Physics

Biography

Biography: György Szabó

Abstract

In evolutionary games players are located on the sites of a network and the interactions among the connected players are described by matrix games when the players choose one of their n options by following a dynamical rule. These players can represent atoms in physical systems, species in ecological models, or different behaviors in human societies. The systematic analysis of  the matrix games threw light on the decomposition of matrices into four classes of elementary interactions.  The symmetric part of elementary games with self- and cross-dependent payoffs represents interactions resembling an external effect without real player-player interactions, while the antisymmetric part is responsible for the emergence of social dilemmas causing serious troubles in human societies and biological systems. The effects of coordinations between the possible strategy pairs are similar to those studied by differents versions of the Ising, Potts, and  Ashkin-Teller models. The tools and results of statistical physics can be adopted for the investigation of potential games which are composed of the latter three elementary interactions and evolve into the Boltzmann distribution if a logit rule controls the evolution. The fourth type of interactions represents cyclic dominance and can be built up from rock-paper-scissors type elementary games.  The presence of cyclic components prevents thermodynamical behavior and results in self-organizing strategy distributions characteristic to living systems.