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Playing for Real This page intentionally left blank Playing for Real A Text on Game Theory Ken Binmore 1 2007 1 OxfordUniversityPress,Inc.,publishesworksthatfurther OxfordUniversity’sobjectiveofexcellence inresearch,scholarship,andeducation. Oxford NewYork Auckland CapeTown DaresSalaam HongKong Karachi KualaLumpur Madrid Melbourne MexicoCity Nairobi NewDelhi Shanghai Taipei Toronto Withofficesin Argentina Austria Brazil Chile CzechRepublic France Greece Guatemala Hungary Italy Japan Poland Portugal Singapore SouthKorea Switzerland Thailand Turkey Ukraine Vietnam Copyright#2007byOxfordUniversityPress,Inc. PublishedbyOxfordUniversityPress,Inc. 198MadisonAvenue,NewYork,NewYork10016 www.oup.com OxfordisaregisteredtrademarkofOxfordUniversityPress Allrightsreserved.Nopartofthispublicationmaybereproduced, storedinaretrievalsystem,ortransmitted,inanyformorbyanymeans, electronic,mechanical,photocopying,recording,orotherwise, withoutthepriorpermissionofOxfordUniversityPress. LibraryofCongressCataloging-in-PublicationData Binmore,K.G.,1940– Playingforreal:atextongametheory/KenBinmore. p.cm. Includesindex. ISBN978-0-19-530057-4 1. Gametheory. 1. Title. QA269.B4752005 519.3—dc22 2005053938 1 3 5 7 9 8 6 4 2 PrintedintheUnitedStatesofAmerica onacid-freepaper I dedicate Playing for Real to my wife, Josephine This page intentionally left blank Preface There are at least threequestions agametheorybook 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 theseaddressmorethan two of the questions. However, answering questions is only part of what this book is about. Just as athletestakepleasureintrainingtheirbodies,sothereisimmensesatisfactiontobe found in training your mind to think in a way that is simultaneously rational and creative.Withallofitspuzzlesandparadoxes,gametheoryprovidesamagnificent mental gymnasium for this purpose. I hope that exercising on the equipment will bringyouthe samekind ofpleasure ithas broughtme. Moving on. Playing for Real isn’t my first textbook on game theory. My earlier book,FunandGames,wasusedquitewidelyforteachingadvancedundergraduate andbeginninggraduatestudents.Ihadoriginallyplannedamodestlyrevisedsecond edition, in which the rather severe introduction would be replaced with a new chapterthatwouldeasestudentsintothesubjectbyrunningthroughalltheangleson 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 Iplannedto make butsomehow 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 viii Preface seemed a little daring at the time now look totally uncontroversial. So I have tried myluck at guessingwhich way the subject is going tojump again. The second reason is that I have moved on as well. In particular, I have done a greatdealofconsultingwork,applyinggametheorytoreal-worldproblemsinorder to raise money for my research center. The biggest project was the design of a telecomauctionthatraised$35billion.Ialwaysknewthatgametheoryworks,but seeingittriumphonsuchascalewasbeyondallexpectation!Ihavealsowrittena book applying game theory to philosophical issues, which taught me a great deal abouthowandwhybeginnersmakemistakeswhenthinkingaboutstrategicissues. BothkindsofexperiencehavecontributedtomakingPlayingforRealabetterbook than its predecessor. My flirtation with philosophy even generated a lot of light- hearted exercises that nevertheless make genuinelyserious 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,sothatstudentswhoseskillsarerustycankeepupwithwhat’sgoing onwithouttoomucheffort.However,thebookasawholecoversfewerbasictopics 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 madeBertrand-Edgeworthcompetitionaccessibletoundergraduates.Itisatragedy thatevolutionarygametheoryhadtogo,butthisimportantsubjecthasgottensobig thatit deserves awholebook toitself. Althoughfewertopicsarecovered,sometopicsarecoveredinmuchmoredetail thaninFunandGames.Theseincludecooperativegametheory,Bayesiandecision theory, games of incomplete information, mechanism 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- understandingsofthetheorythathavebecomecommonplaceinappliedwork,and partlybecauseIwantedtoillustrateitspotentialuseinethicsandmoralphilosophy. Teaching. There is enough material in this book for at least two courses in game phil theory,evenleavingasidethereviewandothersectionsthatareintendedforprivate reading. Ihave tried tomakethings easyfor teacherswho want todesignacourse basedonaselectionoftopics fromthe wholebookbyincludingmarginal notesto 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 ! 1.1 philosophyin thispreface. 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 asmallnumber ofcarefullychosenexercises every week. Preface ix Once they get into the habit, students are often surprised tofind thatsolvingprob- lems can be a lotof fun. By the time the book is published, Jernej Copic will have finished getting his solutions onto a website. Oxford University Press will provide access details to recognized teachers. Thanks. Somanypeoplehavehelpedme,withbothFunandGamesandPlayingfor Real,thatIhavelosttrackofthemall.Ishallthereforementiononlytheveryspecial debt of gratitude I owe to my long-time 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 Moore Scholar. I should also acknowledge the Victorian artist John Tenniel, whose mag- nificentillustrationsfromLewisCarroll’sAlicebooksIhaveshamelesslystolenand messed around with. Apologies. Let me aopolgize in advance for the errors that have doubtless found theirwayintoPlayingforReal.Ifyoufindanerror,pleasejointhemanyotherswho have helped me by letting me know about it at [email protected]. I will be genuinely grateful. Finally,Ineedtoapologizenotonlyformymistakesbutalsoformyattemptsat humor. Oscar Wilde reported that a piano in a Western saloon carried a notice saying,‘‘Pleasedon’tshootthepianist.He’sdoinghisbest.’’Thesamegoesforme, too. It isn’t easy to write in a light-hearted style when presenting mathematical material, butIdid mybest. Ken Binmore