Restoring Fun to Game TheoryAuthor(s): Avinash DixitSource: The Journal of Economic Education, Vol. 36, No. 3 (Summer, 2005), pp. 205-219Published by: Taylor & Francis, Ltd.Stable URL: http://www.jstor.org/stable/30042655 .Accessed: 16/02/2015 06:27Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp .JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range ofcontent in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new formsof scholarship. For more information about JSTOR, please contact support@jstor.org. .Taylor & Francis, Ltd. is collaborating with JSTOR to digitize, preserve and extend access to The Journal ofEconomic Education.http://www.jstor.org This content downloaded from 134.219.234.121 on Mon, 16 Feb 2015 06:27:14 AMAll use subject to JSTOR Terms and ConditionsRestoring Funto Game Theory AvinashDixit Abstract:The author suggests methodsfor teachinggametheory at an introduc- tory level, using interactive games to be played in theclassroomor in computer clusters, clips frommoviesto be screenedand discussed, and excerpts from novelsand historicalbooksto be readand discussed. JEL codes: A22, C70 Game theory startswithan unfair advantage overmostotherscientific subjects-it is applicable to numerous interesting and thought-provokingaspects of decision- making in economics,business, politics, social interactions, andindeedto muchof everyday life, making it automaticallyappealing to students. However, too many teachersandtextbookauthorslose this advantagebytreating the subject in suchan abstractandformal way thatthestudents' eyesglaze over.Eventheinterestsofthe abstracttheoristswillbe betterservedif introductory coursesare motivated using examples and classroom games that engage thestudents'interestand encourage themto go on to moreadvancedcourses.This willcreate larger audiencesforthe abstract game theorists; then they can teachstudentsthemathematicsandthe rigor thatare surelyimportantaspects ofthe subject at the higher levels. Game theory has becomea part of thebasic frameworkof economics, along with, or even replacing in many contexts, thetraditional supply-demand frame- workin partial and generalequilibrium. Thereforeeconomicsstudentsshouldbe introducedto gametheoryright at the beginning oftheirstudies.Teachersofeco- nomics usually introduce gametheoryby using economics applications; Cournot duopoly is the favoritevehicle. However, I prefer a different approach. Even before anyone is exposed to any economics, everyone has beeninvolvedin many strategicgames.Undergraduates have played such games with siblings, friends, and parents;strategy is an importantaspect of manysportsthey have played and watched; and many moviesandbookshavethemesor episodes with game-theoretic content. Following thetime-honored principle of teaching thatone shouldstart withwhatthestudents already knowand proceed to buildon it, I prefer to teach introductorygame theoryby usingexamples drawnfromsuch sources.1 I have foundthatthis approach makes it not only possible, but also productive and enjoyable, to introduce gametheory at an elementary levelin colleges and even in thebetter high schools. In the earlydays of gametheory, eventhemathematicianswhocreateditsfoun- dationsshoweda sense of fun.Von Neumannand Morgenstern(1953, 176-78) AvinashDixit is a professorof economicsat Princeton University(e-mail:dixitak@princeton.edu). TheauthorthanksWilliamBecker for commentson a preliminarydraft. Summer2005205 This content downloaded from 134.219.234.121 on Mon, 16 Feb 2015 06:27:14 AMAll use subject to JSTOR Terms and Conditionsexpounded mixed strategyequilibriausing the story of SherlockHolmes trying to evadethe pursuing Professor Moriarty. Williams (1966) gave an exposition oftwo- person zero-summinimax theorybyusingmanyamusingexamples,althoughthey verged on thetrivialbecauseoftherestricted scope. Tucker's1950inventionofthe story of the prisoner's dilemma (Nasar 1998, 118) was surely a strokeof genius. Mostrecenttheoristshavebeen comparativelyhumorless, even thoughthey invent amusing names, suchas the centipede, horse, or beer-quiche, fortheirmathemati- cal examples. It is timefuncamebackto gametheory. I have developed suchan elementary courseand taught it at Princetonforsev- eral years. Susan Skeathhas donethesameat Wellesley. We havewrittena text- book (Dixit and Skeath 2004), now in its second edition, forsuch a course, comparable in level and style to anyintroductory or principles textbookin eco- nomics, political science, or naturalsciences.In this article, I offersome teaching ideas and tricksthatI havelearnedfromthis experience. I restrictmostof my remarksto the teaching of game theoryper se and not as a part of an economicscourse.This is because I hold a ratherradicalview: An introductionto game theory should precede, not follow, the introductory economicscoursesin microand macro. Knowing the concepts of strategy, roll- back, and Nash equilibriumhelps one unifymanyapparently distinctideas and phenomena in economics. Therefore, previousknowledge of elementarygame theory will make learning economicseasier.For example, if students already know assurance games, Keynesianunemployment becomes a coordination failure leading to a wrongequilibrium selection, ratherthan a mysterious crossing of two graphs, and many marketfailuresin microfall intothecom- mon frameworkof the prisoner's dilemma. Also, the view of competition as live interactionof strategies is more appealing to beginners thanthatof an impersonaladjustment of prices by an invisiblehand. Elaborationof this themeof teaching economicswith gametheory meritsan article by itself; how- ever, I believe that approach to be appropriate for an intermediatelevel of teachinggametheory to economics students, whereashereI focuson theintro- ductory