微观经济学（第八版-英文）课件：Game Theory and Competitive Strategy

13.1

GamingandStrategicDecisions13.2

DominantStrategies13.3

TheNashEquilibriumRevisited13.4

RepeatedGames13.5

SequentialGames13.6

Threats,CommitmentsandCredibility13.7 EntryDeterrence13.8 Auctions

GameTheoryandCompetitiveStrategyCHAPTEROUTLINEGamingandStrategicDecisions13.1●

gameSituationinwhichplayers(participants)makestrategicdecisionsthattakeintoaccounteachother’sactionsandresponses.●

payoffValueassociatedwithapossibleoutcome.●

strategyRuleorplanofactionforplayingagame.●

optimalstrategyStrategythatmaximizesaplayer’sexpectedpayoff.IfIbelievethatmycompetitorsarerationalandacttomaximizetheirownpayoffs,howshouldItaketheirbehaviorintoaccountwhenmakingmydecisions?Determiningoptimalstrategiescanbedifficult,evenunderconditionsofcompletesymmetryandperfectinformation.NoncooperativeversusCooperativeGames●

cooperativegameGameinwhichparticipantscannegotiate

bindingcontractsthatallowthemtoplanjointstrategies.●

noncooperativegameGameinwhichnegotiationandenforcementofbindingcontractsarenotpossible.Itisessentialtounderstandyouropponent’spointofviewandtodeducehisorherlikelyresponsestoyouractions.HOWTOBUYADOLLARBILLAdollarbillisauctioned,butinanunusualway.Thehighestbidderreceivesthedollarinreturnfortheamountbid.However,thesecond-highestbiddermustalsohandovertheamountthatheorshebid—andgetnothinginreturn.Ifyouwereplayingthisgame,howmuchwouldyoubidforthedollarbill?Classroomexperienceshowsthatstudentsoftenendupbiddingmorethanadollarforthedollar.Notethatthefundamentaldifferencebetweencooperativeandnoncooperativegamesliesinthecontractingpossibilities.Incooperativegames,bindingcontractsarepossible;innoncooperativegames,theyarenot.EXAMPLE13.1ACQUIRINGACOMPANYYourepresentCompanyA,whichisconsideringacquiringCompanyT.YouplantooffercashforallofCompanyT’sshares,butyouareunsurewhatpricetooffer.ThevalueofCompanyTdependsontheoutcomeofamajoroilexplorationproject.Iftheprojectsucceeds,CompanyT’svalueundercurrentmanagementcouldbeashighas$100/share.CompanyTwillbeworth50percentmoreunderthemanagementofCompanyA.Iftheprojectfails,CompanyTisworth$0/shareundereithermanagement.Thisoffermustbemadenow—beforetheoutcomeoftheexplorationprojectisknown.You(CompanyA)willnotknowtheresultsoftheexplorationprojectwhensubmittingyourpriceoffer,butCompanyTwillknowtheresultswhendecidingwhethertoacceptyouroffer.Also,CompanyTwillacceptanyofferbyCompanyAthatisgreaterthanthe(pershare)valueofthecompanyundercurrentmanagement.Youareconsideringpriceoffersintherange$0/share(i.e.,makingnoofferatall)to$150/share.WhatpricepershareshouldyouofferforCompanyT’sstock?Thetypicalresponse—toofferbetween$50and$75pershare—iswrong.Theanswerisprovidedlaterinthischapter,butweurgeyoutotrytofindtheansweronyourown.DominantStrategies13.2●

equilibriumindominantstrategiesOutcomeofagameinwhicheachfirmisdoingthebestitcanregardlessofwhatitscompetitorsaredoing.●

