Lecture-7-Games

1Lecture7:Games2博弈论与新产业组织Gametheory：研究人们的策略行为，或如何在相互影响的环境中进行选择。寡头市场的特征：企业的行为会影响到市场上的其他企业，即企业会相互影响3什么是博弈论（game）?ABAB你的对手p你70,7060,9090,6080,80game1：不要被你的同桌看见，在纸上写下A或B。然后随机地把两个人分为一组，但你不知道你和谁一组。假如考试的成绩按如下方式确定这不是博弈结果矩阵(outcomematrix)4什么是博弈论（game）?ABAB你的对手p你1,10,33,02,2Normalform标准式-静态博弈这才是博弈收益矩阵Lessonfromthegame1,不要选择劣势策略（dominatedstrategy）,应该选择占优策略（dominatingstrategy）；2，换位思考（putyourselfinothers’shoes）什么是博弈论（game）?game2：选数字游戏不要被你的同桌看见，从数字1-100中选一个数字，把你的学号、姓名以及你选的数字写在纸上，交上来。我们会计算数字的平均数，谁选的数最接近平均分的2/3,那么谁就是赢家，赢家平时成绩可以加分举例来说：如果有三个同学，选的数字分别为40，45和95，则平均数是(40+45+95)/3=180/3=60,60*2/3=40;那么第一个同学是赢家什么是博弈论（game）?达到均衡1的要求：1，每个人都是理性的；2，每个人都知道所有人是理性的；3，每个人都知道“每个人都知道所有人是理性的”；。。。。。。“理性”是“共同信息”（commonknowledge）,即我们不仅知道参与人是理性的，而且知道，关于理性的知识我是理性的，你也是理性的；我知道“我是理性的，你是理性的”，你也知道“我是理性的，你是理性的”。。。。。。如果再做一遍游戏，你会选什么数字？8博弈的基本概念博弈的基本结构:参与人：players（你和你的对手）策略：strategies(A或B)结果：outcome（考试的得分）收益或效用：payoffsforeachplayerfromallcombinationsofstrategieschosenbyplayers.信息：完全信息与不完全信息均衡：给定其他人的策略，没有一方会单独改变策略(NashEquilibrium)占优策略dominantstrategy:A是占优策略的含义是，不管对手选择什么策略，“你”选择A的收益都大于选择B的收益.劣势策略dominatedstrategy：在上例中，B是劣势策略理性行为可能导致糟糕的结果9NashEquilibriumAnotherverycommongame（囚徒困境）prisoner’sdilemmagameillustratesthattheresultingNEoutcomemaybe‘inefficient’.SotheonlyNashequilibriumforthisgameis(C,C),eventhough(D,D)givesboth1and2betterjailterms.TheonlyNashequilibriumisinefficient.criminal1(-6,-6)(-1,-10)(-10,-1)(-3,-3)ConfessDon’tconfessConfessDon’tConfesscriminal2AnExampleTwoairlinesPricesset:competeindeparturetimes70%ofconsumersprefereveningdeparture,30%prefermorningdepartureIftheairlineschoosethesamedeparturetimestheysharethemarketequallyPay-offstotheairlinesaredeterminedbymarketsharesRepresentthepay-offsinapay-offmatrixTheexample(cont.)ThePay-OffMatrixAmerican美国航空Delta达美航空MorningMorningEveningEvening(15,15)Theleft-handnumberisthepay-offtoDeltaTheright-handnumberisthepay-offtoAmerican(30,70)(70,30)(35,35)Whatistheequilibriumforthisgame?Theexample(cont.)ThePay-OffMatrixAmericanDeltaMorningMorningEveningEvening(15,15)IfAmericanchoosesamorningdeparture,Deltawillchooseevening(30,70)(70,30)(35,35)IfAmericanchoosesaneveningdeparture,DeltawillstillchooseeveningThemorningdepartureisadominatedstrategyforDeltaandsocanbeeliminated.TheNashEquilibriummustthereforebeoneinwhichbothairlineschooseaneveningdeparture(35,35)ThemorningdepartureisalsoadominatedstrategyforAmericanandagaincanbeeliminatedTheexample(cont.)NowsupposethatDeltahasafrequentflierprogramWhenbothairlinechoosethesamedeparturetimesDeltagets60%ofthetravelersThischangesthepay-offmatrixTheexample(cont.)ThePay-OffMatrixAmericanDeltaMorningMorningEveningEvening(18,12)(30,70)(70,30)(42,28)However,amorningdepartureisstilladominatedstrategyforDelta(Eveningisstilladominantstrategy.IfDeltachoosesamorningdeparture,AmericanwillchooseeveningButifDeltachoosesaneveningdeparture,AmericanwillchoosemorningAmericanhasnodominatedstrategyAmericanknowsthisandsochoosesamorningdeparture(70,30)NashEquilibriumAgainWhatiftherearenodominatedordominantstrategies?TheNashequilibriumconceptcanstillhelpusineliminatingatleastsomeoutcomesChangetheairlinegametoapricinggame:60potentialpassengerswithareservationpriceof$500120additionalpassengerswithareservationpriceof$220pricediscriminationisnotpossible(perhapsforregulatoryreasonsorbecausetheairlinesdon’tknowthepassengertypes)costsare$200perpassengernomatterwhentheplaneleavestheairlinesmustchoosebetweenapriceof$500andapriceof$220ifequalpricesarechargedthepassengersareevenlysharedOtherwisethelow-priceairlinegetsallthepassengersThepay-offmatrixisnow:Theexample(cont.)ThePay-OffMatrixAmericanDelta达美航空公司PH=$500($9000,$9000)($0,$3600)($3600,$0)($1800,$1800)PH=$500PL=$220PL=$220Ifbothpricehighthenbothget30passengers.Profitperpassengeris$300IfDeltapriceshighandAmericanlowthenAmericangetsall180passengers.Profitperpassengeris$20IfDeltapriceslowandAmericanhighthenDeltagetsall180passengers.Profitperpassengeris$20Ifbothpricelowtheyeachget90passengers.Profitperpassengeris$20NashEquilibrium(cont.)ThePay-OffMatrixAmericanDeltaPH=$500($9000,$9000)($0,$3600)($3600,$0)($1800,$1800)PH=$500PL=$220PL=$220(PH,PL)cannotbeaNashequilibrium.IfAmericanpriceslowthenDeltashouldalsopricelow($0,$3600)(PL,PH)cannotbeaNashequilibrium.IfAmericanpriceshighthenDeltashouldalsopricehigh($3600,$0)(PH,PH)isaNashequilibrium.Ifbotharepricinghighthenneitherwantstochange($9000,$9000)(PL,PL)isaNashequilibrium.Ifbotharepricinglowthenneitherwantstochange($1800,$1800)TherearetwoNashequilibriatothisversionofthegameThereisnosimplewaytochoosebetweentheseequilibria.Butevenso,theNashconcepthaseliminatedhalfoftheoutcomesasequilibriaCustomandfamiliaritymightleadbothtopricehigh“Regret”mightcausebothtopricelowNashEquilibrium(cont.)ThePay-OffMatrixAmericanDeltaPH=$500($9000,$9000)($0,$3600)($3600,$0)($1800,$1800)PH=$500PL=$220PL=$220(PH,PL)cannotbeaNashequilibrium.IfAmericanpriceslowthenDeltawouldwanttopricelow,too.($0,$3600)(PL,PH)cannotbeaNashequilibrium.IfAmericanpriceshighthenDeltashouldalsopricehigh($3600,$0)(PH,