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On the Existence of Undominated Nash Equilibria in Normal Form Games

Authors
Journal
Games and Economic Behavior
0899-8256
Publisher
Elsevier
Publication Date
Volume
14
Issue
2
Identifiers
DOI: 10.1006/game.1996.0049

Abstract

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 in R nand (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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