level. GAMES IN CLASS Playing a few well-designedgames in class and watching others play them brings to lifethe concepts of strategy, backward induction, and Nash equilibrium farbetterthan any amountofformalstatementor problem-set drill. Indeed, I like to start mygame theory coursewithtwo classroom games, before teaching or even mentioningany ofthese concepts at all. The conceptsemergenaturally dur- ing thediscussionof each game. A Sequential-Move Game This simple Nim-like game can be played in many formats.A particularly attractiveone comes fromits use in one of the "Survivor"TV series,namely episode 6 of "SurvivorThailand,"whichairedin fall2002. In this episode, there 206JOURNALOF ECONOMICEDUCATION This content downloaded from 134.219.234.121 on Mon, 16 Feb 2015 06:27:14 AMAll use subject to JSTOR Terms and Conditionswere21 flags and two players, who alternated in taking turns to removesome flags. At each turn, the player hadto remove 1, 2, or 3 flags; thiswas the player's choiceat each move.The player who removedthelast flag(whether as thesole remainingflag or one of thelast surviving set of 2 or 3 flags) was thewinner. Insteadof usingflags, theinstructorcan use coins; lay themouton the glass of theoverhead projector so thewholeclass can easily see whatis going on. In the "Survivor" show, the game was played as an "immunitychallenge" betweentwo teams, calledtribes.The losing tribehadto voteoutone ofitsmem- bers,weakening it forfuture competitions. In the specific context, thisloss had a crucialeffecton theeventualoutcomeof the game. Thus a million-dollar prize hinged on the ability to do the simple calculation.A video clip ofthe competition is available fromthe Web site for the show, http://www.cbs.com/primetime/ survivor5/show/episode06/s5story.shtml. Withthe right kindof equipment avail- ableinthe classroom, theinstructorcan downloadandshowthe clip, "MoreAction at the ImmunityChallenge," availablefrom page fiveof thissite.The actual play- ers got almostall oftheirmoves wrong, so seeing itfirstandthen playing a similar game themselveswillbe a goodway forstudentsto learnthe concepts. The correctsolutionis simple. If player 1 (or team 1) leaves player 2 (or team 2) withfour flags,player 2 mustremove 1, 2, or 3, and then player 1 can takethe restand win.To makesurethat player 1 leaves player 2 withfour flags,player 1 mustleave player 2 facingeightflags on the immediatelypreceding turn. The log- ical sequence thenis to leave 12, 16, and 20 on previous turns. Therefore, start- ing with21 flags,player 1 shouldremoveone and proceed to takefourminus whatever player 2 takesat the immediatelypreceding turn. The firsttimea pair of students play this game,they makechoicesalmostat random.Aftertheir game is over, watched by the whole class, the instructor choosestwoothers. They do betterthanthefirst pair;theyfigure outone or per- haps eventwoofthefinalrounds correctly.By thethirdor at mostthefourth time, the players willhave figured outthefullbackwardinduction. The instructorshouldthenholda briefdiscussionand nudge or guide thedis- cussiona littletowardthreeconclusions. First, theidea of backward induction, or the importance of solvingsequential-movegames backwardfromthe final moves. Second, the idea of correct strategies thatconstitutea solutionof the game. Tell thestudentsthatit will soon be given a formal name, rollback equi- librium. Finally, theidea thatone can learncorrect strategiesby actuallyplaying a game. Withthiscomestheidea thatifa game is playedbyexperiencedplayers, one mightexpect to observecorrect strategies and equilibrium outcomes.This will give thestudentssomeconfidenceinthe concepts ofbackwardinductionand rollback equilibrium. The lastremarkmotivatesa brief digression. Overthe past decade, behavioral game theoristshave made a valuablecontributionto the stockof interesting games thatcan be played inclassrooms. However, many ofthemcometo thesub- ject witha negativeagenda,namely to argue that everything inconventional game theory is wrong.My own experiencesuggests otherwise.To be sure,ittakestime and experiencemerely to understandtherulesof anygame and a lotof practice and experimentation to play it well; but students learn quite fast.Advanced Summer2005207 This content downloaded from 134.219.234.121 on Mon, 16 Feb 2015 06:27:14 AMAll use subject to JSTOR Terms and Conditionsresearchers delight in thedifficultiesof learning and on howactualoutcomescan differfromthe equilibriumpredictions. However, it is counterproductive to give the impression to beginners thatwhat they are aboutto learnis all wrong; it destroys theirwhole motivationto learn.I findit betterto convey a sense of guardedoptimism about the standardNash theory, without pretending thatit closes the subject. Of course, I believethisto be thetruthof thematter. A Simultaneous-MoveGame My second game is a versionof the famous "generalizedbeauty contest." Choose 10 studentsin theclass and give themblankcards.Each studentis to writehis or hernameon thecardand a numberbetween0 and 100; collectthe cardsand average thenumberson them.The studentwhosechoiceis closestto halfof the average is thewinner.Theserulesare of course explained in advance and in public. The Nash equilibrium of this game is 0. In fact, it resultsfroman iterated dominance argument. Because.the average can neverexceed 100, half of the average can neverexceed 50. Therefore, any choice above 50 is dominated by 50. Thenthe average can neverexceed 50, .... The firsttimethe game is played, the winneris usually close to 25. This fits Nagel's (1995) observationthatthe outcomeis as if thestudents expect theothersto choose at random, averaging 50, and thenchoosehalfofthat. Next, choosea differentsetof 10 studentsfrom theclass (who havewatchedtheoutcomeofthefirst group'sgame). This second group chooses muchsmaller numbers, and thewinneris close to 10 (as if one moreroundof thedominancecalculationwas performed) or even 5 or 6 (as if twomoreroundswere performed). The third group of 10 choosesmuchsmaller numbers, including several zeros, and thewinner'schoice is as low as 3 or 4. Incidentally, I have foundthat learningproceeds somewhatfaster by watching others play thanwhenthesame group of 10 playssuccessively.Perhaps thebrain does a better job of observationand interpretation if the ego is not engaged in playing the game. Again, hold a briefdiscussion.The instructorshould bring out the following points: 1. The logicalconcept of dominance, iteratedeliminationofdominatedstrate- gies, and theculminationin a Nash equilibrium. 