哈佛博弈论讲义section1.ppt

GOV 2005:Game TheorySection 1Alexis Diamondadiamondfas.harvard.edu.AgendaWhat is game theory?Exercise:convergence to equilibriumKey terms and definitionsFormal theory:what Leo has to say about itHow do you do it(using formal theory)Application:Alliance FormationFinal thoughts.What Defines Game Theory?Mathematically preciseList of playersComplete description of allowable movesDescription of informationSpecification of how actions cause outcomesSpecification of players preferencesFormal Analysis of Strategic Settings.Exercise:Moving to EquilibriumPlayer 2A Game in Normal FormAvg payoff for playing with prob distribution p,given others play strategies with prob distribution qExpected Value:.Three or Four Important ConceptsDominant StrategyOne best strategy no matter what your opponent doesWeakly dominant versus strongly(strictly dominant)strategiesMixed StrategyMoves are chosen randomly from the set of pure strategiesEvery simultaneous move game has a Nash equilibrium in mixed strategiesNash equilibrium:When each player is playing a best response to Nash equilibrium:When each player is playing a best response to the strategies of the othersthe strategies of the othersBeliefs:Probability distribution over strategies of other playersBeliefs:Probability distribution over strategies of other players.Key Terms and DefinitionsNormal form and extensive formNodes(initial,terminal)Information setsStrategy:complete contingent planOne for every information setEquilibrium:a stability conceptWelfarePareto optimality:no free lunch.Formal Theory:Whats it good for?We have absolutely certain or scientific knowledge only of those subjects of which we are the causes The construction must be conscious construction;it is impossible to know a scientific truth without knowing at the same time that we have made it.The world of our constructs is therefore the desired island that is exempt from the flux of blind and aimless causation.“We understand only what we make”-Leo Strauss“We understand only what we make”-Leo Strauss.Applying Formal TheoryGoal(research question)Story(model)Formalization(abstraction)Analysis(manipulation)Solution(definition of equilibrium)Translation(external and internal validity)General Equilibrium:General Equilibrium:interactions among many(infinite)agents,interactions among many(infinite)agents,where any one agents actions have no effect on other agents.where any one agents actions have no effect on other agents.Game Theory is just one of several formal modeling approachesGame Theory is just one of several formal modeling approaches.Example:Alliance FormationGoal:Gain insight into dynamics of power and motivationWhat motivates countries to form alliances?Story:Setting:3 countries fighting a warEach has power(military capability),which is positively associated with probability of winningEach is rational and has its own interests at heartExample taken from Altfield and Bueno de Mesquita 1979.FormalizationStates are identified as(A,B,C)Their capabilities are(a,b,c)If B helps A,probability that A wins is (a+b)/(a+b+c)=PBAIf B helps C,probability that C wins is (b+c)/(a+b+c)=PBCAmount that B values a victory by A is UBACost to B of helping A is KBACost of neutrality is zeroB vs.nature:B moves,then either A or C wins.Analysis:Whither Alliances?Adopt the perspective of a player:BBs utility from an alliance with A=PBA(UBA)+(1-PBA)(UBC)-KBA Bs utility from an alliance with C=PBC(UBC)+(1-PBC)(UBA)-KBC(1)(2)What if equation 1 equation 2?What if equation 2 equation 1?.Solution:EquilibriumWhat is the point at which B is indifferent?PBA(UBA)+(1-PBA)(UBC)-KBA)=PBC(UBC)+(1-PBC)(UBA)-KBC)Simplifies to.(PBA+PBC-1)(UBA-UBC)=(KBA-KBC)Simplifies to.b/(a+b+c)(UBA-UBC)=(KBA-KBC).Translation:ValidityWhat is the point at which B is indifferent?b/(a+b+c)(UBA-UBC)=(KBA-KBC)b/(a+b+c)=resources B can contribute(UBA-UBC)=Bs motivation for A vs.C(KBA-KBC)=Bs costs for A vs.CThe decision to help in a dispute depends on ones ability to influence the The decision to help in a dispute depends on ones ability to influence the outcome,ones level of motivation,and the costliness of getting involvedoutcome,ones level of motivation,and the costliness of getting involvedCalibration,comparative statics,case studies are all ways of assessing model validity.Final thoughtsGiven B is indifferent to allying whenb/(a+b+c)(UBA-UBC)=(KBA-KBC),andb/(a+b+c)=resources B can contribute(UBA-UBC)=Bs motivation for A vs.C(KBA-KBC)=Bs costs for A vs.CEquilibrium,perturbed:If the left-hand side is the right-hand side then B would rather partner with AWhat real-world events might prompt this?.