shortrun,capacityis xedandcustomersarehencerationed.Thisimpliesthatthe rmwithahigherpricewillfaceapositiveresidualdemand,leadingtoequilibriumpricesabovemarginalcost.However,ifcapacityitselfisviewedasastrategicvari-able, rmswillanticipatetheimpactofsaidcapacitychoicesonsubsequentpricecompetition.Iftheyanticipatecorrectly,howmuchcapacitywillduopolistschoose?Game-theoretictoolsofextensive-formgames(orsequential-movegames)andtheprincipleofsubgameperfectionhelpprovideananswer,whichwewilldiscussbelow.

Commitmentisimportantinbusinessstrategy.Beingabletocommitearlyoftenleadstoa rst-moveradvantage,whichisparticularlysigni cantinthemoderneconomywherenetworkexternalityisprevalent.Thee ectivenessofcommitment,however,dependsonwhethersuchanactioniscredible.Withoutunderstandingtheroleofcredibility,anyrecommendationofbusinessstrategiesandgovernmentpolicieswouldbeine ective,andsometimesincorrect.Toanalyzeissuesrelatedtocommitmentandcredibility,weneedtomodelsequencesofmovesinagame.Thisiswhatthetheoryofgamesinextensive-form(orsequential-movegames)o ers.Toruleoutnon-crediblethreatsanotherequilibriumconceptisoftenused,namelysubgameperfectequilibrium.Subgameperfectequilibriacanbecalculatedbysolvingtheextensive-formgamebackward.

Oneofthemostimportantgamesinextensive-forminindustrialeconomicsispresentedinthefollowingexample.Dooligopolistschoosepricesorquantities?KrepsandScheinkman(1983)proposeaningenuousanswertothisquestion.Theystudyatwo-stagegameinwhich rms rstsimultaneouslychoosetheircapacityandthensimultaneouslyselectpricesafterobservingthecapacityofall rms.Consideronlytwo rms.Apurestrategyfora rmconsistsofacapacitylevelandapricefunctionofcapacitypair.Thepayo speci cationdependsonwhichrationingruletouse,i.e.,whathappenswhenthelow-price rmdoesnothavethecapacitytoservetheentiremarket.Underthee cientrationingrule,consumerswiththehighervaluationsbuyatthelowerprice.Undertheproportionalrationingrule,everyconsumerhasthesameprobabilityofbuyingatthelowerprice.Assumingthee cientrationingruleandconcavedemandfunction,KrepsandScheinkman(1983)showthatatthesubgameperfectequilibriumtheduopolistschoosecapacitylevelsequaltotheCournotquantitylevels.Inotherwords,the rmsbehavelikeCournotcompetitorsinthe rststageandlikeBertrandcompetitorsinthesecondstage.Theycommitnottoengageinruthlesspricecompetition,andasaresult,theequilibriumofthepricinggamewillbeoneinwhicheach rmsetsthesameprice.ThatpriceturnsouttobeequaltothepriceresultingfromtheCournotmodel.

ThisexampleprovidesalinkbetweentheBertrandpricecompetitionandCournotquantitycompetition.Moreimportantly,asarguedinTirole(1988),thistwo-stage