yale的知識管理講座4

1、Introduction to Game TheoryYale BraunsteinJune 2003General approachBriefHistory of GameTheoryPayoffMatrixTypesofGamesBasicStrategiesEvolutionaryConceptsLimitationsandProblemsBriefHistory of GameTheory1913 -E.Zermeloprovidesthefirsttheoremofgame theory;assertsthat chess is strictly determined1928 -Jo

2、hnvonNeumannprovesthe minimaxtheorem1944 -JohnvonNeumann& Oskar Morgenstern writeTheory of Games andEconomicBehavior”1950-1953-John Nashdescribes NashequilibriumRationalityAssumptions:humansare rational beingshumansalways seekthe bestalternativeinasetofpossiblechoicesWhyassume rationality?narrowdown

3、therangeofpossibilitiespredictabilityUtility TheoryUtility Theorybasedon:rationalitymaximizationofutilitymaynot be alinear function of incomeorwealthItisa quantification of apersonspreferenceswithrespect to certainobjects.What is GameTheory?Game theoryisa study of howtomathematicallydeterminethe bes

4、tstrategyfor given conditionsinordertooptimizethe outcomeGame TheoryFinding acceptable, if notoptimal,strategies in conflict situations.Abstractionofreal complexsituationGame theoryishighlymathematicalGame theoryassumes allhumaninteractionscan be understoodand navigatedbypresumptions.Whyisgametheory

5、important?Allintelligentbeings makedecisions allthetime.AIneedstoperform these tasks as aresult.Helpsustoanalyze situationsmorerationally andformulateanacceptablealternativewith respecttocircumstance.Usefulinmodelingstrategic decision-makingGamesagainst opponentsGamesagainst natureTypesofGamesSequen

6、tialvs.SimultaneousmovesSinglePlayvs.IteratedZerovs.non-zerosumPerfectvs.ImperfectinformationCooperativevs.conflictZero-SumGamesThesum of thepayoffs remainsconstantduring thecourseofthe game.TwosidesinconflictBeingwell informed alwayshelpsa playerNon-zeroSumGameThesum of payoffsisnot constant during

7、thecourse of gameplay.Players mayco-operate or competeBeingwell informed mayharm aplayer.GamesofPerfect InformationTheinformationconcerninganopponents moveiswellknowninadvance.Allsequentialmove games areofthis type.ImperfectInformationPartial or no information concerningthe opponent is given in adva

8、ncetothe players decision.Imperfectinformationmay be diminishedovertime if thesame gamewiththesameopponentistoberepeated.KeyAreaofInterestchancestrategyNon-zeroImperfectMatrixNotationNotes:Player IsstrategyA maybedifferentfromPlayerIIs.P2canbeomittedifzero-sumgamePrisoners Dilemma&OtherfamousgamesA

9、sampleofothergames:MarriageDisarmament(mygeneralsaremore irrationalthanyours)Prisoners Dilemma10, 10BlameDontBlameDont20, 00 ,201 ,1Prisoner1Prisoner2Notes:Higherpayoffs (longersentences)arebad.Non-cooperativeequilibrium Joint maximumNCEJt.max.GamesofConflictTwosidescompeting againsteachotherUsually

10、 causedbycompletelack of information about theopponentorthegameCharacteristicofzero-sumgamesGamesofCo-operationPlayers mayimprove payoffthroughcommunicatingforming bindingcoalitions& agreementsdonotapplytozero-sumgamesPrisoners Dilemmawith CooperationPrisoners DilemmawithIterationInfinitenumberofite

11、rationsFear of retaliationFixednumberofiterationDominoeffectBasicStrategies1.Plan ahead andlook back2.Useadominating strategy if possible3.Eliminateany dominatedstrategies4.Look foranyequilibrium5.Mixupthe strategiesPlan ahead andlook backStrategy2Strategy1150100025Strategy1Strategy2- 10YouOpponentI

12、fyouhavea dominatingstrategy,useitStrategy2Strategy1150100025Strategy1Strategy2- 10YouOpponentUse strategy 1Eliminateany dominatedstrategyStrategy2Strategy1150100025Strategy1Strategy2- 10YouOpponentStrategy3-15160Eliminate strategy 2 as its dominated by strategy 1Look foranyequilibriumDominating Equ

13、ilibriumMinimax EquilibriumNash EquilibriumMaximin &MinimaxEquilibriumMinimax -tominimizethe maximumloss(defensive)Maximin -tomaximizethe minimumgain(offensive)Minimax =MaximinMaximin &MinimaxEquilibriumStrategiesStrategy2Strategy1150100025Strategy1Strategy2- 10YouOpponentStrategy3-15160Min1000150-

14、10-15160MaxDefinition:Nash EquilibriumIsthis aNashEquilibrium?Strategy2Strategy1150100025Strategy1Strategy2- 10YouOpponentStrategy3-15160Min1000150- 10-15160MaxCost to press button= 2unitsWhen buttonispressed,food given =10unitsBoxedPigs Example5 ,1PressWaitPressWait9 ,-14 ,40 ,0LittlePigBigDecision

15、s, decisions.Time forreal-lifedecisionmakingHolmes&MoriarityinTheFinalProblemWhat would youdoIfyouwereHolmes?IfyouwereMoriarity?Possiblyinterestingdigressions?Whywas Moriaritysoevil?What reallyhappened?What do we meanbyreality?What changedthe reality?MixedStrategySafe 2Safe 1$ 0$10,000$100,000Safe 1

16、Safe 2$ 0MixedStrategySolutionThePayoff Matrixfor Holmes& MoriarityPlayer #1Player #2Strategy #1Strategy #2Strategy #1Strategy #2Payoff (1,1)Payoff (1,2)Payoff (2,1)Payoff (2,2)CanterburyCanterburyDoverDover0100500HolmesMoriartyEvolutionaryGameTheoryNatural selectionreplacesrationalbehaviorSurvivalo

17、fthefittestWhyuse evolutiontodetermineastrategy?Hawk /DoveGameEvolutionaryStable StrategyIntroduced by MaynardSmithand Price (1973)Strategybecomes stablethroughout thepopulationMutationsbecomingineffectiveHawkDoveHawkDove22100100-5-5HawkDoveHawkDove22100100-5-5Whereisgame theorycurrently used?EcologyNetworksEconomicsLimitations& ProblemsAssumes playersalways maximize their outcomesSome outcomes aredifficulttoprovidea utilityforNotall of thepayoffs canbequantifiedNotapplicabletoallproblem