16 Backward induction reputation and duels.docx
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16 Backward induction reputation and duels.docx
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16Backwardinductionreputationandduels
GameTheory:
Lecture16Transcript
Overview:
Inthefirsthalfofthelecture,weconsiderthechain-storeparadox.Wediscusshowtobuildtheideaofreputationintogametheory;inparticular,insettinglikethiswhereathreatorpromisewouldotherwisenotbecredible.Thekeyideaisthatplayersmaynotbecompletelycertainaboutotherplayers'payoffsoreventheirrationality.Inthesecondhalfofthelecture,westageaduel,agameofpre-emption.Thekeystrategicquestioninsuchgamesiswhen;inthiscase,whentofire.Weusetwoideasfromearlierlectures,dominanceandbackwardinduction,toanalyzethegame.FinallywediscusstwobiasesfoundinAmericans:
overconfidenceandover-valuingbeingpro-active.
October31,2007
< ProfessorBenPolak: Sothisiswhatwedidlasttime: welookedatagameinvolvinganentrantandanincumbentinamarket;andtheentranthadtodecidewhethertoenterthatmarketornot;andiftheystayedouttheincumbentremainedamonopolist;andthemonopolistmade3millioninprofit.Iftheentrantgoesin,thentheincumbentcandecidewhethertoaccommodatetheentrantandjustsettleforduopolyprofits,makingamillioneach;ortheincumbentcanfight,inwhichcasetheincumbentmakesnomoneyatallandtheentrantlosesamilliondollars.Wepointedoutanumberofthingsaboutthisgame.OnewasthatwhenweanalyzeditinamatrixformwequicklyfoundthatthereweretwoNashEquilibria,thatNashEquilibriumwere: inandnotfight;andoutandfight. Butwearguedthatbackwardinductiontellsusthatthesensibleanswerisinandnotfight.Oncetheincumbentknowstheentrantisinthey'renotgoingtofightbecause1isbiggerthan0,andtheentrantanticipatingthiswillenter.Whenwetalkedalittlebitmorewesaidthisotherequilibrium,thisoutfightequilibrium--itisanequilibriumbecauseiftheentrantbelievestheincumbent'sgoingtofightthentheentrantisgoingtostayout,andit'scostlessfortheincumbentto"fight"ifinfacttheentrantdoesstayoutbecausetheynevergetcalledupontofightanyway. Sotheideaofthiswasthatfortheincumbenttosaythey'regoingtofightisan"incrediblethreat."That'sterribleEnglish.It'sthewayitisalwaystaughtinthetextbooks.Itneedstobecalleda"notcredible"threat.Andthat"notcredible"threatis: he'snotreallygoingtofightiftheentrantcomesin,andtherefore,theentrantshouldcomeinandinfacttheincumbentwillaccommodateit.Sowhatwe'veshownhereisthat,ifwebelievethisargument,thentheentrantwillcomeinandtheincumbentisgoingtolethimin.Attheend,westartedtalkingaboutthisinaslightlymoreelaboratesetting,solet'sjustremindyouofwhatthatmoreelaboratesettingis. Themoreelaboratesettingissupposethatthereisonefirm,onemonopolist,andthatmonopolistholdsamonopolyintendifferentmarkets.Sowe'llhaveourmonopolistbeAle.Sohere'sAle.He'sourmonopolist,andheownspizzeriamonopoliesintendifferentmarkets.Andeachofthesetendifferentmarketsareseparate,theyaredifferenttowns.Andineachofthosetenmarketshethinks--heknowshe'sgoingtofaceanentrantandthoseentrantsaregoingtocomeinorder.Solet'sjusttalkaboutwhothoseentrantsaregoingtobe.Theentrantsaregoingtobethisperson,thispersonandsoon.Let'sfindoutwhotheyare,soyournameis? Student: Isabella ProfessorBenPolak: Whereareyoufrom? Student: Miami. ProfessorBenPolak: Miami,soMiamiisoneofthemarkets.Yournameis? Student: Scott. ProfessorBenPolak: Fromwhere? Student: Wisconsin. ProfessorBenPolak: WhereinWisconsin? Student: Madison. ProfessorBenPolak: Madison: we'vegottwotowns.We'rejustgoingtodotownsnow. Student: MynameisLang.I'mfromBridgeport,Connecticut. ProfessorBenPolak: Okay,we'vegotthreetowns. Student: I'mfromMiamitoo. ProfessorBenPolak: TalkaboutYalediversity.Wellwe'llpretendyou'refromsomewhereelse.PuthiminNewOrleansorsomething. Student: ChrisfromBoston. ProfessorBenPolak: FromBoston,allright. Student: FromOrange,Connecticut. ProfessorBenPolak: FromOrange,Connecticutsojustdowntheroad. Student: St.Louis,Missouri. ProfessorBenPolak: Allright,havewegottenyet? I'mnotquiteatten.One,two,three,four,five,six,seven. Student: Saffron,NewYork. ProfessorBenPolak: Allright. Student: HongKong. ProfessorBenPolak: HongKong,that'swayaway. Student: LongIsland. ProfessorBenPolak: LongIsland.IthinkI'veprobablygottenmarketshere.SoAleownsapizzashop.He'sthemonopolypizzashopownerineachofthesetenmarkets.Andwhatwe'regoingtoseeiswe'regoingtoseewhathappensas,sequentially,theseentrantstrytoenter.Thewaythatthisgame'sgoingtoworkisthatthey'relinedup--weknowtheorderinwhichtheentrantsaregoingtocome.They'regoingtostartoff,thefirstpersonwhoisgoingtohavetomakeadecisionis- Student: Enter.Isabella. ProfessorBenPolak: IsIsabella,right? We'regoingtoseehowourmonopolistresponds.Solet'shavealookatthis.SoIsabellawhoisinwhichmarketagain? Student: Miami. ProfessorBenPolak: InMiami,okaywhatareyougoingtodo? Student: Enter. ProfessorBenPolak: Whatareyougoingtodo? Student: Iwillfight. ProfessorBenPolak: Ohdear,soyouowemeamilliondollars.Sooneperson'sdownamilliondollars,let'sseewhathappensnext. Student: I'mgoingtostayout. ProfessorBenPolak: Whichmarketwasthis? Student: Scott.Madison. ProfessorBenPolak: Madisonstayedout. Student: I'mgoingtostayout. ProfessorBenPolak: Stayingout.SoBridgeportstayedout. Student: IguessI'llstayout. ProfessorBenPolak: Stayedoutagain. Student: Stayout. ProfessorBenPolak: Whichmarketareweuptonow,somewhereinOrangeCountywasn'tit? Wherewerewe? StudentOrange,Connecticut.Stayout. ProfessorBenPolak: Stayout. Student: IthinkI'llstayin. ProfessorBenPolak: You'llcomeinokay,andwhichmarketisthis? Student: St.Louis,Missouri. ProfessorBenPolak: St.Louis,Missouri.Soyouowemea milliondollarsaswell,okay.Acoupleofmilliondollarsisagoodclass.We'regoingtohaveplentyofmoneyforlunch. Student: I'malsogoingtofight. ProfessorBenPolak: You'regoingtofight,whichmarketisthat? Student: Saffron,NewYork. ProfessorBenPolak: Whereabouts? Student: Saffron. ProfessorBenPolak: Saffron,NewYork.Whereareweat? One,two,three,four,five,six,seven,eight,Ale? TA: Fight. ProfessorBenPolak: Youfight? Soyouowemeamilliondollarstoo.Thatwaseight,nine? Student: Out. ProfessorBenPolak: Outandten? Student: Stayout. ProfessorBenPolak: Staysout,okay.Nowlet'sjustnoticesomethinghere,whichwasthetenthmarket? Whattownwereyou? Student: LongIsland. ProfessorBenPolak: WhereaboutsinLongIsland? Student: Huntington. ProfessorBenPolak: SoifHuntington,LongIslandourlastmarkethadcomein,supposeyou'dsaidin,whatwouldAlehavesaid? TA: Iwouldnothavefought. ProfessorBenPolak: Wouldnothavefought,aha! Okay,sowhathappenedhere? Whenweanalyzedthislasttimeasanindividualmarket,wearguedthateachentrantshouldcomeinjustasourfirstentrantcamein,andourmonopolistshouldnotfight: .That'swhatwehaveupontheboard.That'swhatbackwardinductionsuggests.Butinfact,Alefought.Awholebunchofpeoplecamein,andawholebunchofthemstayedout,isthatright? Nowwhy? WhywasAlefightingtheseguysandwhyweretheystayingout? Let'stalkaboutwhy,andwhatmarketwereyouagain? Student: Madison,Wisconsin. ProfessorBenPolak: SowhydidMadison,Wisconsinstayout? Student: Wellwetalkedaboutitlasttimehowhehasanincentivetofightnowbecausethere'smorethatjustouranalysisupthereintermsofestablishingthathe'llfighttokeeppeopleout. ProfessorBenPolak: Allright,soitlooksliketheremightbesomereasonforfightingtokeepyouout.Solet'sjusttalkaboutitalittlebitmore,let'sgotothethirdguy.Whichmarketareyouagain? Student: Bridgeport. ProfessorBenPolak: Bridgeport,sowhydidyoustayout? Student: BecauseIknewhewasgoingtofight. ProfessorBenPolak: Youknewhewasgoingtofight.Nowhowdidyouknowhewasgoingtofight? Student: Becausehehasanincentivetoestablish,heestablishedthathewasgoingtofightforeverysinglemarketandsoIwasgoingtoloseout. ProfessorBenPolak: Allright,soweknow--wethinkweknowthatAleis--youknowhe'sthistoughItalianpizzeriaownerandwethinkhe'sgoingtotryandestablishwhat: areputationasbeingatoughpizzeriaownerbyfightingtheseguys,perhapsfightingafewguysearlyoninordertokeeptheseguysout.Infact,hehadtofightthefirstpersonbuthekeptout2,3,4,5,6andthispersoncamein,so7and8camein,butthen9and10hekeptout.Sohekeptalotofpeopleoutofthemarketbyfightingearlyon.Nowthisargumentsoundsright: itseemstoringtrue.It'saboutestablishingreputation,butnowIwanttoshowyouthatthere'saworrywiththisargument. Theworryisthisisasequentialgameandlikeallsequentialgamesofperfectinformationwe'veseenintheclass,weshouldanalyzethisgamehow? Nowthatwasn'tloudenough,how? Backwardinduction.Sowhere'stheback? Where'sthebackofthisgame? Waybackhere--sorryfortheguysinthebalcony.Waybackherewehavethelastmarketintown--whichwasthelastmarket? Andifwelookatthislastmarket,weinfactsawthatifthelastmarketcamein,Aleinfactgavein.Alegavein.NowwhydidAlegivein,inthelastmark
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