2010/07/05 by Sung‐Ha Hwang, Markos A. Katsoulakis, Hwang, Sung-Ha +3
Social Sciences · Biochemistry, Genetics and Molecular Biology · Medicine · #Evolutionary Game Theory and Cooperation #Evolution and Genetic Dynamics #Mathematical and Theoretical Epidemiology and Ecology Models
paper · doi:10.48550/arxiv.1007.0723
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.