replicatingaBertrandgameorCournotgame nitelyorin nitelymanytimes,wecanapplythebackwardinductionmethodandsubgameperfectequilibriumconcepttostudytheimportantissueoftacitcollusion.

Twomoreapplicationsofgametheoryinmodellingstrategicbehaviorwarrantsomediscussion:Strategictradepolicyandmanagerialincentives.Anationalgov-ernmentmayhaveincentivestosettradepolicieshelpingits rmswhentheycompeteagainstforeign rmsinaninternationalmarket.Thesepoliciesmayincludedirectsubsidies,taxbene ts,andlow-interestloans.Suchpoliciesoftenimprovedomestic rms’strategicpositionsandputrivalsinadisadvantageousposition.However,ifallgovernmentsusesimilarpolicies,theymaynotnecessarilybene t.Thisprob-lem,whichinspiredalargeliteratureonstrategictradepolicy,was rststudiedbyBranderandSpencer(1985).Similarargumentshavebeenusedtostudymanage-rialincentivesbyFershtmanandJudd(1984).Whenmanagersplayanoligopolygame,ownersmaywanttomotivatemanagersbycompensatingthembasedonacombinationofpro tsandrevenues.

Firmsoftenhaveprivateinformationabouttheircostsandmarketdemand.Toanalyzetheimpactofprivateinformationon rms’strategies,weneedtoapplythetheoryofgameswithincompleteinformation.AgoodapplicationistheBertrandpricecompetitionmodelwithprivatelyknownmarginalcosts.Supposethatanum-berof rmscompetebysettingpricessimultaneously.Each rmknowsitsown(constant)marginalcostbutcannotobserveitsrivals’marginalcosts.Assumethatthemarginalcostsareindependentlydrawnfromthesamedistribution.Each rm’sstrategyisafunctionofitsownmarginalcost.The rmsbehaveasBayes-Nashplayerschoosingpricesbasedontheexpectationsoftheother rms’equilibriumstrategies.Inasettingwithgeneralcostfunctions,Spulber(1995)showsthatthereexistsauniquesymmetricequilibriumpricingstrategy,andthatinequilibriumall rmsexceptforthehighestcosttypemakepositivepro ts.ThisanalysisprovidesanalternativewayofresolvingtheBertrandparadox.

Moreimportantly,thisexampleprovidesalinkbetweenoligopolytheoryandauctiontheory.Thesettingisessentiallythesameasthestandardauctionenviron-mentwithindependentprivatevaluesandvariableunitsofquantities.TheBertrandcompetitionisliketheruleof rst-pricesealed-bidauctions.ABayes-Bertrand-Nashequilibriumisapro leofbiddingstrategiesthatcanbecomputedusingthestandardtechniqueinauctiontheoryandgametheory.

Manyprocurementprojectswith xed-pricecontractsarecompetitivelyawardedthroughBertrand-like rst-priceauctionprocedures.Examplesincludehighwaycon-structioncontracts,schoolmilkdeliverycontracts,anddefenseprocurementcon-tracts.AswewilldiscussinSection4,thetheoryofmarketdesigndealswith