2. Getting close to the Nash equilibriumby the experience of playing the game. Whetherit is a crucialflaw of the theory that0 is rarelyexactly attained, or the theorygives a good approximation, can be a point to be debated depending on thetimeavailable. 3. The idea thatifone has a good reasontobelievethatotherswillnotbe play- ing theirNash equilibriumstrategies, thenone's optimal choice will also differfromone's ownNash equilibriumstrategy. The discussioncan also touchon the question: Whatif the object is to come closestto the average, nothalfof the average? That gameis, of course,Keynes' famous metaphor forthestockmarket,where everyone is trying to guess what 208JOURNALOF ECONOMICEDUCATION This content downloaded from 134.219.234.121 on Mon, 16 Feb 2015 06:27:14 AMAll use subject to JSTOR Terms and Conditionseveryone else is trying to guess. The game has multiple Nash equilibria, each sus- tained by itsown bootstraps. Detailsof thisare best postponed to a later point in thecoursewhentheinstructorcovers multipleequilibria more systematically, but a quick mentionin thefirstclass provides the studentsan interesting economic application attheoutset.The instructorcan also stressthe importance ofthis game in thestudents'ownlives.Partorevenall oftheirretirementfundsare likely tobe in individualaccounts.When they decidehowto investthis sum, they willhaveto think through the question: Will thehistorical pattern of returnsand volatility of variousassets persist when everyone makesthesamedecisionsthatI am nowcon- templating? This interactionbetweenindividualchoice (strategy) and aggregate outcomes (equilibrium) comes naturally to someonewho is trainedto thinkin game theories, butothersare oftenliableto forget theeffectof everyone's simul- taneouschoices.In thecontextof saving for retirement, thiscan be verycostly. All-Pay Auction In later classes, I play severalother games, suchas the centipede and ultima- tum games, and, of course, severalvariantsof prisoners' dilemmasand collective action games, each of whichillustratesa basic theoretical concept or some way in whichthe experience of realitydeparts fromthe theory. An amusing climaxI havetriedin the very lastclass is the applause auction.Princetonhas a tradition thatat theendoftheinstructors'lastlecturesin each course theyget a brief polite roundof applause. At this point, I offera reward, usually $20 butsometimesas muchas $50, to the person who continuouslyapplauds the longest. Thisis an all- pay auction; thestudentsare bidding in kind, namelyapplause, and all bidders pay their bids, winor lose. Most students drop out withinthefirst15 or 20 minutes, but a few remain applauding for absurdlylongperiods. The recordto dateis whenthreestudents applauded for 41/2 hours.To complete theeducational purpose of the game (and to avoidtheriskof a headline, "Professor BuysApplause," in thestudentnews- paper), I sendan e-mailto theclass explaining the game. I point outthat all-pay auctionsare quite common:The contestantsin sportingcompetitions or elections spend their time,efforts, and money, withno refundsforthelosers.Suchcontests can escalate, and thenucleararmsrace was a classic example of overbidding. I referthemto Hirshleiferand Riley (1992, ch. 10) and Bulow and Klemperer (1999) forthe theory of such games. I tell themabout any interestingspecial occurrencesin that year's competition. One year, for example, six people remainedand were discussingsplitting the prize; five agreed, butone refused.At that point, theotherfive gotangry and threatenedto stay as long as necessary to outlastthesixth.Aftera fewminutesof experiencing the credibility of this threat, thesixth gaveup, andthentheotherfive stoppedsimultaneously to sharethe prize. This was a nice example of people's instinctive willingness to punish antisocial behaviorevenat a personal cost (Fehr and Gichter 2000). The combined experience of teachersof gametheory is graduallycreating an impressive collectionofclassroom games. Anotherrecent example is Brokawand Merz (2004). Summer2005209 This content downloaded from 134.219.234.121 on Mon, 16 Feb 2015 06:27:14 AMAll use subject to JSTOR Terms and ConditionsRole-Playing Gameswheretheclass is split intoteamsthat play differentrolesin acting out a strategic situationcan be very instructive.I haverunsuch sessions, forexam- ple, one whereterroristsorbankrobbershavetaken hostages, andtheauthorities are negotiating fortheir release, and anotheron negotiation for peace in the MiddleEast. I assign some generalbackgroundreading, butotherwiseleave the studentsto devisetheirown agendas and strategies. I findthat they takethese exercises seriously andthinkhardandwell.The MiddleEast peace negotiation is a case in point. The studentsdevised imaginative and realistic strategies. The Israeli delegation did notshow up butinsteadsenta declaration saying that they wouldnot negotiate untiltheviolenceended.The Palestinian delegation showed up with good intentionsbutcould not crediblypromise