Rentsen Enkhbat, Sukhee Batbileg, Anton Anikin, Natsagdorj Tungalag, Alexander Gornov, “A note on four-players triple game”, Contributions to Game Theory and Management, 2019, Volume 12,Pages <nobr>100

A note on four-players triple game

Rentsen Enkhbat^a, Sukhee Batbileg^b, Anton Anikin^c, Natsagdorj Tungalag^a, Alexander Gornov^c

^a National University of Mongolia, School of Business, Ikh toiruu-4, Ulaanbaatar, Mongolia
^b National University of Mongolia, School of Engineering and Applied Sciences, Ikh Surguuliin-1 P.O.BOX-46A/523, 14201, Ulaanbaatar, Mongolia
^c Matrosov Institute for System Dynamics and Control, Theory of Siberian Branch of Russian Academy of Sciences, Russia, 664033, Irkutsk, Lermontova st., 134

Abstract: We introduce so-called four-players triple game and define Nash equilibrium. The problem of numerical finding of a Nash equilibrium in a four-players triple game has been examined. Such a game can be completely described by twelve matrices, and it turns out to be equivalent to the solving a nonconvex optimization problem. Special methods of local and global search for the optimization problem are proposed. The proposed algorithm was implemented on test problems by "GAMUT" (http://gamut.stanford.edu).

Keywords: nonconvex optimization, four-players triple game, local and global search algorithm, Nash equilibrium.

Language: English