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Potts game on graphs: static equilibria

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  • Andrey Leonidov

    (P.N. Lebedev Physical Institute
    Moscow Institute of Physics and Technology)

Abstract

Static equilibria in noisy multinomial Q-nary choice (Potts) games on graphs are considered. Equations defining expectation (quantal response) equilibria for arbitrary noise distribution and topology of the underlying graph are written. A detailed analysis of Potts game for complete and random graphs is presented. One-parameter solution reflecting restructuring of solution space is analyzed. It is shown that for the Potts game on the complete graph and Gumbel noise this Ansatz leads to the same equilibrium-defining equation as one of the two equilibrium defining equations in the Potts model in statistical physics. A difference in properties of the mean field Potts model and equilibria in the Potts game on complete graphs is commented upon. The equations defining Potts game equilibria for random graphs for the special case of configuration model in the annealed approximation are derived. A one-parameter solution analogous to that in the Potts game on complete graphs is constructed and the corresponding equation for the case of Gumbel noise is derived.

Suggested Citation

  • Andrey Leonidov, 2024. "Potts game on graphs: static equilibria," Computational Management Science, Springer, vol. 21(1), pages 1-10, June.
    • Handle: RePEc:spr:comgts:v:21:y:2024:i:1:d:10.1007_s10287-023-00490-y
    DOI: 10.1007/s10287-023-00490-y
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