to controltheirextreme factions. Finally, theextremist grouppulled outwater pistols and held everyone hostage! The UnitedNations delegation shouldhave thought of thisand should have postedguards at thedoorto check backpacks. Because I give thestudentsa lotof freedom, I havetothinkaheadandbe ready fora large numberof alternativescenariosthatcould develop, but, on occasion, I havebeen pleasantlysurprisedby thestudents'ideas. Otherteachers mayprefer a somewhat tighter structure, butI thinkthateven they willlearn something from suchexercises. Computer Games: The Wild-WestShootout Finally, itis possible to program moreelaborate games on a computer network. Numerous games ofthiskindare readily available; CharlesHoltofthe University of Virginia offersan excellentcollectionof Web-based games on his Web site, http://www.people.virginia.edu/-cah2k/teaching.html. VesnaPrasnikarof Carnegie Mellon University has softwarecalled Comlabgames, and Paul Romer'sWeb- based educationalmaterials companyAplia (http://www.aplia.com) markets game-playing software. However, I findthat many such games aretoo abstract- they offermatricesor treesto which payoffs can be added, and thestudentsare askedto taketheroworcolumnroles.I prefer oneswithcontextand appeal better relatedto thekindsof computergames studentswillhave played before. My bestsuch game is a four-person, three-bulletduel. (The nameofthe game could be "The Good, the Bad, the Bold, and the Beautiful.") Studentsin the class are seatedat terminalsin the computer clusterand randomly matchedinto foursomes.Each person in a foursomesees on his orherscreena square divided intofour quadrants; thisis schematicallyreproduced in Figure 1. Each player startswiththree bullets, and as long as he or she is still"alive"in the game, can shootat any of theothersat any time.To shootat a player, thestudentmoves thecursorintotheintendedvictim's quadrant and clickson theleftmousebut- ton.The probability of scoring a hitincreaseswith time, and thisis indicated by the shrinkage of a central square that overlaps the four quadrants. At any time,the probability of hitting an adjacentplayer is higher thanthatof hitting the diagonallyoppositeplayer. The ruleshandedout at the beginning of the game 210JOURNALOF ECONOMICEDUCATION This content downloaded from 134.219.234.121 on Mon, 16 Feb 2015 06:27:14 AMAll use subject to JSTOR Terms and ConditionsTime remaining = 85seconds Playcr A Alive Shotsleft:2 Player B Dead Shotsleft:I ...... MOM" Player D Dead Shotsleft:3 Player C Alive Shotsleft:2 FIGURE 1. The four-person, three-bulletduel. statetheformulasfortheincreasesin probabilities. The total shrinkage timeis twominutes.The player's scorein any one such playequals thenumberof sec- ondsthestudent stays alive, plus a bonusof 50 points ifthe player is aliveat the endofthetwo minutes, andan additionalbonusof 100 points ifthestudentis the onlyplayer in thefoursometo remainaliveat theendofthetwominutes (to dis- courage collusionwhereno one shoots). This game is played several times, with varying matches, so thatno foursomesare repeated. Indeed, the identity oftheothersin one'sfoursomein any one play is not madeknown.Eachstudent'sscoreforthesessionis the average overall the games he orshe plays. Thisformsa small part ofthecourse credit, so thestakesare quitehigh. Therearealso setsof repetitions underdifferentinformationconditions.In the first, everyplayer knowswhethereach oftheothersis aliveordead andthenum- berof bullets they have left; thisis theconditionshownin Figure 1. In thesec- ond, each player knowswhethertheothersare aliveor dead butnotthenumber of bullets they have left; thusthe last of the threeinformationlines does not appear inthissetof repetitions. In the third, the players do notevenknowwhether theothersarealiveor dead; thisis as if they are hiding behinda building or a tree in an actualWild-Westshootout. As faras I know, this game has no analytical solution. My observationfromthe classroom performance is that reasonablypatientstrategies do well and thatless patience is slightly betterin thelaterlimitedinformationconditionsbutthatmost studentsaretoo impatient andshoottoo many bulletstoo quickly. I havealso tried sessionsof the gameaccompaniedby suitably tensemusic (Bolero or theJames Bond theme) and found, as expected, thatthisleads to itchier fingers on the trig- ger.Playing this game severaltimesandin differentinformationconditions gives thestudentsa good hands-on way of learning howto develop heuristicsfor games in whichthe calculationof Nash equilibrium is too difficult. (See Simon and Summer2005211 This content downloaded from 134.219.234.121 on Mon, 16 Feb 2015 06:27:14 AMAll use subject to JSTOR Terms and ConditionsSchaeffer 1992; Dixitand Skeath 2004, sec. 3.5B, fora discussionofchessfrom this perspective.) This game has its counterparts in economicsand business.The general idea is that you facea tradeoffbetween shooting lateto increasethe probability of scor- ing a hitand shootingearly to reducetheriskof getting shot by someoneelse. Thisis thesamesituationthatfirmsin high-technology industriesfacewhen they are deciding whento introducea new product-wait to makeit more perfect or rushto be firstin themarket?The gamegives studentsan interesting hands-on experience of thecalculationand thetensioninvolvedin suchdecisions. The code forthe game is specific to Princeton's computer cluster system, but if instructorswantto implement the game in theirown institution, anycompetent computer science major shouldbe able to writethecode forthecluster during the summerbetween junior and senior years. I have implemented twoother games- a prisoner's dilemmaanda bargaininggame-and can supply similarinformation aboutthemon request forteacherswho wantto get them programmed