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A global optimization algorithm for solving a four-person game

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Abstract

The nonzero sum four-person game was considered. We show that the game can be reduced to a global optimization problem by extending Mills’ result (J Soc Ind Appl Math 8(2):397–402, 1960). For solving the problem, we propose a global optimization method that combines the ideas of the classical multistart and an estimation of a convexity degree of the function. The proposed algorithm was tested numerically on some problems created by the well-known generator GAMUT (GAMUT is a Suite of Game Generators. http://gamut.stanford.edu) and allowed us to find solutions to the four-person game.

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Acknowledgements

This work was partially supported by the research Grants P2016-1228 of National University of Mongolia and by the research Grant 15-07-03827 of Russian Foundation for Basic Research. We would like to thank anonymous referees for their valuable comments and suggestions which much improved the earlier version of the paper.

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Authors and Affiliations

  1. National University of Mongolia, Ulaanbaatar, Mongolia

    S. Batbileg & N. Tungalag

  2. Matrosov Institute for Systems Dynamics and Control Theory SB RAS, Irkutsk, Russia

    A. Anikin, A. Gornov & E. Finkelstein

Authors
  1. S. Batbileg
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  2. N. Tungalag
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  3. A. Anikin
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  4. A. Gornov
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  5. E. Finkelstein
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Correspondence to S. Batbileg.

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Batbileg, S., Tungalag, N., Anikin, A. et al. A global optimization algorithm for solving a four-person game. Optim Lett 13, 587–596 (2019). https://doi.org/10.1007/s11590-017-1181-2

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  • DOI: https://doi.org/10.1007/s11590-017-1181-2

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