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On the Existence of Undominated Nash Equilibria in Normal Form Games
Authors:Hannu Salonen
Institution:Department of Economics, University of Oulu, Linnanmaa, Oulu, Finland, 90570
Abstract:In this paper the existence problem of undominated Nash equilibrium in normal form games is analyzed. It is shown that an undominated Nash equilibrium exists, if (a) strategy sets are convex polytopes inRnand (b) utility functions are affine with respect to each player's own strategy. It is shown by counterexamples that, first, it is not sufficient to have concave utility functions instead of affine under condition (b) even when condition (a) is satisfied, and, second, it is not sufficient to have just compact and convex strategy sets instead of polytopes in condition (a) even when condition (b) is satisfied.
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