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Effectiveness of Nash Equilibrium Search Algorithms in Four-Person Games in General and Multi-matrix Settings

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Advances in Optimization and Applications (OPTIMA 2020)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1340))

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Abstract

The effectiveness of using the local search algorithm (mountain climbing) and the Lemke–Howson method for searching for Nash equilibrium in 4-person games in general and multi-matrix settings using the Matlab, Python, and FORTRAN software environments are studied. The local search procedure implemented in the Python environment, involving the use of multiplication of a multi-dimensional matrix by a vector, turned out to be an effective tool. The modification of the Lemke–Howson method for multi-matrix formulation showed very good results.

The work was supported by the Russian Foundation for Basic Research (project No. 20-010-00169a).

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References

  1. Batbileg, S., Tungalag, N., Anikin, A., Gornov, A., Finkelstein, E.: A global optimization algorithm for solving a four-person game. Optim. Lett. 13(3), 587–596 (2017). https://doi.org/10.1007/s11590-017-1181-2

    Article  MathSciNet  MATH  Google Scholar 

  2. Enkhbat, R., Bathileg, S., Anikin, A., Tungalag, N., Gornov, A.: A note on four-players triple game. Contrib. Game Theory Manag. 12, 100–112 (2019)

    MathSciNet  MATH  Google Scholar 

  3. Golshtein, E.: A numerical method for solving finite three-person games. Economica i Matematicheskie Metody 50(1), 110–116 (2014). (in Russian)

    Google Scholar 

  4. Golshtein, E., Malkov, U., Sokolov, N.: The Lemke-Howson algorithm solving finite non-cooperative three-person games in a special setting. DEStech Trans. Comput. Sci. Eng. (optim) 265–272 (2018). https://doi.org/10.12783/dtcse/optim2018/27938. (Supplementary volume)

  5. Konno, H.: A cutting plane algorithm for solving bilinear programs. Math. Program. 11(1), 14–27 (1976)

    Article  MathSciNet  Google Scholar 

  6. Lemke, C., Howson, C.: Equilibrium points of bimatrix games. J. Soc. Ind. Appl. Math. 12(2), 413–423 (1964)

    Article  MathSciNet  Google Scholar 

  7. Orlov, A., Strekalovsky, A., Batbileg, S.: On computational search for nash equilibrium in hexamatrix games. Optim. Lett. 10(2), 369–381 (2014)

    Article  MathSciNet  Google Scholar 

  8. Strekalovskii, A.S., Enkhbat, R.: Polymatrix games and optimization problems. Autom. Remote Control 75(4), 632–645 (2014). https://doi.org/10.1134/S0005117914040043

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Central Economics and Mathematics Institute of Russian Academy of Science, Nakhimovsky Prospect 32, 117418, Moscow, Russia

    Ustav Malkov

  2. Dorodnicyn Computing Centre, FRC CSC RAS, Vavilov St. 40, 119333, Moscow, Russia

    Vlasta Malkova

Authors
  1. Ustav Malkov
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  2. Vlasta Malkova
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Corresponding author

Correspondence to Ustav Malkov .

Editor information

Editors and Affiliations

  1. FRC CSC RAS, Moscow, Russia

    Nicholas Olenev

  2. FRC CSC RAS, Moscow, Russia

    Yuri Evtushenko

  3. Krasovsky Institute of Mathematics and Mechanics, Yekaterinburg, Russia

    Michael Khachay

  4. FRC CSC RAS, Moscow, Russia

    Vlasta Malkova

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Malkov, U., Malkova, V. (2020). Effectiveness of Nash Equilibrium Search Algorithms in Four-Person Games in General and Multi-matrix Settings. In: Olenev, N., Evtushenko, Y., Khachay, M., Malkova, V. (eds) Advances in Optimization and Applications. OPTIMA 2020. Communications in Computer and Information Science, vol 1340. Springer, Cham. https://doi.org/10.1007/978-3-030-65739-0_15

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  • DOI: https://doi.org/10.1007/978-3-030-65739-0_15

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-65738-3

  • Online ISBN: 978-3-030-65739-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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