with pizza for sale If all of these scenarios are games,... was a faster runner than Adam because she won a race in which she was given a head start Let us therefore compare how well Alice and Adam will do when they play under the same conditions First imagine what would happen if both were to play against Bob, and then imagine what would happen if both were to play against Eve When they play against Bob, Alice goes to jail for one year, and Adam for no years... invented paradox of rationality than to explain why strong swimmers drown when thrown in Lake Michigan with their feet encased in concrete No paradox of rationality exists Rational players don’t cooperate in the Prisoners’ Dilemma because the conditions necessary for rational cooperation are absent in this game 1.3.3 The Twins Fallacy One of the many attempts to resolve the paradox of rationality supposedly... group of players as a whole Karl Marx is the most famous exponent of this error.9 The biological version of the mistake is called the group selection fallacy Pareto Efficiency A standard assumption in cooperative game theory is that a rational agreement will be Pareto efficient Pareto efficiency comes in a weak form and a strong form The weak form is easiest to defend It says that an agreement is Pareto efficient... Von Neumann and Morgenstern’s theory of cooperative games, in which the players are assumed to negotiate a binding agreement on what strategies to use before play begins Such critics are usually sold on the idea that rationality resides in groups rather than individuals They therefore think that rational behavior on the part of an individual player lies merely in agreeing to whatever is rational for. .. this case, the district attorney trumps up a tax evasion charge against both players, and they each go to jail for one year Adam’s payoff for (dove, dove) is therefore À 1 If Adam and Eve both confess, the outcome is (hawk, hawk) Each is found guilty, but since confession is a mitigating circumstance, each receives a penalty of only 9 years Adam’s payoff for (hawk, hawk) is therefore À9 The payoffs... game theory says will result from rational play 9 Recall that he treated abstractly conceived coalitions like Capital and Labor as though they had the single-minded and enduring aims of individual people 1.7 Collective Rationality? Philosophers who think that this fact reveals a contradiction between noncooperative and cooperative game theory overlook the importance of the assumption in cooperative game. .. ready application in economics The dismal science is supposedly about the allocation of scarce resources If resources are scarce, it is because more people want them than can have them Such a scenario creates all the necessary ingredients for a game Moreover, neoclassical economists proceed on the assumption that people will act rationally in this game Neoclassical economics is therefore essentially... year Naive critics think that this observation is enough to formulate an unassailable argument They say that there are two theories of rational play to be compared Their theory recommends that everybody should play dove in the Prisoners’ Dilemma Game theory recommends that everybody should play hawk If Alice and Bob play according to the naive theory, each will go to jail for only one year If Adam and . the other cars. Art lovers at an auction are playing a game with the rival bidders for an old master. A firm and a union negotiating next year’s wage contract are playing a bargaining game. When. points. Material. As a text on game theory for undergraduates with some mathematical training, Playing for Real improves on Fun and Games in a number of ways. It continues to be suitable for courses attended. intentionally left blank Preface There are at least three questions a game theory book might answer: What is game theory about? How do I apply game theory? Why is game theory right? Playing for Real