Scandinavian Working Papers in Economics

SSE/EFI Working Paper Series in Economics and Finance,
Stockholm School of Economics

No 641: The Geometry of Nash Equilibria and Correlated Equilibria and a Generalization of Zero-Sum Games

Yannick Viossat ()
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Yannick Viossat: Dept. of Economics, Stockholm School of Economics, Postal: Stockholm School of Economics, P.O. Box 6501, SE-113 83 Stockholm, Sweden

Abstract: A pure strategy is coherent if it is played with positive probability in at least one correlated equilibrium. A game is pre-tight if in every correlated equilibrium, all incentives constraints for non deviating to a coherent strategy are tight. We show that there exists a Nash equilibrium in the relative interior of the correlated equilibrium polytope if and only if the game is pre-tight. Furthermore, the class of pre-tight games is shown to include and generalize the class of two-player zero-sum games.

Keywords: correlated equilibrium; Nash equilibrium; zero-sum games; dual reduction

JEL-codes: C72

32 pages, August 29, 2006

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