dominantstrategyStrategythatisoptimalnomatterwhatanopponentdoes.TABLE13.1PAYOFFMATRIXFORADVERTISINGGAMEFirmBAdvertiseDon’tadvertiseFirmAAdvertise10,515,0Don’tadvertise6,810,2AdvertisingisadominantstrategyforFirmA.ThesameistrueforFirmB:NomatterwhatfirmAdoes,FirmBdoesbestbyadvertising.Theoutcomeforthisgameisthatbothfirmswilladvertise.TABLE13.2MODIFIEDADVERTISINGGAMEFirm2AdvertiseDon’tadvertiseFirm1Advertise10,510,10Don’tadvertise6,820,2NowFirmAhasnodominantstrategy.ItsoptimaldecisiondependsonwhatFirmBdoes.IfFirmBadvertises,FirmAdoesbestbyadvertising;butifFirmBdoesnotadvertise,FirmAalsodoesbestbynotadvertising.Unfortunately,noteverygamehasadominantstrategyforeachplayer.TheNashEquilibriumRevisited13.3DominantStrategies: I’mdoingthebestIcannomatterwhatyoudo. You’redoingthebestyoucannomatterwhatIdo.NashEquilibrium: I’mdoingthebestIcangivenwhatyouaredoing. You’redoingthebestyoucangivenwhatIamdoing.THEPRODUCTCHOICEPROBLEMTwonewvariationsofcerealcanbesuccessfullyintroduced—providedthateachvariationisintroducedbyonlyonefirm.TABLE13.3PRODUCTCHOICEPROBLEMFirm2CrispySweetFirm1Crispy–5,–510,10Sweet10,10–5,–5Inthisgame,eachfirmisindifferentaboutwhichproductitproduces—solongasitdoesnotintroducethesameproductasitscompetitor.Thestrategysetgivenbythebottomleft-handcornerofthepayoffmatrixisstableandconstitutesaNashequilibrium:Giventhestrategyofitsopponent,eachfirmisdoingthebestitcanandhasnoincentivetodeviate.BEACHLOCATIONGAMEFIGURE13.1THEBEACHLOCATIONGAMEYou(Y)andacompetitor(C)plantosellsoftdrinksonabeach.Ifsunbathersarespreadevenlyacrossthebeachandwillwalktotheclosestvendor,thetwoofyouwilllocatenexttoeachotheratthecenterofthebeach.ThisistheonlyNashequilibrium.IfyourcompetitorlocatedatpointA,youwouldwanttomoveuntilyouwerejusttotheleft,whereyoucouldcapturethree-fourthsofallsales.Butyourcompetitorwouldthenwanttomovebacktothecenter,andyouwoulddothesame.●

maximinstrategy Strategythatmaximizestheminimumgainthatcanbeearned.TABLE13.4MAXIMINSTRATEGYFirm2Don’tinvestInvestFirm1Don’tinvest0,0–10,10Invest–100,020,10Inthisgame,theoutcome(invest,invest)isaNashequilibrium.ButifyouareconcernedthatthemanagersofFirm2mightnotbefullyinformedorrational—youmightchoosetoplay“don’tinvest.”Inthatcase,theworstthatcanhappenisthatyouwilllose$10million;younolongerhaveachanceoflosing$100million.MaximinStrategiesIfFirm1isunsureaboutwhatFirm2willdobutcanassignprobabilitiestoeachfeasibleactionforFirm2,itcouldinsteaduseastrategythatmaximizesitsexpectedpayoff.MAXIMIZINGTHEEXPECTEDPAYOFFtheidealoutcomeisoneinwhichneitherprisonerconfesses,sothatbothgettwoyearsinprison.Confessing,however,isadominantstrategyforeachprisoner—ityieldsahigherpayoffregardlessofthestrategyoftheotherprisoner.Dominantstrategiesarealsomaximinstrategies.TheoutcomeinwhichbothprisonersconfessisbothaNashequilibriumandamaximinsolution.Thus,inaverystrongsense,itisrationalforeachprisonertoconfess.THEPRISONERS’DILEMMATABLE13.5PRISONERS’DILEMMAPrisonerBConfessDon’tconfessPrisonerAConfess–5,–5–1,–10Don’tconfess–10,–1–2,–2●

purestrategy Strategyinwhichaplayermakesaspecificchoiceortakesaspecificaction.Inthisgame,eachplayerchoosesheadsortailsandthetwoplayersrevealtheircoinsatthesametime.IfthecoinsmatchPlayerAwinsandreceivesadollarfromPlayerB.Ifthecoinsdonotmatch,PlayerBwinsandreceivesadollarfromPlayerA.NotethatthereisnoNashequilibriuminpurestrategiesforthisgame.Nocombinationofheadsortailsleavesbothplayerssatisfied—oneplayerortheotherwillalwayswanttochangestrategies.MixedStrategiesMATCHINGPENNIESTABLE13.6MATCHINGPENNIESPlayerBHeadsTailsPlayerAHeads1,–1–1,1Tails–1,11,–1●

