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# lec1 - Lecture 1 Normal Form Games Renements and Correlated...

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Lecture 1: Normal Form Games: Re fi nements and Correlated Equilibrium Albert Banal-Estanol April 2006

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Lecture 1 2 Albert Banal-Estanol Today’s Lecture Trembling hand perfect equilibrium: Motivation, de fi nition and examples Proper equilibrium: Motivation and examples Correlated equilibrium: Motivation, de fi nition and examples
Lecture 1 3 Albert Banal-Estanol Motivation for "Trembling Hands" Rationality does not rule out weakly dominated strategies In fact, NE can include weakly dominated strategies Example: (D,R) in L R U 1 , 1 0,-3 D -3 , 0 0, 0 But should we expect players to play weakly dominated strategies? Players should be completely sure of the choice of the others But, what if there is some risk that another player makes a "mistake"?

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Lecture 1 4 Albert Banal-Estanol Trembling Hand Perfection For Γ N = [ I, { ( S i ) } , { u i () } ] de fi ne... for each i and s i , ε i ( s i ) (0 , 1); ε ( S i ) = { σ i : σ i ( s i ) ε i ( s i ) for all s i S i and Σ s i σ i ( s i ) = 1 } ; "the perturbed game" as Γ ε = [ I, { ε ( S i ) } , { u i () } ] Interpretation: each strategy s i is played with some minimal probability this is the unavoidable probability of a mistake A NE σ is trembling hand perfect if there is some sequence of perturbed games { Γ ε k } k =1 converging to Γ N for which there is some associated sequence of NE { σ k } k =1 converging to σ
Lecture 1 5 Albert Banal-Estanol Alternative De fi nition and Properties Problem: need to compute equilibria of many possible perturbed games Proposition: σ is trembling hand perfect

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lec1 - Lecture 1 Normal Form Games Renements and Correlated...

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