Games-of-Strategy---Introduction-(Harvard-Business

DONOTCOPYHarvardBusinessSchool9-187-159Rev.April13,1992ProfessorVijayKrishnapreparedthiscaseasthebasisforclassdiscussionratherthantoillustrateeithereffectiveorineffectivehandlingofanadministrativesituation.Copyright©1987bythePresidentandFellowsofHarvardCollege.Toordercopiesorrequestpermissiontoreproducematerials,call1-800-545-7685,writeHarvardBusinessSchoolPublishing,Boston,MA02163,orgoto—electronic,mechanical,photocopying,recording,orotherwise—withoutthepermissionofHarvardBusinessSchool.1GamesofStrategy:AnIntroductionThepurposeofthisnoteistointroduceyoutosomeofthebasictoolswewilluseinthiscourseandtoserveasabackgroundtoourclassdiscussions.Itshouldalsoserveasadictionarycumreferencemanualfortheminimalnecessaryterminologyofthesubject.Letusbeginbyaskingwhatagameofstrategyis.Looselyspeaking,anysituationwherethefatesoftwoormorepersonsareinexorablylinkedmaybecalledagameofstrategy.Nowclearly,thisdefinitionistoogeneralandallencompassing.Evenifalloflifeisindeedagame,wehaveamoremodestandnarrowergoal.Letusqualifyourfirstclumsyattemptatadefinitionandtryagain.Anysituationwherethechoicesoftwoormorerationaldecisionmakerstogetherleadtogainsandlossesforthemiscalledagame.Inaddition,agamemaysimultaneouslyinvolveelementsofbothconflictandcooperationamongthedecisionmakers.Theuseofthewordgameisunfortunate.Althoughmostparlorgameslikebridge,chessetc.qualifybyourdefinition,thesubjectisinterestingonlybecauseitdealswithmoreseriousmattersalso.Itishardtofindabusinesssituationthatdoesnotqualifyasagame.Biologistshaveusedthesubjecttogaininsightintoevolutionaryprocesses.Politicalscientistsusethesubjecttostudythemostseriousgameofallthearmsrace.Forbetterorworse,thetermgameiscommonlyusedtodescribesuchsituationsandwearestuckwithit.1Letusstartbylookingatanextremelysimple,stylizedproblem.Supposethatasthemanagerofafirmyouareconsideringthepossibilityofenteringacompletelynewmarketinwhichthereisjustoneotherfirmoperatingatpresent.Whilethenewmarketappearsprofitableandyouareprettyconfidentofyourabilitytomakemoneyinit,thebiggestuncertaintyyoufaceishowtheentrenchedincumbentfirmwillreacttoyourentry.Itcouldbeaccommodating,allowingyoutocarveyourownnicheinthemarket.Ontheotherhand,itcouldfollowanaggressiveresponse,meet-ingyouwithpricecutsanddiscounts.Supposethatinthefirstcaseyourprofitswouldbe$5millionandinthesecondcaseyouwouldsufferlossestotaling$7million.Thedecisionanalysisapproachtothisproblemwouldaskyoutoassesssomeprobabilitiesfortheuncertaintythatyoufacetheresponseofyourrivalandthenaskwhetherentryintothisnewmarketisworthwhile.Supposethatyouassesstheprobabilityofaggressivebehavioronthepartofyourrivalasone-half.Youmightconsiderdrawingadecisiontreethatlookssomewhatlikethefollowing:1Goetheoncecomplained:MathematiciansarelikeFrenchmen:whateveryousaytothemtheytranslateintotheirownlanguage,andforthwithitissomethingentirelydifferent.DONOTCOPY187-159GamesofStrategy:AnIntroduction2Fromhereon,theanalysisisextremelysimple,youwouldlookattheexpectedmonetaryvalue(EMV)ofeachdecision.Ifyouenter,theEMVis$[0.5×5+0.5×(7)]=$1millionandthusyouexpectlosses.Itdoesnotmakesensetoenterthenewmarket.Isthiscorrect?Itis,ifyoubelievethetreewehavedrawnandthedataitcontains.Thekeyaspectoftheproblemisthecorrectassessmentoftheprobabilities.Iftherivalfirmwerelesslikelytofollowanaggressivestrategyinresponsetoyourentry,itcouldbeworthwhiletoenterthisnewmarket.Sowhatarethecorrectprobabilities?Thefeaturethatdistinguishesgametheoryfromdecisionanalysisisthatiftheuncertaintyyoufaceisaresultofanotherdecisionmaker'sactionsinthiscase,therivalfirmyoushouldexpectthattheotherdecisionmakerwillactinhisorherowninterestsalso.Whilethisseemslikeanobviousidea,itdoeshavefarreachingconsequences.Letusreexaminethesimplifiedproblemwebeganwithagain,thistimeadoptingthegametheoreticviewpoint.Fromyourrival'spointofview,thebestoutcomewouldbeifyouwouldstayoutofthemarketaltogether.Supposethatifitistheonlyfirmoperating,therival'sprofitsare$10million.Ifyoudoenterandtherivalfirmisaccommodating,itsprofitsare$8million.Thesearehigherthanyourprofitsinthiseventbecausetherivalfirmhasbeeninthemarketforsometimeandprobablyhasaloyalcustomerbase.Finally,ifyouenterandtherivalfirmmeetsyouwithanaggressiveresponseofpricecutsanddiscounts(whichyouwillhavetomatch)itsprofitsareamere$2million.Withthisinformation,letusdrawanewtree,thistimenotadecisiontreebutratherwhatiscalledagametree.Themajordifferencehereisthattheuncertainbehavioroftherival,whichwasdepictedasaneventnode(acircle)hasbeenreplacedbyadecisionnode(asquare).Todistinguishbetweendecisionmakerswehaveidentifiedthenodeswithnumbers.Theenteringfirmisfirm1andtherivalincumbentfirmisfirm2.Furthermore,asend-consequences,wewritetheprofitsofbothfirms.Thefirstnumberdenotestheprofitsoffirm1andthesecondthoseoffirm2.DONOTCOPYGamesofStrategy:AnIntroduction187-1593Havingdrawnthegametreeweproceedtofolditback,justaswewouldfoldbackadecisiontree.Wereasonasfollows.Ifyo