mixedstrategy Strategyinwhichaplayermakesarandomchoiceamongtwoormorepossibleactions,basedonasetofchosenprobabilities..AlthoughthereisnoNashequilibriuminpurestrategies,thereisaNashequilibriuminmixedstrategies.Inthematchingpenniesgame,forexample,PlayerAmightsimplyflipthecoin,therebyplayingheadswithprobability1/2andplayingtailswithprobability1/2.Infact,ifPlayerA

followsthisstrategyandPlayerBdoesthesame,wewillhaveaNashequilibrium:Bothplayerswillbedoingthebesttheycangivenwhattheopponentisdoing.Notethatalthoughtheoutcomeisrandom,theexpectedpayoffis0foreachplayer.Itmayseemstrangetoplayagamebychoosingactionsrandomly.ButputyourselfinthepositionofPlayerAandthinkwhatwouldhappenifyoufollowedastrategyotherthanjustflippingthecoin.Supposeyoudecidedtoplayheads.IfPlayerBknowsthis,shewouldplaytailsandyouwouldlose.EvenifPlayerBdidn’tknowyourstrategy,ifthegamewereplayedrepeatedly,shecouldeventuallydiscernyourpatternofplayandchooseastrategythatcounteredit.Onceweallowformixedstrategies,everygamehasatleastoneNashequilibrium.TherearetwoNashequilibriainpurestrategiesforthisgame—theoneinwhichJimandJoanbothwatchmudwrestling,andtheoneinwhichtheybothgototheopera.Thisgamealsohasanequilibriuminmixedstrategies:Joanchooseswrestlingwithprobability2/3andoperawithprobability1/3,andJimchooseswrestlingwithprobability1/3andoperawithprobability2/3.ShouldweexpectJimandJoantousethesemixedstrategies?Unlessthey’reveryrisklovingorinsomeotherwayastrangecouple,probablynot.Byagreeingtoeitherformofentertainment,eachwillhaveapayoffofatleast1,whichexceedstheexpectedpayoffof2/3fromrandomizing.THEBATTLEOFTHESEXESTABLE13.7THEBATTLEOFTHESEXESJimWrestlingOperaPrisonerAWrestling2,10,0Opera0,01,2RepeatedGames13.4●

repeatedgameGameinwhichactionsaretakenandpayoffsreceivedoverandoveragain.TABLE13.8PRICINGPROBLEMFirm2LowpriceHighpriceFirm1Lowprice10,10100,–50Highprice–50,10050,50Supposethisgameisrepeatedoverandoveragain—forexample,youandyourcompetitorsimultaneouslyannounceyourpricesonthefirstdayofeverymonth.Shouldyouthenplaythegamedifferently?TIT-FOR-TATSTRATEGYInthepricingproblemabove,therepeatedgamestrategythatworksbestisthetit-for-tatstrategy.●

tit-for-tatstrategyRepeated-gamestrategyinwhichaplayerrespondsinkindtoanopponent’spreviousplay,cooperatingwithcooperativeopponentsandretaliatingagainstuncooperativeones.WhenmycompetitorandIrepeatedlysetpricesmonthaftermonth,