at their schools. Some Advicefor Conducting ClassroomGames My experience leads me to makesome suggestions on how to, and how not to, conductsuch games. First, use real money for prizes. Even smallamounts raise studentinterestand attention.The students'scoresin the game can count fora smallfractionof thecoursecreditbutdo notchoose games wheretheout- come dependssignificantly on chanceratherthanskill. Next, use games with stories, not just abstracttreesor matrices, butdo notmakethe story ofthe game so complex thatthe main conceptualpoint is smothered. Finally, followeach game immediately witha discussionthat brings out the generalconcepts or methodsof analysis thatthe game was supposed to illustrate.If thereis not enough timefora good discussion, circulatean explanation or post it on the courseWeb site. MOVIES AND TV SHOWS Many moviescontainscenesthatillustratesome aspect of strategic interaction. These scenescan be screenedin class as an introductionto that topic, and a dis- cussioncan lead to theoretical analysis of it. Nash Equilibrium One cannotask fora bettermovieto get studentsto improve their understanding ofthisbasic concept of gametheory thanA Beautiful Mind, whichwas based, how- ever loosely, on thelifeofJohnNash himself, andin turnon Nasar's (1998) biog- raphy, which, although it emphasized the psychological andmental aspects,gave a correctaccountoftheNash equilibriumconcept. Thecrucialscenefromthemovie, whereNashis supposed to havediscoveredhis concept of equilibrium, showshim in a barwiththreemalefriends.A blondeandherfourbrunettefriendswalkin.All 212JOURNALOF ECONOMICEDUCATION This content downloaded from 134.219.234.121 on Mon, 16 Feb 2015 06:27:14 AMAll use subject to JSTOR Terms and Conditionsfourmenwouldliketo wintheblonde'sfavor. However, if they all approach her, each will standat besta one-fourth chance; actually, themovieseemsto suggest thatshewould reject all four.The menwillhaveto turnto the brunettes, butthen thebrunetteswill reject them also, because"no one likesto be secondchoice."In the movie, Nash says thatthesolutionis forthemall to ignore theblondeand go forthebrunettes.One of theothermenthinksthisis just a ploy on Nash's part to get theothersto go forthebrunettesso he can be theblonde'ssole suitor.If one thinksaboutthesituation usinggametheory, theNash characteris wrong and the friendis right. The strategyprofile whereall men go forthebrunettesis nota Nash equilibrium: Giventhe strategies ofthe others, any one ofthem gainsbydeviating and going fortheblonde.In fact, Andersonand Engers(2002) showthatthe game has multipleequilibria, butthe only outcomethatcannotbe a Nash equilibrium is the supposedly brilliantsolutionfound by theNashcharacter! Mixed Strategies The concept of mixed strategies is often initially counterintuitive. Although many situationsin sports serveto introduce it, I likeone scenefromThePrincess Bride, a whimsical comedy thathas theadded advantage of being a favoriteteen movie.In this scene, thehero (Westley)challenges one ofthevillains (Vizzini) to a duelofwits. Westley will poison one of twowine cups withoutVizzini observ- ing hisactionand setone in frontofeachofthem.Vizziniwilldecidefromwhich cup he will drink; Westley thenmustdrinkfromthe other cup. Vizzini goes through a whole sequence of arguments as to whyWestley wouldor wouldnot chooseto poison one cup ortheother. Finally, he believeshe knowswhich cup is safeanddrinksfromit. Westley drinksfromtheother.Justas Vizziniis laughing and advisingWestley to "never go against a Sicilianwhendeathis on the line," Vizzini drops dead. Pausethe videotape ordiscat this point andhavea briefdiscussion.The students will quickly seethat eachof Vizzini's arguments is inherently self- contradictory. If Westley thinks through to the same point thatleads Vizzinito believethata particularcup willcontainthe poison, he shouldinstead put the poison in theother cup.Anysystematic actioncan be thoughtthrough anddefeated by the other player. Therefore, the only correct strategy is tobe unsystematic orrandom. Asymmetric Information Actually, thisis notthemain point of the story. Resumethe tape or disc. The princess is surprised to findthat Westley had put the poison in the cup he placed closerto himself. "They wereboth poisoned," he replies. "I have been building up immunity to locainefor years." Thusthe gamebeingplayed was really one of asymmetric information; Vizzini did not know Westley'spayoffs and did not thinkthe strategy of poisoning both cups was open to him.At this point,you can showa clip fromanothermovieclassic,Guys and Dolls. Sky Mastersonrecalls advicefromhisfather:"Son, no matterhowfar youtravel, or howsmart youget, always rememberthis:Some day,somewhere, a guy is going to cometo you and Summer2005213 This content downloaded from 134.219.234.121 on Mon, 16 Feb 2015 06:27:14 AMAll use subject to JSTOR Terms and Conditionsshow you a nicebrand-newdeckof cardson whichtheseal is never broken, and this guy is going to offerto bet you thatthe jack of spades will jump outof this deckand squirt ciderin your ear.But son, do notbet him, foras sureas you do you are going to get an ear fullof cider" (Runyon 1933 [1992]). Brinkmanship Many movieshavescenesthatdeal withthe question of howto get somevital informationthat onlyyouradversarypossesses becausehe knowsthatthethreatof killing him is not credible.The situation plays out differently in High Windin Jamaica, Crimson Tide, TheMaltese Falcon, andTheGodsMustBe Crazy. You can show excerpts fromall fourandthenholda discussionto compare andcontrastthem. In High Windin Jamaica, the piratecaptain, Chavez (the information seeker), backsoffandtriesa different approach. In Crimson Tide, theU.S. Navy submarine captainRamsey threatensto killa co-conspirator