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Nash Equilibria in Pure Strategies

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  • Abderrahmane Ziad

Abstract

We consider an n‐person non‐zero‐sum non‐cooperative game in normal form, where the strategy sets are some closed intervals of the real line. It is shown that if the pay‐off functions are continuous on the whole space and if for each pay‐off function the smallest local maximum in the strategy variable is a global maximum, then the game possesses a pure strategy Nash equilibrium.

Suggested Citation

  • Abderrahmane Ziad, 2003. "Nash Equilibria in Pure Strategies," Bulletin of Economic Research, Wiley Blackwell, vol. 55(3), pages 311-317, July.
    • Handle: RePEc:bla:buecrs:v:55:y:2003:i:3:p:311-317
    DOI: 10.1111/1467-8586.00178
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    1. Partha Dasgupta & Eric Maskin, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, I: Theory," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(1), pages 1-26.
    2. Partha Dasgupta & Eric Maskin, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, II: Applications," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(1), pages 27-41.
    3. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321.
    4. Ziad, Abderrahmane, 1999. "Pure strategy Nash equilibria of non-zero-sum two-person games: non-convex case," Economics Letters, Elsevier, vol. 62(3), pages 307-310, March.
    5. Ziad, Abderrahmane, 1997. "Pure-Strategy [epsiv]-Nash Equilibrium inn-Person Nonzero-Sum Discontinuous Games," Games and Economic Behavior, Elsevier, vol. 20(2), pages 238-249, August.
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