Geodesic
A parallel search of equilibrium points in bimatrix games
Numerical methods and programming, Tome 8 (2007) no. 3, pp. 233-243

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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.
Mots-clés : bimatrix games
Keywords: Nash equilibrium, local search, global search, parallel computing, mathematical programming. 
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     author = {I. L. Vasiliev and K. B. Klimentova and A. V. Orlov},
     title = {A parallel search of equilibrium points in bimatrix games},
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     pages = {233--243},
     publisher = {mathdoc},
     volume = {8},
     number = {3},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2007_8_3_a2/}
}
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I. L. Vasiliev; K. B. Klimentova; A. V. Orlov. A parallel search of equilibrium points in bimatrix games. Numerical methods and programming, Tome 8 (2007) no. 3, pp. 233-243. http://geodesic.mathdoc.fr/item/VMP_2007_8_3_a2/