Geodesic
A computational method for solving $N$-person game
The Bulletin of Irkutsk State University. Series Mathematics, Tome 20 (2017), pp. 109-121 Cet article a éte moissonné depuis la source Math-Net.Ru

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The nonzero sum $n$-person game has been considered. It is well known that the game can be reduced to a global optimization problem [5; 7; 14]. By extending Mills' result [5], we derive global optimality conditions for a Nash equilibrium. In order to solve the problem numerically, we apply the Curvilinear Multistart Algorithm [2; 3] developed for finding global solutions in nonconvex optimization problems. The proposed algorithm was tested on three and four person games. Also, for the test purpose, we have considered competitions of 3 companies at the bread market of Ulaanbaatar as the three person game and solved numerically.
Keywords: Nash equilibrium, mixed strategies, curvilinear multistart algorithm.
Mots-clés : nonzero sum game 
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R. Enkhbat; S. Batbileg; N. Tungalag; Anton Anikin; Alexander Gornov. A computational method for solving $N$-person game. The Bulletin of Irkutsk State University. Series Mathematics, Tome 20 (2017), pp. 109-121. http://geodesic.mathdoc.fr/item/IIGUM_2017_20_a7/

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