ofthe person whohas thecrucial firing codesforthesubmarine'smissiles.This works; the persongivesup thecode. The conspirators were trying to prevent thestartofa possiblyunnecessary nuclear warin whichmillionswould die, butit is interesting thattheimmediatedeathof someone you knowcan weigh morein your calculationthanabstract megadeaths. In TheMaltese Falcon, the hero, Samuel Spade (playedbyHumphreyBogart), is the onlyperson whoknowswherethe pricelessgem-studded falconis hidden, andthechief villain, Caspar Gutman (SydneyGreenstreet), is threatening himfor thisinformation.This produces a classic exchange, herecitedfromthe book (Hammett1930,223-24) but reproduced almostverbatimin themovie. Spadeflung hiswordsoutwitha brutalsortofcarelessnessthat gave themmore weight than they couldhave got fromdramatic emphasis orfromloudness."If you kill me, howare yougoing to get thebird?IfI know you can'taffordtokillmetill you have it, howare yougoing toscaremeinto giving itto you?" Gutmancockedhisheadtotheleftandconsideredthese questions. His eyes twin- kled between puckered lids. Presently, he gave his genial answer: "Well,sir, thereare othermeansof persuasion besides killing and threatening tokill." "Sure,"Spadeagreed, "but they're notmuch good unlessthethreatofdeathisbehind themtoholdthevictimdown.See whatI mean?If youtrysomething I don'tlikeI won'tstandforit.I'll makeita matterof yourhaving tocallitofforkill me, know- ingyou can'taffordtokillme." "I see what you mean."Gutmanchuckled."Thatis an attitude,sir, thatcallsforthe mostdelicate judgment on both sides,because, as you know,sir, menare likely to forget intheheatofactionwheretheirbestinterestslieandlettheiremotions carry them away." Spade toowasall smiling blandness."That'sthe trick, from my side," he said, "to make myplaystrongenough thatitties youup, but yet notmake you mad enough to bump meoff againstyour better judgment." The class discussioncan explore thenatureofthese strategies. The scenecan be seenas an example of Schelling's(1960, 17-18) ideaofthe (strategic)rationality of (seeming)irrationality; Gutmanis making histhreatcredible bypointing outthathe may act irrationally. It is betterseen as an example of the dynamicgame of 214JOURNALOF ECONOMICEDUCATION This content downloaded from 134.219.234.121 on Mon, 16 Feb 2015 06:27:14 AMAll use subject to JSTOR Terms and Conditionsbrinkmanship(Schelling 1960, ch. 8; 1966, ch. 3). Both parties,bypersisting intheir actions-Gutmanin histortureand Spade in hisdefiance-are raising theriskthat Gutman maygetangry anddo somethingagainst hisownrationalinterest.Each is exploring therisktoleranceofthe other, inthe hope thatitis lowerthanhisownrisk toleranceso thattheotherwillblinkfirst.A moreformal analysis ofthisinthecon- textoftheCubanmissilecrisisis foundin DixitandSkeath (2004, ch. 14). The scenefromThe Gods MustBe Crazy makesthisescalationof riskmore explicit. An assassination attempt on thedictatorof an African country has failed, andone oftheteamof gunmen has been captured. He is beinginterrogated forthe locationofthe group'sheadquarters andtheleader.The sceneis theinsideofa hel- icopter. The blindfolded gunman is standing withhisbackto the open door.Above thenoiseofthe rotors, the army officer questions the gunman a couple oftimesand getsonly shakesofthehead.Thenhe simplypushes the gunman outthedoor.The sceneswitchestotheoutsideofthe helicopter, whichwe nowsee is justbarely hov- ering abovethe ground, andthe gunman hasfallensixfeeton tohisback.The army officer appears at thedoorand says, "The nexttimeitwillbe a littlebit higher." Brinkmanship arisesin many economic contexts, most notably thatof wage bargaining wheretheriskof a strikeor a lockoutincreasesas protractednegotia- tionsfail to produce results. Understanding the subtletiesand the risksof this strategy is thereforean importantpart of an economist's education, and these moviescenesillustrateit in memorable ways. Dr. Strangelove This is a universalfavorite strategic movie; it illustrates many issuesof com- mitments,threats, and promises, all withina compelling narrativefulloftension and satiricalhumor.Two scenesin the Pentagon warroomareessential viewing: (a) the one in whichthe U.S. PresidentMerkin Muffley hearshow General Ripper has made irreversiblehis unauthorized launching of a nuclearattackon theSovietUnion by cutting offall communicationwithhisbase and withtheair- craftand (b) the one in whichDr. Strangeloveexplainswhy the doomsday machineis sucha credibledeterrent.Whenthe president asks, "Buthowis it pos- sibleforthemachineto be triggeredautomatically and yetimpossible to de-trig- ger?"Strangelovereplies, "Mr. President, it is not onlypossible; it is essential. Thatis the whole idea." Then he asks the Soviet ambassador, "But the whole point ofthemachineis lostif youkeep ita secret. Why didn't you telltheworld?" Thereare numerousotherincidentsin themoviethatillustrateother points of strategy, and a good case can be made for screening thewhole movieand dis- cussing it. However, thecontextofthecold war may be too datedfor today's stu- dents, and theymay findthe periodatmosphere-the black-and-white film, the sexist jokes-unappealing. Witha little priorexplanation ofthecontextandwarn- ings thatthe offensive-sounding bitsare satirical, my studentshave enjoyed the movie; however, a large fractionof them (having been brainwashed by Hollywood)expected to thelast minutethattherewouldbe a happyending in whichsomehowthe plane wouldbe recalled. Summer2005215 This content downloaded from 134.219.234.121 on Mon, 16 Feb 2015 06:27:14 AMAll use subject to JSTOR Terms and ConditionsThese moviesare just a fewof the large collectionthatis available; I am sure otherteachershave theirown differentfavorites.Televisioncan also be a good