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 The Bulletin of Irkutsk State University. Series Mathematics: Year: Volume: Issue: Page: Find

 The Bulletin of Irkutsk State University. Series Mathematics, 2015, Volume 11, Pages 80–95 (Mi iigum219)

Oligopolistic banking sector of Mongolia and polymatrix games of three players

A. V. Orlova, S. Batbilegb

a Matrosov Institute for System Dynamics and Control Theory of the Siberian Branch of Russian Academy of Sciences, 134, Lermontov st., Irkutsk, 664033
b National University of Mongolia, Baga toiruu 4, Sukhbaatar district, Ulaanbaatar, 14200

Abstract: A problem of competition between the three largest banks of the Mongolia major crediting sector is investigated. Modeling of the conflict is carried out using the apparatus of three person polymatrix games (hexamatrix games). To find a Nash equilibrium in the constructed game we use an approach based on its reduction to a non-convex optimization problem with bilinear structure in the objective function. To solve the latter problem we apply Global Search Theory due to A. S. Strekalovsky. According to the theory, local and global search algorithms for formulated game are developed. Local search method is based on the idea of sequential solving of auxiliary linear programming problems followed from the formulation of the problem. Global search based on a specific Global Search Strategy in the d.c. maximization problems as the objective function of the reduced optimization problem can be represented as a difference of two convex functions. The results of a computational simulation is presented and analized.

Keywords: oligopoly, polymatrix game of three players, Nash equilibrium, nonconvex optimization problems, computational simulation.

Full text: PDF file (275 kB)
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UDC: 519.853.4
MSC: 90C26

Citation: A. V. Orlov, S. Batbileg, “Oligopolistic banking sector of Mongolia and polymatrix games of three players”, The Bulletin of Irkutsk State University. Series Mathematics, 11 (2015), 80–95

Citation in format AMSBIB
\Bibitem{OrlBat15} \by A.~V.~Orlov, S.~Batbileg \paper Oligopolistic banking sector of Mongolia and polymatrix games of three players \jour The Bulletin of Irkutsk State University. Series Mathematics \yr 2015 \vol 11 \pages 80--95 \mathnet{http://mi.mathnet.ru/iigum219}