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1、Someideasaboutthecombinationofrepeatedgame, niteautomatatheoryandSTPmethodYiPeng2012/10/22x1IntroduceautomatatodescribethestrategyofrepeatedgameandtheconsiderationofcomplexityTodescribethestrategyofrepeatedgameinsomeFolkTheorem,Rubinsteinintroducedtheconceptofautomatainhisbook"ACourseinGameTheor
2、y".Inthetextbook,di erentautomatawereusedtodescribedi erentTriggerstrategywhichresultindi erentFolkTheoren.Oneoftheotherprimalideatointroduceautomatatogametheoryisthatautomatacandescribetheprocessofhumandecisionmaking.Andboundedrationalityistheunderlyingconceptbehindthegameautomata,whichmeanstha
3、tthenumberofthestateoftheautomatatoimplementthestrategycanre
ectthecomplexityofthestrategy.Rubinstein(1986,1988)consideredthetradeo betweenthecomplexityofstrategyandthepayo ofthestrategy.Heassumedthateverystateoftheautomatabringsaconstantcosttotheplayernomatterhowfrequenttheyareused.Themodelcanb
4、edescribedbelow:twopersonrepeatedgameG=whereSiisa nitesetofstrategiesforplayeri.HereRubinsteinonlyconsideredthepurestrategy,sothestrategysetequalstotheactionset.Andui:S1S2!Risthepayo functionofplayeri.Heuseda nitemooremachinetodescribedthestrategy.ThatisMi:istheMoorema
5、chineforplayeri.Qiisthe nitesetofstateswithq0astheinitialstate.i:Qi!SiistheoutputfunctionoftheMooremachineandi:QiSj!Qi(j6=i)isthetransitionfunctionoftheMoorefunction.Thismeansthatthenumberofstatescanbebiggerthanthenumberofactions,thatis]Qi]Si.Thisworkhavebeenstudiedin1980'sbyRubbinstein(,198
6、6,1988),Samuelson(1992),Kalai(1990),Neyman(1998,2000),andtheyhaveplentyofresultaboutthestructureofNashEquilibrium,thestabilityoftheevolutionofautomataandsomelimitcharacteristic(Thiskindofworkhasbeensummarizedindi erenttextbook).Infactwhattheycareistheconceptofsolution,1howto ndthesolutionisnotme
7、ntioned,whichisnotinfavorofSTPmethodButwecanintroducetheconceptofSTPtodescribetheprocessofthegame.Denotingtheactionsetofplayerias4mi,andthestatesetofplayerias4si,wecandescribethestrategyofplay1asx1(t+1)=M1nx1(t)u2(t);u1(t+1)
