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

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  • Wojciech Połowczuk
  • Piotr Więcek
  • Tadeusz Radzik

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

Suggested Citation

  • Wojciech Połowczuk & Piotr Więcek & Tadeusz Radzik, 2007. "On the existence of almost-pure-strategy Nash equilibrium in n-person finite games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 65(1), pages 141-152, February.
    • Handle: RePEc:spr:mathme:v:65:y:2007:i:1:p:141-152
    DOI: 10.1007/s00186-006-0105-1
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    References listed on IDEAS

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    1. Gomez, E, 1988. "Games with Convex Payoff Function in the First Variable," International Journal of Game Theory, Springer;Game Theory Society, vol. 17(3), pages 201-204.
    2. Radzik, Tadeusz, 1991. "Saddle Point Theorems," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(1), pages 23-32.
    3. Radzik, Tadeusz, 1993. "Nash Equilibria of Discontinuous Non-Zero-Sum Two-Person Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 21(4), pages 429-437.
    4. Tadeusz Radzik, 2000. "Characterization of optimal strategies in matrix games with convexity properties," International Journal of Game Theory, Springer;Game Theory Society, vol. 29(2), pages 211-227.
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    Cited by:

    1. Tadeusz Radzik, 2014. "Poor convexity and Nash equilibria in games," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(1), pages 169-192, February.

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