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Games, graphs and Kirchhoff laws

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  • Szabó, György
  • Borsos, István
  • Szombati, Edit

Abstract

Evolutionary potential games represent a set of biological and ecological models equivalent to multiparticle physical systems for a suitable dynamical rule. In these systems the pair interaction is described by a payoff matrix of two-player games possessing a wider class of interactions. Potential games satisfy criteria related to the Kirchhoff laws and have pure Nash equilibria. Using the bi-matrix formalism of game theory we show a simple method for checking the existence of potential which is related to the absence of cyclic components. It will be shown that potential exists if the game is orthogonal to a suitable set of cycling elementary games resembling voluntary matching pennies games. Relationships among these cyclic components and consequences of player’s equivalence are also discussed.

Suggested Citation

  • Szabó, György & Borsos, István & Szombati, Edit, 2019. "Games, graphs and Kirchhoff laws," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 416-423.
    • Handle: RePEc:eee:phsmap:v:521:y:2019:i:c:p:416-423
    DOI: 10.1016/j.physa.2019.01.071
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    References listed on IDEAS

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