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This article is cited in 4 scientific papers (total in 4 papers)
A computational method for solving $N$-person game
R. Enkhbata, S. Batbilega, N. Tungalagb, Anton Anikinc, Alexander Gornovc a Institute of Mathematics, National University of Mongolia
b The school of business, National University of Mongolia
c Matrosov Institute for System Dynamics and Control Theory, SB of RAS
Abstract:
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, nonzero sum game, mixed strategies, curvilinear multistart algorithm.
Citation:
R. Enkhbat, S. Batbileg, N. Tungalag, Anton Anikin, Alexander Gornov, “A computational method for solving $N$-person game”, Bulletin of Irkutsk State University. Series Mathematics, 20 (2017), 109–121
Linking options:
https://www.mathnet.ru/eng/iigum308 https://www.mathnet.ru/eng/iigum/v20/p109
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Abstract page: | 258 | Full-text PDF : | 114 | References: | 34 |
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