Deterministic Equations for Stochastic Spatial Evolutionary Games
Probability
2010-07-06 v1 Pattern Formation and Solitons
Populations and Evolution
Abstract
Spatial evolutionary games model individuals who are distributed in a spatial domain and update their strategies upon playing a normal form game with their neighbors. We derive integro-differential equations as deterministic approximations of the microscopic updating stochastic processes. This generalizes the known mean-field ordinary differential equations and provide a powerful tool to investigate the spatial effects in populations evolution. The deterministic equations allow to identify many interesting features of the evolution of strategy profiles in a population, such as standing and traveling waves, and pattern formation, especially in replicator-type evolutions.
Cite
@article{arxiv.1007.0723,
title = {Deterministic Equations for Stochastic Spatial Evolutionary Games},
author = {Sung-Ha Hwang and Markos Katsoulakis and Luc Rey-Bellet},
journal= {arXiv preprint arXiv:1007.0723},
year = {2010}
}