Assume that we have a finite game and let us have the probability measures over action...
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Assume that we have a finite game and let us have the probability measures over action profiles (alpha denotes mixed action) za (a) = i=1 α₁ (a₁) Moreover, define Z to be: Z = {a, a is Nash equilibrium} CA(M) i.e., Z is such a set and is a subset of some set of mixed actions M. How do we probe that any point in the convex hull of Z represents correlated equilibrium? Do we use any of the following theorems? Brouwers/Kakutani Fixed Point, Closed Graph Lemma? Thank you Hint:Firstly, prove that if an action profile is a Nash equilibrium, it means that the probability distribution over action profiles represents correlated equilibrium. Afterwards, show that the set of correlated equilibria of a finite game is compact and convex. Assume that we have a finite game and let us have the probability measures over action profiles (alpha denotes mixed action) za (a) = i=1 α₁ (a₁) Moreover, define Z to be: Z = {a, a is Nash equilibrium} CA(M) i.e., Z is such a set and is a subset of some set of mixed actions M. How do we probe that any point in the convex hull of Z represents correlated equilibrium? Do we use any of the following theorems? Brouwers/Kakutani Fixed Point, Closed Graph Lemma? Thank you Hint:Firstly, prove that if an action profile is a Nash equilibrium, it means that the probability distribution over action profiles represents correlated equilibrium. Afterwards, show that the set of correlated equilibria of a finite game is compact and convex.
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Related Book For
Computer Architecture A Quantitative Approach
ISBN: 978-8178672663
5th edition
Authors: John L. Hennessy, David A. Patterson
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