forever,

cooperativebehavior(i.e.,chargingahighprice)isthenthe

rationalresponsetoatit-for-tatstrategy.(Thisassumesthatmycompetitorknows,orcanfigureout,thatIamusingatit-for-tatstrategy.)Itisnotrationaltoundercut.Withinfiniterepetitionofthegame,theexpectedgainsfromcooperationwilloutweighthosefromundercutting.ThiswillbetrueeveniftheprobabilitythatIamplayingtit-for-tat(andsowillcontinuecooperating)issmall.INFINITELYREPEATEDGAMEFINITENUMBEROFREPETITIONSNowsupposethegameisrepeatedafinitenumberoftimes—say,Nmonths.(Ncanbelargeaslongasitisfinite.)Ifmycompetitor(Firm2)isrationalandbelievesthatIamrational.Inthiscase,bothfirmswillnotconsiderundercuttinguntilthelastmonth,beforethegameisover,soFirm1cannotretaliate.However,Firm2knowsthatIwillchargealowpriceinthelastmonth.Butthenwhataboutthenext-to-lastmonth?Becausetherewillbenocooperationinthelastmonth,anyway,Firm2figuresthatitshouldundercutandchargealowpriceinthenext-to-lastmonth.But,ofcourse,Ihavefiguredthisouttoo.Intheend,theonlyrationaloutcomeisforbothofustochargealowpriceeverymonth.Thetit-for-tatstrategycansometimesworkandcooperationcan

prevail.Therearetwoprimaryreasons.First,mostmanagersdon’tknowhowlongtheywillbecompetingwiththeirrivals.Theunravellingargumentthatbeginswithaclearexpectationofundercuttinginthelastmonthnolongerapplies.Aswithaninfinitelyrepeatedgame,itwillberationaltoplaytit-for-tat.Second,mycompetitormighthavesomedoubtabouttheextentofmyrationality.“Perhaps,”thinksmycompetitor,“Firm1willplaytit-for-tatblindly,chargingahighpriceaslongasIchargeahighprice.”Justthepossibilitycanmakecooperativebehavioragoodstrategy(untilneartheend)ifthetimehorizonislongenough.Althoughmycompetitor’sconjectureabouthowIamplayingthegamemightbewrong,cooperativebehaviorisprofitableinexpectedvalueterms.Withalongtimehorizon,thesumofcurrentandfutureprofits,weightedbytheprobabilitythattheconjectureiscorrect,canexceedthesumofprofitsfrompricecompetition,evenifmycompetitoristhefirsttoundercut.Thus,inarepeatedgame,theprisoners’dilemmacanhaveacooperativeoutcome.Sometimescooperationbreaksdownorneverbeginsbecausetherearetoomanyfirms.Moreoften,failuretocooperateistheresultofrapidlyshiftingdemandorcostconditions.TIT-FOR-TATINPRACTICEEXAMPLE13.2OLIGOPOLISTICCOOPERATIONINTHEWATERMETERINDUSTRYForsomefourdecades,almostallthewatermeterssoldintheUnitedStateshavebeenproducedbyfourAmericancompanies:RockwellInternational,BadgerMeter,NeptuneWaterMeterCompany,andHerseyProducts.Mostbuyersofwatermetersaremunicipalwaterutilities,whoinstallthemetersinordertomeasurewaterconsumptionandbillconsumersaccordingly.Withinelasticandstabledemandandlittlethreatofentrybynewfirms,theexistingfourfirmscouldearnsubstantialmonopolyprofitsiftheysetpricescooperatively.If,ontheotherhand,theycompeteaggressively,profitswouldfalltonearlycompetitivelevels.Thefirmsthusfaceaprisoners’dilemma.Cancooperationprevail?Itcanandhasprevailed.Thereisrarelyanattempttoundercutprice,andeachfirmappearssatisfiedwithitsshareofthemarket.Allfourfirmshavebeenearningreturnsontheirinvestmentsthatfarexceedthoseinmorecompetitiveindustries.EXAMPLE13.3COMPETITIONANDCOLLUSIONINTHEAIRLINEINDUSTRYInMarch1983,AmericanAirlinesproposedthatallairlinesadoptauniformfareschedulebasedonmileage.Thisproposalwouldhavedoneawaywiththemanydifferentfaresthenavailable.Mostothermajorairlinesreactedfavorablytotheplanandbegantoadoptit.Wasitreallyto“helpreducefareconfusion”?No,theaimwastoreducepricecompetitionandachieveacollusivepricingarrangement.Priceshadbeendrivendownbycompetitiveundercutting,asairlinescompetedformarketshare.Theplanfailed,avictimoftheprisoners’dilemma.Eachairline,therefore,hasanincentivetolowerfaresinordertocapturepassengersfromitscompetitors.Inaddition,thedemandforairtraveloftenfluctuatesunpredictably.Suchfactorsasthesestandinthewayofimplicitpricecooperation.Thus,aggressivecompetitionhascontinuedtobetheruleintheairlineindustry.Discountairlines,reductioninfaresinordertoattractcustomers,and“fareshopping”intheInternethaveforcedseveralmajorairlinesintobankruptcyandresultedinrecordlossesfortheindustry.SequentialGames13.5●

