Theoretical Economics, Volume 8, Number 3 (October 2013)

Theoretical Economics 8 (2013), 829–874

Deterministic equations for stochastic spatial evolutionary games

Sung-Ha Hwang, Markos Katsoulakis, Luc Rey-Bellet


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.

Keywords: Evolutionary games, mean-field interactions, deterministic approximation, Kac potentials, pattern formation, traveling wave solutions

JEL classification: C70, C72, C73

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