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CORR
2010
Springer

A new proof of Nash's Theorem via exchangeable equilibria

8 years 3 months ago
A new proof of Nash's Theorem via exchangeable equilibria
We give a novel proof of the existence of Nash equilibria in all finite games without using fixed point theorems or path following arguments. Our approach relies on a new notion intermediate between Nash and correlated equilibria called exchangeable equilibria, which are correlated equilibria with certain symmetry and factorization properties. We prove these exist by a duality argument, using Hart and Schmeidler's proof of correlated equilibrium existence as a first step. In an appropriate limit exchangeable equilibria converge to the convex hull of Nash equilibria, proving that these exist as well. Exchangeable equilibria are defined in terms of symmetries of the game, so this method automatically proves the stronger statement that a symmetric game has a symmetric Nash equilibrium. The case without symmetries follows by a symmetrization argument.
Noah D. Stein, Pablo A. Parrilo, Asuman E. Ozdagla
Added 09 Dec 2010
Updated 09 Dec 2010
Type Journal
Year 2010
Where CORR
Authors Noah D. Stein, Pablo A. Parrilo, Asuman E. Ozdaglar
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