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On computational search for Nash equilibrium in hexamatrix games

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Abstract

The problem of numerical finding of a Nash equilibrium in a 3-player polymatrix game is considered. Such a game can be completely described by six matrices, and it turns out to be equivalent to the solving a nonconvex optimization problem with a bilinear structure in the objective function. Special methods of local and global search for the optimization problem are proposed and investigated. The results of computational solution of the test game are presented and analyzed.

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Acknowledgments

This work is carried out under partial financial support of Russian Foundation for Basic Research (Project No. 13-01-92201-Mong_a). The authors are Grateful to anonymous referees for valuable remarks, which helped to improve the presentation of the paper.

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Authors and Affiliations

  1. Institute for System Dynamics and Control Theory SB RAS, Lermontov str., 134, Irkutsk, 664033, Russia

    Andrei V. Orlov & Alexander S. Strekalovsky

  2. National University of Mongolia, Baga toiruu 4, Sukhbaatar district, Ulaanbaatar, Mongolia

    S. Batbileg

Authors
  1. Andrei V. Orlov
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  2. Alexander S. Strekalovsky
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  3. S. Batbileg
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Correspondence to Andrei V. Orlov.

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Orlov, A.V., Strekalovsky, A.S. & Batbileg, S. On computational search for Nash equilibrium in hexamatrix games. Optim Lett 10, 369–381 (2016). https://doi.org/10.1007/s11590-014-0833-8

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