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A global optimization approach to nonzero sum six-person game

Авторы: Enkhbat R., Batbileg S., Tungalag N., Anikin A., Gornov A.

Журнал: Annals of the International Society of Dynamic Games

Том: 16

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Год: 2020

Отчётный год: 2020

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Аннотация: The nonzero sum six-person game has been examined. It is well known that nonzero sum n-person game reduces to a nonconvex optimization problem (Enkhbat et al, IGU Ser Mat 20:109121, 2017). Based on Mills’ result (Mills, J Soc Ind Appl Math 8(2):397–402, 1960), we derive a sufficient condition for a Nash equilibrium. To find a Nash equilibrium numerically, we apply the curvilinear multistart algorithm (Gornov and Zarodnyuk, Mach Learn Data Anal 10(1):1345–1353, 2014) developed for nonconvex optimization. The algorithm was tested numerically on six-person game. The game data was generated by “Gamut” (website: http://gamut.stanford.edu/db/generators.html). The number of variables of the reduced optimization problems was varied from 29 to 33. In all cases, Nash equilibriums were found.

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