game theory博弈论

gametheorySpeaker:YangXiaolanMajor:theoreticaleconomicsWhatisgametheoryabout?“Gametheoryisatechniqueusedtoanalysesituationswherefortwoormoreindividuals(orinstitutions)theoutcomeofanactionbyoneofthemdependsnotonlyontheparticularactiontakenbythatindividualbutalsoontheactionstakenbytheother(orothers).”—F.Carmichael“Agameisbeingplayedwheneverpeoplehaveanythingtodowitheachother.”—K.Binmore“Gametheoryisthemathematicalstudyofstrategicinteractionsamongparticipants.”—E.MaskinPredecessorsofGameTheoryDanielBernoulli(1700-1782)Swiss(瑞士)mathematician,investigatedthe“St.Petersburgparadox”（圣彼得堡悖论）:Agentsdonotcaredirectlyaboutthemoneyprizesofagame(theycareabouttheutilitythemoneyprovides).StartingPointofmodernGameTheoryTheoryofGamesandEconomicBehavior(1944),byJohnvonNeumann(1903-1957)OskarMorgenstern(1902-1977)AHungarian-American(美籍匈牙利)MathematicianandanAustrianeconomistwhorevolutionizedthefieldofeconomics.Althoughtheirworkitselfwasintendedsolelyforeconomists,itsapplicationstopsychology,sociology,politics,warfare(战争),recreational（娱乐性的）games,andmanyotherfieldssoonbecameapparent.BasicsElementsofagamea.Players:Whoparticipatesinthegame?b.Actions/Strategies:Whatcaneachplayerdo?Inwhatorderdotheplayersact?c.Outcomes/Payoffs:Givenacertainchoiceofactions,whatistheoutcomeofthegame?Inaddition:(private)informationaboutsomeaspectofthegameandeachplayer’sbeliefsaboutsomeunknownparameter（参数）oftheenvironment.AnexampleofclassicgameExample1.1(Rousseaugame卢梭游戏)Ifagroupofhunterssetouttotakeastag,theyarefullyawarethattheywouldallhavetoremainfaithfullyattheirpostsinordertosucceed;butifaharehappenstopassnearoneofthem,therecanbenodoubtthathepursueditwithoutqualm（疑虑）,andthatoncehehadcaughthisprey（猎物）,hecaredverylittlewhetherornothehadmadehiscompanionsmisstheirs.”staghareElementsoftheRousseaugame:Players:Hunters(let’sassumethereareonly2)Actions:HuntstagorhuntharePayoffs:•Payoffforeach:2Bothhuntfor•Payoffforeach:1Bothhuntfor•Payoff•forformer:1,•forlatter:0OneofthemhuntsforThisgamecanberepresentedbythefollowinggamematrice（矩阵）:1\2stagHaredeer2,20,1stag1,01,1Solutionconceptofgames:ThesolutionconceptisthatofNashequilibrium.Achoiceofstrategies,oneforeachplayer,formsanequilibrium,ifnosingleplayercanprofitbychanginghisstrategywhileallotherplayersstayfirm.Inotherwords,achoiceofstrategiesformsanequilibrium,ifthereisnoprofitableunilateral（单边的）deviation（偏离）fromit.modelanalysisInthestaghuntgame（猎鹿博弈）,accordingtothedefinitionofNashequilibrium,thegamehastwoNashequilibriumpoint,thatis:eitherhuntingforstag[2,2];orcatchingrabbitrespectively[1,1]compared[2,2]and[1,1],thepayoffsofonesideincrease,whiletheothersarenotaffected.Namely,comparedwith[1,1],[2,2]hasthemeaningofParetoadvantage（帕累托优势）(resourceshavebeenfullyutilized).TheapplicationofrealityBusinesscombinationCombiningBaoshanIronandSteelCompany(A)withShanghaiIronandSteelGroup(B)•money,benefits,managementandscaleA•productiontechnologyandexperienceBThemoreadvantagesandthegreaterpotentialEnlightenmentifwedonothangtogether,weshallmostassuredlyhangseparately.------BenjaminfranklinIfeveryoneismovingforwardtogether,thensuccesstakescareofitself------HenryFord