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Presenting an algorithm to find Nash equilibrium in two-person static games with many strategies

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  • Mohtadi, Mohammad Mahdi
  • Nogondarian, Kazem

Abstract

This article attempts to present an algorithm to find Nash equilibrium point in large two-person static games. In static games, each player chooses his/her strategy simultaneously with other players. Equilibrium can be easily recognized in static games with a limited number of strategies. This paper focuses on two-person games in which each player deals with many strategies. After reviewing the literature, this article considers concepts such as game, equilibrium, and rationalism in order to identify the problem and the required methodology to solve it; eventually, a heuristic-meta heuristic algorithm will be presented to solve such problems which have been validated using a sample problem.

Suggested Citation

  • Mohtadi, Mohammad Mahdi & Nogondarian, Kazem, 2015. "Presenting an algorithm to find Nash equilibrium in two-person static games with many strategies," Applied Mathematics and Computation, Elsevier, vol. 251(C), pages 442-452.
    • Handle: RePEc:eee:apmaco:v:251:y:2015:i:c:p:442-452
    DOI: 10.1016/j.amc.2014.11.039
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    References listed on IDEAS

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    1. Reny, Philip J. & Robson, Arthur J., 2004. "Reinterpreting mixed strategy equilibria: a unification of the classical and Bayesian views," Games and Economic Behavior, Elsevier, vol. 48(2), pages 355-384, August.
    2. von Stengel, Bernhard, 1996. "Efficient Computation of Behavior Strategies," Games and Economic Behavior, Elsevier, vol. 14(2), pages 220-246, June.
    3. Porter, Ryan & Nudelman, Eugene & Shoham, Yoav, 2008. "Simple search methods for finding a Nash equilibrium," Games and Economic Behavior, Elsevier, vol. 63(2), pages 642-662, July.
    4. Benoît Colson & Patrice Marcotte & Gilles Savard, 2007. "An overview of bilevel optimization," Annals of Operations Research, Springer, vol. 153(1), pages 235-256, September.
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