Games, graphs and Kirchhoff laws

Szabó, György and Borsos, István and Szombati, Edit (2019) Games, graphs and Kirchhoff laws. PHYSICA A - STATISTICAL MECHANICS AND ITS APPLICATIONS, 521. pp. 416-423. ISSN 0378-4371

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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.

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