Spatial effect on stochastic dynamics of bistable evolutionary games

TL;DR

This paper investigates how spatial structure influences the stability and transition times of metastable states in bistable evolutionary games using a semiclassical path integral approach.

Contribution

It introduces a semiclassical approximation method to evaluate metastable state lifetimes considering spatial effects in evolutionary game dynamics.

Findings

Spatial structure accelerates transitions between metastable states.

Lifetimes depend differently on population size with and without spatial structure.

Spatial effects qualitatively change the stability landscape of the system.

Abstract

We consider the lifetimes of metastable states in bistable evolutionary games (coordination games), and examine how they are affected by spatial structure. A semiclassical approximation based on a path integral method is applied to stochastic evolutionary game dynamics with and without spatial structure, and the lifetimes of the metastable states are evaluated. It is shown that the population dependence of the lifetimes is qualitatively different in these two models. Our result indicates that spatial structure can accelerate the transitions between metastable states.