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

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Lecture 1: Normal Form Games: Re f 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 f nition and examples Proper equilibrium: Motivation and examples Correlated equilibrium: Motivation, de f 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 f 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 ANE σ is trembling hand perfect if there is some sequence of perturbed games { Γ ε k } k =1 converging to Γ N fo rwh ichthereissomeassoc iatedsequenceo fNE { σ k }
Lecture 1 5 Albert Banal-Estanol Alternative De f nition and Properties Problem: need to compute equilibria of many possible perturbed games

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## This note was uploaded on 01/26/2012 for the course ECON 14-126 taught by Professor Muhametyildiz during the Spring '11 term at Massachusetts College of Liberal Arts.

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

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