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1、Static(orSimultaneous-Move)GamesofCompleteInformationDominatedStrategiesNashEquilibriumMay20,2003173-347GameTheory--Lecture2OutlineofStaticGamesofCompleteInformationIntroductiontogamesNormal-form(orstrategic-form)representationIteratedeliminationofstrictlydominatedstrategiesNashequilibriumRev
2、iewofconcavefunctions,optimizationApplicationsofNashequilibriumMixedstrategyequilibriumMay20,2003273-347GameTheory--Lecture2Today’sAgendaReviewofpreviousclassDominatedstrategiesIteratedeliminationofstrictlydominatedstrategiesNashequilibriumMay20,2003373-347GameTheory--Lecture2ReviewThenormal-
3、form(orstrategic-form)representationofagameGspecifies:Afinitesetofplayers{1,2,...,n},players’strategyspacesS1S2...Snandtheirpayofffunctionsu1u2...unwhereui:S1×S2×...×Sn→R.Prisoner2MumConfessPrisoner1Mum-1,-1-9,0Confess0,-9-6,-6Allcombinationsofthestrategies.Acombinationofthestrategiesisasetof
4、strategies,oneforeachplayerMay20,2003473-347GameTheory--Lecture2ReviewStatic(orsimultaneous-move)gameofcompleteinformationEachplayer’sstrategiesandpayofffunctionarecommonknowledgeamongalltheplayers.Eachplayerichooseshis/herstrategysiwithoutknowledgeofothers’choices.Theneachplayerireceiveshis/
5、herpayoffui(s1,s2,...,sn).Thegameends.May20,2003573-347GameTheory--Lecture2SolvingPrisoners’DilemmaConfessalwaysdoesbetterwhatevertheotherplayerchoosesDominatedstrategyThereexistsanotherstrategywhichalwaysdoesbetterregardlessofotherplayers’choicesPrisoner2MumConfessPrisoner1Mum-1,-1-9,0Confes
6、s0,-9-6,-6May20,2003673-347GameTheory--Lecture2Definition:strictlydominatedstrategyregardlessofotherplayers’choicessi”isstrictlybetterthansi’Prisoner2MumConfessPrisoner1Mum-1,-1-9,0Confess0,-9-6,-6May20,2003773-347GameTheory--Lecture2ExampleTwofirms,ReynoldsandPhilip,sharesomemarketEachfirmea
7、rns$60millionfromitscustomersifneitherdoadvertisingAdvertisingcostsafirm$20millionAdvertisingcaptures$30millionfromcompetitorPhilipNoAdAdReynoldsNoAd60,6030,70Ad70,3040,40May20,2003873-347GameTheory--Lecture22-playergamewithfinitestrategiesS1