source.Trandel (1999) offersan earlyexample froma game show. Manyepisodes of theBBC sitcoms "Yes, Minister"and "Yes, PrimeMinister"are outstanding lessons in strategy:bargaining, commitment, signaling, and screening. Unfortunately, the setting is toounfamiliarto non-British students, andthe period is also getting datedfor many of them, even though itis barely 10 to 20 yearsago. Finally, in thefirstof theCBS "Survivor" series, theeventual winner, Richard Hatch, used a clever "losing to win" strategy to get to thefinaltwosome.This is too lengthy to explain here, butthe scene is availablefromtheCBS Web site http://www.cbs.com/primetime/survivor/show/episodel 13/story.shtml. The immu- nitychallenge whenthree players are leftis thecrucialscene.A game-theory- based analysis is foundin Dixitand Skeath (2004, sec. 3.7). AdviceforMovie Screenings As withclassroom games,my own experience of movie screenings leadsme to makesome suggestions. First, instructorsshouldtake suggestions fromstudents aboutothermoviesor games theclass can use-students'ideas aremore likely to be appealing to otherstudentsthanarethe instructors', which may datebacka few years and therefore may be unfamiliarand uninteresting to today'syoung adults. Instructorsshouldask and discussin advance just what strategic issuethe excerpt illustrates.Oncethe students' interestsare engaged, instructorscan enlisttheir help in acquiringtapes or DVDs. Next, instructorsneed to come prepared withtheir videotapes woundto theexact point that they wantthemovieto start.Ifinstructors needto showtwoormore disjointexcerpts fromthesame movie, they should bring the appropriate numberof copies ofthe tape, eachcuedtothe rightplace. Ifinstruc- torsare using DVDs, they needto makea noteoftheexacttime (minutes and sec- onds) wherethedesired excerptbegins and practice in advancehow to startthe DVD quickly at the rightpoint. If thestudentshaveto waitwhileinstructorsfind the rightplace orthe right button, orwhileinstructorswindthe tape tothenextstart- ingpoint, thestudentsare distracted, andthemovieorTV clips lose effectiveness. Instructorsshould not assume thatstudentsknow the generalplots of the moviesfromwhich they are showingexcerpts.They should prepare a brief expla- nationof thesituationand thecharactersas theypertain to the excerpt and give the explanationjust before starting the videotape. Instructorsshouldnotshowa wholemovieor a longclip when only a small pointpertains to strategy; thestu- dentswill get distracted by too many of theotherincidental aspects. LITERATURE Novelsand shortstoriesare an evenrichercollectionof illustrationsof strate- gies in action.Les Liaisons Dangereuses mustbe an unmatchedsourceforana- lyzing issues of credibility and of private informationaboutmotives (players' types). Historical literaturealsohas valuable insights;Thucydides' The Peloponnesian War recountsdebates and speeches that have outstanding 216JOURNALOF ECONOMICEDUCATION This content downloaded from 134.219.234.121 on Mon, 16 Feb 2015 06:27:14 AMAll use subject to JSTOR Terms and Conditionsexpositions of strategic themes.In Shakespeare'sHenry V, the famous speech beforethebattleof Agincourt is an excellent example of incentivesto motivate soldiersto fight(see thediscussionin Dixit and Nalebuff [1991, 161-63]), and Othellois fullof strategic issues. Many novelsof crimeand detection, withtheirthemesof informationand betrayal, are also excellentsourcesfor illustrating these ideas. My personal favoriteis Cogan's Trade by Higgins (1974). In it, theBostonmafia protects a high-stakespokergame. The person(Trattman) who runsthe game himself arranges forit to be robbed. By thetimethemafiabosses find this, all thefuss has died down, and because Trattmanis well-liked, the bosses do nothing. However, someothers got theidea thatif they robthe game, Trattmanwouldbe the automatic suspect, and they would escape detection.The mafiabosses dis- coverthe truth, but they facea biggerproblem-theirreputation as effective pro- tectorshas been ruinedand mustbe rebuilt.For this, they need a signaling strategy, and to makeit crediblein thestandard Spencian manner, the signal has to be carriedto excess, in this instance, literally to overkill. Cogan, the up-and- coming enforcer, explains the argumentveryclearly and explicitly to thecon- siglieri(Higgins 1974, ch. 8). "It'shis responsibility,"Cogan said."He didit beforeandhe liedbeforeandhe fooled everybody, andI said... 'They should'vewhackedhimoutbefore.'...Nowit happenedagain. It'shis responsibility forwhatthe guysthink...." "He didn'tdo it," thedriversaid."Notthis time, anyway." "That'snotwhat everybody knows," Cogan said. "Shit, we're gonna havekidswait- ing in line,[to] knockthemfuckin' games over, theyopenupagain.... Ifhe getsaway with this,well, we mightjust as well forget it, onceandfor all, and justquit.... Tell [thegodfather], ask him, wherethe guys come from, in the game....They're not gonna come in, is all.Trattmandidit before, [theythink] Trattmandidit again.... Trattman's gotta be hit." When he gets the godfather'sgo-ahead to executethe overkill strategy of whacking out everyone involved (includingTrattman),Cogan formsa temporary alliancewithone ofthemiscreantsinthesecond robbery, to get his cooperation in settingup anotherforthehit. However, the ally failstothink through the game and to solveitbackward. Therefore, he does notrealizethat Cogan'spromise to spare himis notcredible.Of course, Cogan knows perfectly well whatis going to hap- pen: He responds to the consiglieri'squestion when outlining his plan forthehit (Higgins 1974, ch. 16): "Willhe be all right?"