Game-theoretic analysis of cooperation among suppl

Game-TheoreticAnalysisofCooperationAmongSupplyChainAgents:ReviewandExtensionsMaheshNagarajan•GreysSoˇsi´cSauderSchoolofBusiness,UniversityofBritishColumbia,Vancouver,B.C.,CanadaV6T1Z2MarshallSchoolofBusiness,UniversityofSouthernCalifornia,LosAngeles,[e-mail]•[e-mail]2005;RevisedMay2006;AcceptedforpublicationinEuropeanJournalofOperationalResearch,May2006AbstractThispapersurveyssomeapplicationsofcooperativegametheorytosupplychainmanagement.Specialemphasisisplacedontwoimportantaspectsofcooperativegames:profitallocationandstability.Thepaperfirstdescribestheconstructionofthesetoffeasibleoutcomesincommonlyseensupplychainmodels,andthenusescooperativebargainingmodelstofindallocationsoftheprofitpiebetweensupplychainpartners.Indoingso,severalmodelsareanalyzedandsurveyed,andincludesupplierssellingtocompetingretailers,andassemblersnegotiatingwithcomponentmanufacturerssellingcomplementarycomponents.Thesecondpartofthepaperdiscussestheissueofcoalitionformationamongsupplychainpartners.Anexhaustivesurveyofcommonlyusedstabilityconceptsispresented.Further,newideassuchasfarsightednessamongsupplychainplayersarealsodiscussedandanalyzed.Thepaperalsoopenssomeavenuesoffutureresearchinapplyingcooperativegametheorytosupplychainmanagement.Keywords:Supplychainmanagement,Cooperativegametheory,Bargaining,Coalitions1.IntroductionTraditionalresearchinoperationsmanagementfocusedonprovidingtoolsandrecipestohelpdecisionmakerswithtacticaloperationaldecisions.Theseincludeproductionplanning,capacityinvestmentandallocation,inventorydecisionsonhowmuch(quantity)andwhere(location)toproduce,procureandstore,shipmentschedules,andmorerecently,jointpricingandinventorydecisionsaswell.Thetoolsusedinanalyzingtheseproblemslargelyreliedupondynamicprogrammingandotheroptimizationtech-niques.Thisstreamofresearchwasfruitfulinprovidingpractitionersavarietyofalgorithmsdesignedtocomputeoptimalquantities,schedules,etc.,aswellasprovidetheoreticalinsightstoresearchers.Inthelastseveralyears,theevolutionofsupplychainmanagementrecognizedthat(i)abusinessprocessconsistsofseveraldecentralizedfirmsand(ii)operationaldecisionsofthesedifferententitiesimpacteachothers’profit,andthustheprofitofthewholesupplychain.Withthisunderstandingcameagreatdealofinterestinmodelingandunderstandingtheimpactofstrategicoperationaldecisionsofthevariousplayersinsupplychains.Toeffectivelymodelandanalyzedecisionmakinginsuchmulti-personsituationwheretheoutcomedependsonthechoicemadebyeveryparty,gametheoryisanaturalchoice.Researchersinsupplychainmanagementnowusetoolsfromgametheoryandeconomicstounderstand,predict,andhelpmanagerstomakestrategicoperationaldecisionsincomplexmulti-agentsupplychainsystems.Looselyspeaking,gametheorymodelssituationswhereplayersmakedecisionstomaximizetheirownutility,whiletakingintoaccountthatotherplayersaredoingthesameandthatdecisionsmadebyplayersimpacteachothersutilities.Thereisabroaddivisionofgametheoryintotwoapproaches:thecooperativeandthenoncooperativeapproach.Theseapproaches,thoughdifferentintheirtheoreticalcontentandthemethodologyusedintheiranalysis,arereallyjusttwodifferentwaysoflookingatthesameproblem.ToquotethewordsofAumann:“thegameisoneidealandthecooperativeandnoncooperativeapproachesaretwoshadows”.Thenoncooperativetheoryofgamesisstrategyoriented–i.e.,itstudieswhatonemayexpecttheplayerstodoandthenitty-grittydetailsofhowtheygetthere.Cooperativegametheory,ontheotherhand,takesadifferenttack.Itdirectlylooksatthesetofpossibleoutcomes,studieswhattheplayerscanachieve,whatcoalitionswillform,howthecoalitionsthatdoformdividetheoutcome,andwhethertheoutcomesarestableandrobust.Thus,onemaysaythatthenoncooperativetheoryisamicroapproachinthatitfocusesonprecisedescriptionsofwhathappens.Thefieldofsupplychainmanagementhasseen,inrecentyears,awidevarietyofresearchpapersthatemploynoncooperativegametheorytomodelinteractionbetweenplayers.Foranexcellentsurveyandstateofarttechniques,wereferyoutoCachonandNetessine(2004).Theuseofcooperativegametheoryis,however,muchlessprevalent.Inthispaper,wereviewtheexistingliteratureonapplicationsofcooperativegamestosupplychainmanagement.Indoingso,wealsoshedsomelightoncertainmethodologicalissueswhenmodelingsupplychainproblemsandpossibleareasforfutureresearch.Thispaperfocusesonapplicationsinsupplychainswithtwocentralthemesofcooperativegames.Thefirstthemeisthatoffeasibleoutcomes.Feasibleoutcomesrepresentthetotalsetofallpossibleoutcomesthatplayersmayrealize,evenif,forinstance,theymaynotbeincentivecompatibleforthem.Identifyingthissetanditspropertiesisanimportantstep.Oncethissetisestablishedand1defined,onemovestothequestionofhowplayersactuallyendupwithanoutcomefromthisfeasibleset.Cooperativegametheoryoffersseveralrecipesforthisprocess.Onesuchimportantapplicationisbargainingbetweentheplayers.Inthisstudy,wefocusextensivelyonbargaininggamesandtheirimplicationstosupplychains.Yetanotherimportantthemeisthatofstability.Whenplayersdecideonallocationsfromthesetoffeasibleoutcomes,independentoftheprocess(forinstancebargaining),someorallp