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On the Probability of Existence of Pure Equilibria in Matrix Games

Author

Listed:
  • S. Mishra

    (Centre for Development Studies)

  • T. K. Kumar

    (Indian Statistical Institute)

Abstract

In a recent paper (Ref. 1), Papavassilopoulos obtained results on the probability of the existence of pure equilibrium solutions in stochastic matrix games. We report a similar result, but where the payoffs are drawn from a finite set of numbers N. In the limiting case, as N tends to infinity, our result and that of Papavassilopoulos are identical. We also cite similar results obtained independently by others, some of which were already independently brought to the notice of Papavassilopoulos by Li Calzi as reported in Papavassilopoulos (Ref. 2). We cite a much earlier result obtained by Goldman (Ref. 3). We also cite our related work (Ref. 4), in which we derive the conditions for the existence of mixed strategy equilibria in two-person zero-sum games.

Suggested Citation

  • S. Mishra & T. K. Kumar, 1997. "On the Probability of Existence of Pure Equilibria in Matrix Games," Journal of Optimization Theory and Applications, Springer, vol. 94(3), pages 765-770, September.
    • Handle: RePEc:spr:joptap:v:94:y:1997:i:3:d:10.1023_a:1022669504795
    DOI: 10.1023/A:1022669504795
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    References listed on IDEAS

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    1. Powers, Imelda Yeung, 1990. "Limiting Distributions of the Number of Pure Strategy Nash Equilibria in N-Person Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 19(3), pages 277-286.
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    Cited by:

    1. J. M. Peterson & M. A. Simaan, 2008. "Probabilities of Pure Nash Equilibria in Matrix Games when the Payoff Entries of One Player Are Randomly Selected," Journal of Optimization Theory and Applications, Springer, vol. 137(2), pages 401-410, May.

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