Statistical mechanics of spatial evolutionary games

TL;DR

This paper applies statistical mechanics methods to analyze the long-term behavior and stability of spatial evolutionary games, focusing on the effects of player number and noise, and comparing payoff-maximizing systems to energy-minimizing particles.

Contribution

It introduces a statistical mechanics framework to study spatial evolutionary games, especially potential games, and examines the thermodynamic limit for these models.

Findings

Stochastic stability depends on player number and noise level.

Potential games exhibit thermodynamic limit behavior similar to interacting particle systems.

Insights into the differences between payoff-maximizing and energy-minimizing systems.

Abstract

We discuss the long-run behavior of stochastic dynamics of many interacting players in spatial evolutionary games. In particular, we investigate the effect of the number of players and the noise level on the stochastic stability of Nash equilibria. We discuss similarities and differences between systems of interacting players maximizing their individual payoffs and particles minimizing their interaction energy. We use concepts and techniques of statistical mechanics to study game-theoretic models. In order to obtain results in the case of the so-called potential games, we analyze the thermodynamic limit of the appropriate models of interacting particles.