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On the existence of pure strategy Nash equilibria in two person discrete games


  • Mallick, Indrajit


We construct a generalized two-person discrete strategy static game of complete information where continuity, convexity and compactness cannot be invoked to show the existence of pure strategy Nash equilibrium. We show that, when best responses are unique from both sides, a condition of Minimal Acyclicity is necessary and sufficient for the existence of pure strategy Nash equilibria.

Suggested Citation

  • Mallick, Indrajit, 2011. "On the existence of pure strategy Nash equilibria in two person discrete games," Economics Letters, Elsevier, vol. 111(2), pages 144-146, May.
  • Handle: RePEc:eee:ecolet:v:111:y:2011:i:2:p:144-146

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    References listed on IDEAS

    1. Khan, M. Ali & Yeneng, Sun, 1995. "Pure strategies in games with private information," Journal of Mathematical Economics, Elsevier, vol. 24(7), pages 633-653.
    2. 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.
    3. Partha Dasgupta & Eric Maskin, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, I: Theory," Review of Economic Studies, Oxford University Press, vol. 53(1), pages 1-26.
    4. Guilherme Carmona, 2004. "On the Existence of Pure Strategy Nash Equilibria in Large Games," Game Theory and Information 0412008, EconWPA.
    5. Philip J. Reny, 1999. "On the Existence of Pure and Mixed Strategy Nash Equilibria in Discontinuous Games," Econometrica, Econometric Society, vol. 67(5), pages 1029-1056, September.
    6. Lu, Haishu, 2007. "On the existence of pure-strategy Nash equilibrium," Economics Letters, Elsevier, vol. 94(3), pages 459-462, March.
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    Cited by:

    1. repec:spr:annopr:v:249:y:2017:i:1:d:10.1007_s10479-014-1700-9 is not listed on IDEAS
    2. Wang, Hua & Meng, Qiang & Zhang, Xiaoning, 2014. "Game-theoretical models for competition analysis in a new emerging liner container shipping market," Transportation Research Part B: Methodological, Elsevier, vol. 70(C), pages 201-227.


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