sequentialgameGameinwhichplayersmoveinturn,respondingtoeachother’sactionsandreactions.TheStackelbergmodeldiscussedinChapter12isanexampleofasequentialgame;onefirmsetsoutputbeforetheotherdoes.Therearemanyotherexamplesofsequentialgamesinadvertisingdecisions,entry-deterringinvestment,andresponsestogovernmentregulations.Inasequentialgame,thekeyistothinkthroughthepossibleactionsandrationalreactionsofeachplayer.TABLE13.9MODIFIEDPRODUCTCHOICEPROBLEMFirm2CrispySweetFirm1Crispy–5,–510,20Sweet20,10–5,–5Supposethatbothfirms,inignoranceofeachother’sintentions,mustannouncetheirdecisionsindependentlyandsimultaneously.Inthatcase,bothwillprobablyintroducethesweetcereal—andbothwilllosemoney.Inasequentialgame,Firm1introducesanewcereal,andthenFirm2introducesone.TheExtensiveFormofaGame●

extensiveformofagameRepresentationofpossiblemovesinagameintheformofadecisiontree.PRODUCECHOICEGAMEINEXTENSIVEFORMFIGURE13.2AlthoughthisoutcomecanbededucedfromthepayoffmatrixinTable13.9,sequentialgamesaresometimeseasiertovisualizeifwerepresentthepossiblemovesintheformofadecisiontree.Tofindthesolutiontotheextensiveformgame,workbackwardfromtheend.TheAdvantageofMovingFirst

TABLE13.10CHOOSINGOUTPUTFIRM27.51015FIRM17.5112.50,112.5093.75,12556.25,112.5010125,93.75100,10050,7515112.50,56.2575,500,0Ifbothfirmsmovesimultaneously,theonlysolutiontothegameisthatbothproduce10andearn100.InthisCournotequilibriumeachfirmisdoingthebestitcangivenwhatitscompetitorisdoing.ComparedtotheCournotoutcome,whenFirm1movesfirst,itdoesbetter—andFirm2doesmuchworse.Threats,Commitments,andCredibility13.6TheproductchoiceproblemandtheStackelbergmodelaretwoexamplesofhowafirmthatmovesfirstcancreateafaitaccomplithatgivesitanadvantageoveritscompetitor.

Inthissection,we’llconsiderwhatdetermineswhichfirmgoesfirst.Wewillfocusonthefollowingquestion:Whatactionscanafirmtaketogainadvantageinthemarketplace?RecallthatintheStackelbergmodel,thefirmthatmovedfirstgainedanadvantagebycommittingitselftoalargeoutput.Makingacommitment—constrainingitsfuturebehavior—iscrucial.IfFirm2knowsthatFirm1willrespondbyreducingtheoutputthatitfirstannounced,Firm2wouldproducealargeoutput..TheonlywaythatFirm1cangainafirst-moveradvantageisbycommittingitself.Ineffect,Firm1constrainsFirm2’sbehaviorbyconstrainingitsownbehavior.Intheproduct-choiceproblemshowninTable13.9,thefirmthatintroducesitsnewbreakfastcerealfirstwilldobest.Eachhasanincentivetocommititselffirsttothesweetcereal.Firm1mustconstrainitsownbehaviorinsomewaythatconvincesFirm2thatFirm1hasnochoicebuttoproducethesweetcereal.Firm1mightlaunchanexpensiveadvertisingcampaign,orcontractfortheforwarddeliveryofalargequantityofsugar(andmakethecontractpublic).Firm1can’tsimplythreatenFirm2becauseFirm2haslittlereasontobelievethethreat—andcanmakethesamethreatitself.Athreatisusefulonlyifitiscredible.EmptyThreats

