Deterministic equations for stochastic spatial evolutionary games

Abstract

Spatial evolutionary games model individuals playing a game with their neighbors in a spatial domain and describe the time evolution of the strategy profile of individuals over space. We derive integro-differential equations as deterministic approximations of strategy revision stochastic processes. These equations generalize the existing ordinary differential equations such as replicator dynamics and provide powerful tools for investigating the problem of equilibrium selection. Deterministic equations allow the identification of many interesting features of the evolution of a population's strategy profiles, including traveling front solutions and pattern formation.