... "For a while.Not long, buta while." This instanceof the life-and-death importance of doing backwardinduction correctly is anotherusefullessonto emphasize fromthenovel. Watts (2003) is an excellent compendium of excerpts fromtheliteraturebear- ing on economics.Some of themhave game-theory content:for example, the excerpt fromThe Perfect Storm explains the prisoner's dilemmathatleads to depletion of a fishery, and the excerpt fromTheMerchant of Venicehas brilliant lessonsaboutcommitmentand interpretation of an incompletelyspecified con- tract.Rasmusen (2000) includessome game-theory storiesand cartoonsin his Summer2005217 This content downloaded from 134.219.234.121 on Mon, 16 Feb 2015 06:27:14 AMAll use subject to JSTOR Terms and Conditionscollectionof simpler articleson the subject. A game-theoryequivalent ofWatts' large economics anthology is eagerly awaited. Pending sucha collection, I havefoundthat any substantialuse of literaturein today'sgametheory coursesis problematic becauseit requires thestudentsto do too much reading. If the Harry Potternovelshad good strategiccomponents, the problemmight be solved. Unfortunately, therulesofthe game in thosebooksare hiddenand keep changing somewhat randomly,making them poorly suitedfor illustratinggame-theory ideas.If instructorsarefortunate enough to havestudents whoarewellreador willing to read extensively forthe course, they will getmany good suggestions fortheuse ofliteraturein theircoursesfrom Brams (1994). CONCLUDINGREMARKS Imaginative use of gameplaying, movies,literature, andsuchotherillustrations makes gametheory muchmorefunto teachandto learn.Thiscan be donewith- out sacrificinganyrigor. The ancillary material supplements and elucidatesthe theory; it does not supplanttheory.Although I have barely touchedon specific applications to teaching economics, I hope the few I have mentioned suggest numerousother ways to enrichthat part of teaching also. In short, I believethis approach is a recipe to make everyone betteroff-an all-too-rareinstanceof a feasiblePareto improvement. The suggestions offeredin this articleshould inspire some instructorsto develop and teachcoursesof thiskind. Enjoy, and I add, strategically(and shamelessly), use theDixit-Skeath (2004) textbook! NOTE 1. Iftheinstructorintroducedthe prisoner's dilemma bydeveloping a Cournot duopolygame, thestu- dentswouldhave to learntwonew thingssimultaneously. If theinstructorasks "Why do shared dormrooms usually become veryuntidy?" Studentsknowthe temptation to shirkfroma familiar contextand can easily tieitto the temptation to cut prices in duopoly, andthento theformalcon- cepts of dominant strategies and the prisoner's dilemma. REFERENCES Anderson,S., and M. Engers. 2002. A beautifulblonde:A Nash coordination game.Workingpaper, University of Virginia.http://www.virginia.edu/economics/papers/engers/abb.PDF. Brams,S. 1994. Game theory and literature.Gamesand EconomicBehavior6 (1): 32-54. Brokaw, A. J., and T. E. Merz.2004.Active learning with Monty Hall in a gametheory class.Journal of EconomicEducation35:259-68. Bulow,J., and P. Klemperer. 1999. The generalized warof attrition.AmericanEconomicReview89 (1): 175-89. Dixit,A., and B. Nalebuff.1991. Thinkingstrategically. NewYork:W. W. Norton. Dixit,A., and S. Skeath.2004. Games ofstrategy. 2nded. NewYork:W. W. Norton. Fehr,E., and S. Gdichter. 2000. Cooperation and punishment in publicgoods experiments. American EconomicReview90 (4): 980-94. Hammett, D. 1930. TheMaltese falcon. NewYork: Knopf. Higgins, G. V. 1974. Cogan's trade.NewYork: Knopf. Hirshleifer,J., and J. G. Riley. 1992. The analyticsof uncertainty and information. New York: CambridgeUniversity Press. Nagel, R. 1995. Unraveling in guessinggames: An experimentalstudy. AmericanEconomicReview 85 (5): 1313-26. Nasar,S. 1998.A beautiful mind.NewYork:Simonand Schuster. 218JOURNALOF ECONOMICEDUCATION This content downloaded from 134.219.234.121 on Mon, 16 Feb 2015 06:27:14 AMAll use subject to JSTOR Terms and ConditionsRasmusen,E., ed. 2000. Readings in games and information.Malden, MA: Blackwell. Runyon, D. 1933.The idyll of Miss SarahBrown.Collier's Magazine.Reprinted in Guys and Dolls. NewYork: Viking, 1992. Schelling, T. C. 1960.The strategyofconflict.Cambridge, MA: Harvard University Press. -.1966.Armsand influence. New Haven, CT: Yale University Press. Simon, H. A., andJ.Schaeffer.1992.The game ofchess.In Handbook ofgametheory, vol. I. eds., R. J. Aumannand S. Hart.Amsterdam:North-Holland. Trandel, G. A. 1999. Using a TV game showto explain the concept of a dominant strategy. Journal of EconomicEducation30: 133-40. Von Neumann,J., and 0. Morgenstern. 1953. Theoryof games and economicbehavior3rd ed. Princeton, NJ:Princeton University Press. Watts, M. 2003. The literary book of economics. Wilmington, DE: ISI Books. Williams, J.D. 1966.The compleatstrategyst, rev.ed. NewYork:McGraw-Hill. (Reissuedby Dover, 1986.) TRADE-OFFS An Introductionto Economic Reasoning and Social Issues HAROLDWINTER "This is a delightful book. It made me feel proud to bean economist."-MilesKimball, University of Michigan "Harold Winter's engaging volume, Trade-Offs, is a greatstartingpoint for introducing studentsto the economic approach to policy issues. Where other disciplines see absolutes, economics seestrade- offs. And, as Winter shows, the guidance economics provides as to whatthese trade-offsare and what balance we should strikeis often surprising.Trade-Offs illustratesthe broad range of economic reasoning witha wealthof case studies that run the gamut fromauto safety to organ transplants. This bookwill get studentsexcitedabout learning economics." -W. Kip Viscusi, authorofSmoke-FilledRooms Paper$14.00 The University of Chicago Press 1427 East 6oth Street, Chicago, IL 60637 www.press.uchicago.edu Summer 2005219 This content downloaded from 134.219.234.121 on Mon, 16 Feb 2015 06:27:14 AMAll use subject to JSTOR Terms and Conditions