Geodesic
A note on four-players triple game
Contributions to game theory and management, Tome 12 (2019), pp. 100-112.

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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. 
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Rentsen Enkhbat; Sukhee Batbileg; Anton Anikin; Natsagdorj Tungalag; Alexander Gornov. A note on four-players triple game. Contributions to game theory and management, Tome 12 (2019), pp. 100-112. http://geodesic.mathdoc.fr/item/CGTM_2019_12_a4/

[1] Strekalovsky A. S., Enkhbat R., “Polymatrix games and optimization problems”, Automation and Remote Control, 75:4 (2014), 632–645 | DOI | MR

[2] Orlov A. V., Strekalovsky A. S., Batbileg S., “On computational search for Nash equilibrium in hexamatrix games”, Optimization Letters, 10:2 (2014), 369–381 | DOI | MR

[3] Gornov A., Zarodnyuk T., “Computing technology for estimation of convexity degree of the multiextremal function”, Machine learning and data analysis, 10:1 (2014), 1345–1353

[4] Yanovskaya E. B., “Equilibrium points in polymatrix games”, Latv. Math. Collect., 8 (1968), 381–384 (in Russian)

[5] Enkhbat R., Batbileg S., Gornov A., Anikin A., Tungalag N., “A Computational Method for Solving N-Person Game”, IIGU Ser. Matematika, 20 (2017), 109–121 | MR | Zbl

[6] Strekalovsky A. S., “Global Optimality Conditions for Nonconvex Optimization”, Journal of Global Optimization, 12 (1998), 415–434 | DOI | MR | Zbl

[7] Enkhbat R., Tungalag N., Gornov A., Anikin A., “The Curvilinear Search Algorithm for Solving Three-Person Game”, DOOR 2016, CEUR Workshop Proceedings, 1623, 2016, 574–583 http://ceur-ws.org/Vol-1623/paperme4.pdf

[8] Gornov A., Zarodnyuk T., “Computing technology for estimation of convexity degree of the multiextremal function”, Machine learning and data analysis, 10:1 (2014), 1345–1353 http://jmlda.org

[9] Mangasarian O. L., Stone H., “Two-Person Nonzero Games and Quadratic Programming”, J. Mathemat. Anal. Appl., 9 (1964), 348–355 | DOI | MR | Zbl

[10] Mills H., “Equilibrium Points in Finite Games”, J. Soc. Indust. Appl. Mathemat., 8:2 (1960), 397–402 | DOI | MR | Zbl

[11] Von Neumann J., Morgenstern O., Theory of games and economic, 1944 | MR | Zbl

[12] Melvin Dresher, The Mathematics of Games of Strategy, Dover Publications, 1981 | MR | Zbl

[13] Vorobyev N. N., Noncooperative games, Nauka, 1984 | MR

[14] Germeyer Yu. B., Introduction to Operation Reseach, Nauka, 1976

[15] Strekalovsky A. S., Orlov A. V., Bimatrix Game and Bilinear Programming, Nauka, 2007

[16] Owen, G., Game Theory, Saunders, Philadelphia, 1971 | MR

[17] Gibbons R., Game Theory for Applied Economists, Princeton University Press, 1992

[18] Horst R., Tuy H., Global Optimization, Springer-Verlag, 1993 | MR | Zbl

[19] Howson J. T., “Equilibria of Polymatrix Games”, Management Sci, 18 (1972), 312–318 | DOI | MR | Zbl

[20] GAMUT is a site of game generators, http://gamut.stanford.edu

[21] DATA, https://www.dropbox.com/sh/sd84lbisy5vtifn/AAB2PNVWONtK56egStv8c-Vea?dl=0