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Abstract: Spatial evolutionary games model individuals who are distributed in a spatialdomain and update their strategies upon playing a normal form game with theirneighbors. We derive integro-differential equations as deterministicapproximations of the microscopic updating stochastic processes. Thisgeneralizes the known mean-field ordinary differential equations and provide apowerful tool to investigate the spatial effects in populations evolution. Thedeterministic equations allow to identify many interesting features of theevolution of strategy profiles in a population, such as standing and travelingwaves, and pattern formation, especially in replicator-type evolutions.



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

Source: https://arxiv.org/







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