AslongasFirm1chargesahighpriceforitscomputers,bothfirmscanmakeagooddealofmoney.Firm1wouldprefertheoutcomeintheupperleft-handcornerofthematrix.ForFirm2,however,chargingalowpriceisclearlyadominantstrategy.Thustheoutcomeintheupperright-handcornerwillprevail(nomatterwhichfirmsetsitspricefirst).CanFirm1induceFirm2tochargeahighpricebythreateningtochargealowpriceifFirm2chargesalowprice?No.WhateverFirm2does,Firm1willbemuchworseoffifitchargesalowprice.Asaresult,itsthreatisnotcredible.TABLE13.11PRICINGOFCOMPUTERSANDWORDPROCESSORSFIRM2HighpriceLowpriceFIRM1Highprice100,8080,100Lowprice20,010,20CommitmentandCredibilityHerewehaveasequentialgameinwhichRaceCaristhe“leader.”RaceCarwilldobestbydecidingtoproducesmallcars.Itknowsthatinresponsetothisdecision,FarOutwillproducesmallengines,mostofwhichRaceCarwillthenbuy.CanFarOutinduceRaceCartoproducebigcarsinsteadofsmallones?SupposeFarOutthreatenstoproducebigengines.IfRaceCarbelievedFarOut’sthreat,itwouldproducebigcars.Butthethreatisnotcredible.FarOutcanmakeitsthreatcrediblebyvisiblyandirreversiblyreducingsomeofitsownpayoffsinthematrix,therebyconstrainingitsownchoices.Itmightdothisbyshuttingdownordestroyingsomeofitssmallengineproductioncapacity.ThiswouldresultinthepayoffmatrixshowninTable13.12(b).TABLE13.12(a)PRODUCTIONCHOICEPROBLEMRaceCarMotorsSmallcarsBigCarsFarOutEnginesSmallengines3,63,0Bigengines1,18,3CommitmentandCredibilityNowRaceCarknowsthatwhateverkindofcaritproduces,FarOutwillproducebigengines.NowitisclearlyinRaceCar’sinteresttoproducelargecars.Bytakinganactionthatseeminglyputsitselfatadisadvantage,FarOuthasimproveditsoutcomeinthegame.Althoughstrategiccommitmentsofthiskindcanbeeffective,theyareriskyanddependheavilyonhavingaccurateknowledgeofthepayoffmatrixandtheindustry.Suppose,forexample,thatFarOutcommitsitselftoproducingbigenginesbutissurprisedtofindthatanotherfirmcanproducesmallenginesatalowcost.ThecommitmentmaythenleadFarOuttobankruptcyratherthancontinuedhighprofits.TABLE13.12(b)MODIFIEDPRODUCTIONCHOICEPROBLEMRaceCarMotorsSmallcarsBigCarsFarOutEnginesSmallengines0,60,0Bigengines1,18,3Developingtherightkindofreputationcanalsogiveoneastrategicadvantage.SupposethatthemanagersofFarOutEnginesdevelopareputation

