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General features of Nash equilibria in combinations of elementary interactions in symmetric two-person games

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  • György Szabó

    (Institute for Technical Physics and Material Sciences, Centre for Energy Research)

  • Balázs Király

    (Institute for Technical Physics and Material Sciences, Centre for Energy Research)

Abstract

Two-person games are used in many multi-agent mathematical models to describe pair interactions. The type (pure or mixed) and the number of Nash equilibria affect fundamentally the macroscopic behavior of these systems. In this paper, the general features of Nash equilibria are investigated systematically within the framework of matrix decomposition for n strategies. This approach distinguishes four types of elementary interactions that each possess fundamentally different characteristics. The possible Nash equilibria are discussed separately for different types of interactions and also for their combinations. A relation is established between the existence of infinitely many mixed Nash equilibria and the zero-eigenvalue eigenvectors of the payoff matrix.

Suggested Citation

  • György Szabó & Balázs Király, 2021. "General features of Nash equilibria in combinations of elementary interactions in symmetric two-person games," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 94(5), pages 1-9, May.
    • Handle: RePEc:spr:eurphb:v:94:y:2021:i:5:d:10.1140_epjb_s10051-021-00112-z
    DOI: 10.1140/epjb/s10051-021-00112-z
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    References listed on IDEAS

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    1. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, April.
    2. Giacomo Bonanno, 2015. "Game Theory: Parts I and II. Open access book," Working Papers 124, University of California, Davis, Department of Economics.
    3. Giacomo Bonanno, 2015. "Game Theory: Parts I and II. Open access book," Working Papers 152, University of California, Davis, Department of Economics.
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