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Deterministic Equations for Stochastic Spatial Evolutionary Games (1007.0723v1)

Published 5 Jul 2010 in math.PR, nlin.PS, and q-bio.PE

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.

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