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1、Chapter3ModelingGameswithComputerSoftwareandExperimentingGamesInthischapter,weintroducemodelingtechniquesusingcomputersoftware.First,wereviewtwogamesthatarecommonlydescribedinmanygametheorytextbooks,aswellasasamplegameofdominatedstrategies.Thepurposehereistomodelgamesbyusingk
2、eygametheoryconceptsintroducedinthelastchapter.Thegamesdiscussedinthischapterarepresentedinthesimplestform.Eachcanbeextendedtomoregeneralizedsituationssuchasimperfectinformationgamesandrepeatedgames.BasicformsofthesegamesaremodeledusingMATLABhere,andareillustratedbyVisio.Acom
3、monassumptioningametheoryisthataplayerisconcernedwithmaximiz-inghisindividualutilityfunction.Heisunconcernedwithanotherplayer’sutility.Thisisclearlyanabstractionofactualhumanbehavior.Agameisultimatelydefinedbyitsform,notbythestorybehindthegame.Thisisimportanttokeepinmind,soth
4、atthereaderdoesnotgetlostinunimportantdetails.©2010byTaylorandFrancisGroup,LLC36AppliedGameTheoryandStrategicBehaviorPrisoner’sDilemmaInthisclassicgame,twoplayers,prisonerIandprisonerII,havebeenarrestedonsuspicionofcommittingacrime.Thelawenforcementofficersputtheminseparatero
5、oms.Eachprisonermustindependentlymakethedecisionwhetherornottocon-fesshiscrimewithoutknowinghispartner’sactions.Thelawoffersbothprisonersthefollowingdeal.Ifoneprisonerdeniesthecrimeandremainsquiet,whiletheotherconfesses,thenthelawwillrewardtheconfessorbylettinghimgofree,while
6、thelawwillpunishtheprisonerwhodoesnotconfessbysendinghimtojailfor10years.IfbothprisonerIandprisonerIIconfess,thelawputstheprisonersawayfor5years.Finally,Ifbothoftheprisonerscooperateanddonotconfess,thelawwillhavelittleevidenceandcanonlychargeeachwithaminorviolationresultingin
7、oneyearinjail.Thissituationcanbeseenclearlyinthepayoffmatrixbelow:TABLE3.1NormalFormoftheClassicPrisoner’sDilemmaGamePrisonerIIConfessDenyPrisonerIConfess(−5,−5)(0,−10)Deny(−10,0)(−1,−1)Prisoner’sdilemmagameanalyzedhereisatwo-playersimultaneous-movegame.PrisonerIandprisonerII
8、havethesamesetofactions:{Confess,Deny}.Eachplayerhasaperfectinformat
