Stochastic stability in spatial games

TL;DR

This paper explores the long-term behavior of stochastic dynamics in spatial games with multiple Nash equilibria, highlighting how stability depends on the number of players and the type of dynamics involved.

Contribution

It introduces an example of a spatial game with three strategies where stochastic stability varies with player count and dynamics, advancing understanding of equilibrium stability.

Findings

Stochastic stability depends on the number of players.

Stability varies with the type of dynamics used.

An example with three strategies demonstrates these effects.

Abstract

We discuss similarities and differences between systems of interacting players maximizing their individual payoffs and particles minimizing their interaction energy. Long-run behavior of stochastic dynamics of spatial games with multiple Nash equilibria is analyzed. In particular, we construct an example of a spatial game with three strategies, where stochastic stability of Nash equilibria depends on the number of players and the kind of dynamics.