On the existence of almost-pure-strategy Nash equilibrium in n-person finite games

Wojciech Połowczuk, Piotr Więcek () and Tadeusz Radzik

Mathematical Methods of Operations Research, 2007, vol. 65, issue 1, 152 pages

Abstract: This paper gives wide characterization of n-person non-coalitional games with finite players’ strategy spaces and payoff functions having some concavity or convexity properties. The characterization is done in terms of the existence of two-point-strategy Nash equilibria, that is equilibria consisting only of mixed strategies with supports being one or two-point sets of players’ pure strategy spaces. The structure of such simple equilibria is discussed in different cases. The results obtained in the paper can be seen as a discrete counterpart of Glicksberg’s theorem and other known results about the existence of pure (or “almost pure”) Nash equilibria in continuous concave (convex) games with compact convex spaces of players’ pure strategies. Copyright Springer-Verlag 2007

Keywords: Noncooperative games; Matrix games; Nash equilibrium; Convex payoffs; Two-point strategies (search for similar items in EconPapers)
Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:spr:mathme:v:65:y:2007:i:1:p:141-152

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DOI: 10.1007/s00186-006-0105-1

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