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STRATEGOS Game Theory WorkshopIntroduction toMathematical Game TheoryLucia PusilloUniversity of Genova - ItalyEmail pusillo@dima.unige.iURL nseAthenaeumEst.1471 ADProf. Lucia PusilloEmail: lucia.pusillo@simulationteam.comURL: www.itim.unige.it/strategos
STRATEGOS Game Theory WorkshopIntroduction toMathematical Game TheoryMathematical Game Theory deals with mathematical techniques ableto analyze situations in which two or more individuals make decisionsto influence their and other’s benefits.Situations studied by Game Theorists are not only recreational as the“game” word should suggest, often Game Theory is applied toIndustrial, Business, Geo Political and Military ProblemsGenuenseAthenaeumEst.1471 ADProf. Lucia PusilloEmail: lucia.pusillo@simulationteam.comURL: www.itim.unige.it/strategos
STRATEGOS Game Theory WorkshopOrigins of Game TheoryWe date the beginning of this modern Theory withthe paper of Von Neumann & Morgenstern in 1944(Games and Economic Behavior), the word gameis applied to any social situation involving two ormore individuals: the Players.The Players are rational Decision Makers:they take decisions to maximize the payoffs oftheir expected utilityGame Theory develops methods and techniquesto play Games and to identify Winning StrategiesGenuenseAthenaeumEst.1471 ADProf. Lucia PusilloEmail: lucia.pusillo@simulationteam.comURL: www.itim.unige.it/strategos
STRATEGOS Game Theory WorkshopPayoff & EvolutionAn example of behavior maximizing its payoff could be easily found inthe Evolution Models, inspired by Darwin’s Theory.In an Universe where the increasing disorder is a Physics Law, thecomplex organisms (including humans or in general the socialorganizations) can survive only if they have a Behavior to enhance theirprobabilities of surviving and reproducingGenuenseAthenaeumEst.1471 ADProf. Lucia PusilloEmail: lucia.pusillo@simulationteam.comURL: www.itim.unige.it/strategos
STRATEGOS Game Theory WorkshopPayoff as Complex FunctionCurrently. the Evolutionistic Selection Argument suggests thatindividuals want to maximize the expected value of a Measure related tonatural surviving and reproductive suitability, otherwise they disappear(see Maynard Smith 1982).In general maximizing the expected Utility Payoff is not just the samethat maximizing expected Money Payoff, because the Values of Utilityare not always expressed just in Dollars or EurosGenuenseAthenaeumEst.1471 ADProf. Lucia PusilloEmail: lucia.pusillo@simulationteam.comURL: www.itim.unige.it/strategos
STRATEGOS Game Theory WorkshopDecision Maker AttitudeA Risk Adverse Player enhances its expected utility more by winning adollar when he/she is poor then when he/she is richIt's never too early to start winningIt is always too early to start losingJ.Fleming, 007 GoldfingerGenuenseAthenaeumEst.1471 ADProf. Lucia PusilloEmail: lucia.pusillo@simulationteam.comURL: www.itim.unige.it/strategos
STRATEGOS Game Theory WorkshopDecision TheoryGame Theory can be seen as a generalizationof Decision Theory (with two or moredecision makers), so to understand well thefundamental concepts of Game Theory it isnecessary to study the basicsof Decision TheoryWinston ChurchillUK PM during WWIIGenuenseAthenaeumEst.1471 ADDoug McMillionWall Mart CEO 2020Prof. Lucia PusilloEmail: lucia.pusillo@simulationteam.comURL: www.itim.unige.it/strategos
STRATEGOS Game Theory WorkshopIdentify Goals & ObjectivesDecisions fill up our life and the Capacity of Choosing andExpressing our whishes are the points whichmake the difference between the Life of anIntelligent Being from an Inferior Forms.GenuenseAthenaeumEst.1471 ADProf. Lucia PusilloEmail: lucia.pusillo@simulationteam.comURL: www.itim.unige.it/strategos
