A rare mutation model in a spatial heterogeneous environment: the Hawk and Dove game

TL;DR

This paper introduces a stochastic mutation model in a spatially heterogeneous environment affecting evolutionary game dynamics, with a focus on the Hawk-Dove game, highlighting environmental influence on strategy persistence.

Contribution

It develops a new stochastic model incorporating environmental effects and rare mutations, deriving a Fokker-Planck equation and analyzing strategy persistence.

Findings

Environmental heterogeneity influences strategy stability.

Rare mutations can promote low-fitness strategy persistence.

Monte Carlo simulations support theoretical results.

Abstract

We propose a stochastic model in evolutionary game theory where individuals (or subpopulations) can mutate changing their strategies randomly (but rarely) and explore the external environment. This environment affects the selective pressure by modifying the payoff arising from the interactions between strategies. We derive a Fokker-Plank integro-differential equation and provide Monte-Carlo simulations for the Hawks vs Doves game. In particular we show that, in some cases, taking into account the external environment favors the persistence of the low-fitness strategy.