forbeingirrational—perhapsdownrightcrazy.TheythreatentoproducebigenginesnomatterwhatRaceCarMotorsdoes.Ingamingsituations,thepartythatisknown(orthought)tobealittlecrazycanhaveasignificantadvantage.Developingareputationcanbeanespeciallyimportantstrategyinarepeatedgame.Afirmmightfinditadvantageoustobehaveirrationallyforseveralplaysofthegame.Thismightgiveitareputationthatwillallowittoincreaseitslong-runprofitssubstantially.THEROLEOFREPUTATIONBargainingStrategyHere,thefirmsproducetwocomplementarygoods.BecauseproducingBisadominantstrategyforFirm2,(A,B)istheonlyNashequilibrium.Suppose,however,thatFirms1and2arebargainingovertojoinaresearchconsortiumthatathirdfirmistryingtoform,andFirm1announcesthatitwilljointheconsortiumonlyifFirm2agreestoproduceproductA.Inthiscase,itisindeedinFirm2’sinteresttoproduceA(withFirm1producingB).TABLE13.13PRODUCTIONDECISIONFirm2ProduceAProduceBFirm1ProduceA40,550,50ProduceB60,405,45TABLE13.14DECISIONTOJOINCONSORTIUMFirm2WorkaloneEnterconsortiumFirm1Workalone10,1010,20Enterconsortium20,1040,40EXAMPLE13.4WAL-MARTSTORES’PREEMPTIVEINVESTMENTSTRATEGYHowdidWal-MartStoressucceedwhereothersfailed?ThekeywasWal-Mart’sexpansionstrategy.Tochargelessthanordinarydepartmentstoresandsmallretailstores,discountstoresrelyonsize,nofrills,andhighinventoryturnover.Throughthe1960s,theconventionalwisdomheldthatadiscountstorecouldsucceedonlyinacitywithapopulationof100,000ormore.SamWaltondisagreedanddecidedtoopenhisstoresinsmallSouthwesterntowns.ThestoressucceededbecauseWal-Marthadcreated30“localmonopolies.”Discountstoresthathadopenedinlargertownsandcitieswerecompetingwithotherdiscountstores,whichdrovedownpricesandprofitmargins.Thesesmalltowns,however,hadroomforonlyonediscountoperation.TherearealotofsmalltownsintheUnitedStates,sotheissuebecamewhowouldgettoeachtownfirst.Wal-MartnowfounditselfinapreemptiongameofthesortillustratedbythepayoffmatrixinTable13.15.EXAMPLE13.4WAL-MARTSTORES’PREEMPTIVEINVESTMENTSTRATEGYThisgamehastwoNashequilibria—thelowerleft-handcornerandtheupperright-handcorner.Whichequilibriumresultsdependsonwhomovesfirst.Thetrick,therefore,istopreempt—tosetupstoresinothersmalltownsquickly,beforeCompanyX(orCompanyYorZ)candoso.ThatisexactlywhatWal-Martdid.By1986,ithad1009storesinoperationandwasearninganannualprofitof$450million.Andwhileotherdiscountchainsweregoingunder,Wal-Martcontinuedtogrow.By1999,Wal-Marthadbecometheworld’slargestretailer,with2454storesintheUnitedStatesandanother729storesintherestoftheworld,andhadannualsalesof$138billion.Inrecentyears,Wal-Marthascontinuedtopreemptotherretailersbyopeningnewdiscountstores,warehousestores(suchasSam’sClub),andcombinationdiscountandgrocerystores(Wal-MartSupercenters)allovertheworld.TABLE13.15THEDISCOUNTSTOREPREEMPTIONGAMECompanyXEnterDon’tenterWal-MartEnter–10,–1020,0Don’tenter0,200,0EntryDeterrence13.7Todeterentry,theincumbentfirmmustconvinceanypotentialcompetitorthatentrywillbeunprofitable.TABLE13.16(a)ENTRYPOSSIBILITIESPotentialEntrantEnterStayoutIncumbentHighprice(accommodation)100,20200,0Lowprice(warfare)70,–10130,0IfFirmXthinksyouwillbeaccommodatingandmaintainahighpriceafterithasentered,itwillfinditprofitabletoenterandwilldoso.SupposeyouthreatentoexpandoutputandwageapricewarinordertokeepXout.IfXtakesthethreatseriously,itwillnotenterthemarketbecauseitcanexpecttolose$10million.Thethreat,however,isnotcredible.AsTable13.16(a)shows,onceentryhasoccurred,itwillbeinyourbestinteresttoaccommodateandmaintainahighprice.FirmX’srationalmoveistoenterthemarket;theoutcomewillbetheupperleft-handcornerofthematrix.TABLE13.16(b)ENTRYDETERRENCEPotentialEntrantEnterStayoutIncumbentHighprice(accommodation)50,20150,0Lowprice(warfare)70,–10130,0Ifyoucanmakeanirrevocablecommitmenttoinvestinadditionalcapacity,yourthreattoengageincompetitivewarfareiscompletelycredible.Withtheadditionalcapacity,youwilldobetterincompetitivewarfarethanyouwouldbymaintainingahighprice.Meanwhile,havingdeterredentry,youcanmaintainahighpriceandearnaprofitof$150million.Ifthegameweretobeindefinitelyrepeated