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Num. Meth. Prog., 2007, Volume 8, Issue 3, Pages 233–243 (Mi vmp489)  

This article is cited in 1 scientific paper (total in 1 paper)

Вычислительные методы и приложения

A parallel search of equilibrium points in bimatrix games

I. L. Vasiliev, K. B. Klimentova, A. V. Orlov

Matrosov Institute for System Dynamics and Control Theory of Siberian Branch of Russian Academy of Sciences, Irkutsk

Abstract: The paper is focused on a search for the Nash equilibrium in bimatrix games. In order to solve this problem, we apply the so-called variational approach based on the equivalence theorem of bimatrix games and on a special bilinear programming problem. This bilinear problem is solved using the global search theory. We use the ILOG CIPLEX package to solve auxiliary linear programming problems arising at various stages of the global search algorithm. In addition, a parallel version of this algorithm has been developed. Both the parallel and sequential algorithms have been extensively tested. Our numerical results confirm the efficiency of the implemented parallel version of the algorithm.

Keywords: bimatrix games, Nash equilibrium, local search, global search, parallel computing, mathematical programming.

Full text: PDF file (228 kB)
UDC: 519.853.4, 519.833.3

Citation: I. L. Vasiliev, K. B. Klimentova, A. V. Orlov, “A parallel search of equilibrium points in bimatrix games”, Num. Meth. Prog., 8:3 (2007), 233–243

Citation in format AMSBIB
\Bibitem{VasKliOrl07}
\by I.~L.~Vasiliev, K.~B.~Klimentova, A.~V.~Orlov
\paper A parallel search of equilibrium points in bimatrix games
\jour Num. Meth. Prog.
\yr 2007
\vol 8
\issue 3
\pages 233--243
\mathnet{http://mi.mathnet.ru/vmp489}


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    This publication is cited in the following articles:
    1. A. S. Strekalovskii, R. Enkhbat, “Polymatrix games and optimization problems”, Autom. Remote Control, 75:4 (2014), 632–645  mathnet  crossref  isi
  • Numerical methods and programming
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