GraduateGameTheoryLecture-BayesianGames - Game Theory Lecture 5 Bayes Nash Equilibrium Prof John Patty 1 Bayes's Rule Let be a set of states of nature

GraduateGameTheoryLecture-BayesianGames - Game Theory...

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Game Theory Lecture 5 Bayes Nash Equilibrium Prof. John Patty 1
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In games,State of nature: Decision NodeEvent: Information Set“Given that I am in information sete, what is the probability that I am atnodeν?” 3
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Letγbe a finite extensive form game with a set of playersN, a set ofinformation sets for each playeri,Ei, and for eacheEi, a set of nodesν(e).The a set ofbeliefsfor playeriNis a mappingβisuch that for alleEi,βi(e)Δ(ν(e)). 4
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For a strategy profileσ={σi}iNin an extensive form gameγand for anydecision nodeνinγ, letPrσ[ν]denote the probability ofνoccurring if theplayers play according toσ.Consistent BeliefsA set of beliefsβ={βi}iNisconsistentgiven a strategy profileσif, foreach playeri
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  • Spring '11
  • JohnPaddy
  • Game Theory, Bayes Nash equilibrium

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