STRATEGOS Game Theory WorkshopDifferent Decisions & GamesEvery Day we make Decisions, but some of them have sosmall importance that we forget them within a few minutes, whileothers are so important that weconduct a Very Accurate Analysisbefore to take the Final DecisionGarry K.Kasparov, Legendary World Chess ChampionGenuenseAthenaeumEst.1471 ADProf. Lucia PusilloEmail: lucia.pusillo@simulationteam.comURL: www.itim.unige.it/strategos
STRATEGOS Game Theory WorkshopAnalysis and People inGame TheoryWhat is an accurate Analysis?Who is a good Decision Maker?Russia isInterventionistRussia is nNo meniaUSARussia3.3;3.3Jeff BezosAmazon FounderGenuenseAthenaeumEst.1471 ADProf. Lucia PusilloEmail: lucia.pusillo@simulationteam.comURL: www.itim.unige.it/strategos
STRATEGOS Game Theory WorkshopGame Theory MatrixExampleThis is just a Fictional Scenariowithout any reference to real events andcreated ad hoc to propose an ExampleCampaignNo ;3.3Payoff expressed as Revenues in Canada in bUSD based on Commercial PromotionsGenuenseAthenaeumEst.1471 ADProf. Lucia PusilloEmail: lucia.pusillo@simulationteam.comURL: www.itim.unige.it/strategos
STRATEGOS Game Theory WorkshopGame Theory TreeExampleRussia isInterventionistRussia is iaUSAUSARussiaThis is just a Fictional Scenariowithout any reference to real events andcreated ad hoc to propose an ExampleGenuenseAthenaeumEst.1471 ADx1Russiax2x3x4x5x6x7x8x9Prof. Lucia PusilloEmail: lucia.pusillo@simulationteam.comURL: www.itim.unige.it/strategosxn
STRATEGOS Game Theory WorkshopDelegate or Decide?Sometimes we have precise ideas about who is a Good Decision Maker,then we will be able to criticize the decisions of our delegates.Often we have to delegate others and we would like to be sure theydecide well, but only if we are able to recognize a goodDecision Maker, we can be really sure of this.One goal of Mathematical GameTheory is to build Mathematical Toolsto make Good Decisions and interactStrategically with others’ DecisionsDeep Blue by IBMLuigi Einaudi1st Computer able to winPresident of Italyagainst the human Chess World Champion1948-1955GenuenseAthenaeumEst.1471 ADProf. Lucia PusilloEmail: lucia.pusillo@simulationteam.comURL: www.itim.unige.it/strategos
STRATEGOS Game Theory WorkshopCooperative &Not Cooperative GamesTwo very important frameworks in Game Theory are: Non Cooperative Games Cooperative Games.These two interesting kinds of Games are very different respect theMathematical Tools that we need to use in order to properlyaddress and solve themGenuenseAthenaeumEst.1471 ADProf. Lucia PusilloEmail: lucia.pusillo@simulationteam.comURL: www.itim.unige.it/strategos
STRATEGOS Game Theory WorkshopStaticSimultaneousNon ral SumGenuenseAthenaeumEst.1471 -StageImperfectInformationClassification ofGamesThere are many different ways toclassify GamesThis is an example related to CyberAttacks and include considerationsabout Static & Dynamic Games,Games with Perfect &Imperfect Info, Complete &Incomplete Games, ZeroInfinite:General SumSum & General Sum GamesProf. Lucia PusilloEmail: lucia.pusillo@simulationteam.comURL: www.itim.unige.it/strategos
STRATEGOS Game Theory Workshop“Chess” (Persian شاه shāh, King) is aStrategy Game bornaround VI in Indiaand turned popular inEurope around 1000AD.It has taken up toFebruary 10, 1996 togetaWorldChampion (i.e. G.K.Kasparov)tobedefeatedbyaComputer (Deep Bluefrom IBM) able tolook forward up to 16billion movesLa partita a scacchi di Gerolamo Induno. Galleria d'arte moderna, Milano. Artista: Brogi (1915-1920 ca.)GenuenseAthenaeumEst.1471 ADProf. Lucia PusilloEmail: lucia.pusillo@simulationteam.comURL: www.itim.unige.it/strategos
Introduction to Mathematical Game Theory Mathematical Game Theory deals with mathematical techniques able to analyze situations in which two or more individuals make decisions to influence their and other’s benefits. Situations studied by Game Theorists are not only recreational as the “game” word
