Deterministic Equations for Stochastic Spatial Evolutionary Games

Sung-Ha Hwang, Markos Katsoulakis () and Luc Rey-Bellet ()
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Markos Katsoulakis: Department of Mathematics and Statistics, University of Massachusetts, U.S.A. Department of Applied Mathematics, University of Crete and Foundation of Research and Technology-Hellas, Greece
Luc Rey-Bellet: Department of Mathematics and Statistics, University of Massachusetts, U.S.A.

No 1004, Working Papers from Nam Duck-Woo Economic Research Institute, Sogang University (Former Research Institute for Market Economy)

Abstract: Spatial evolutionary games model individuals who are distributed in a spa- tial domain and update their strategies upon playing a normal form game with their neighbors. We derive integro-differential equations as deterministic ap- proximations 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 determin- istic 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. (search for similar items in EconPapers)
Pages: 44 pages
Date: 2010-04
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https://econ.sogang.ac.kr/front/cmsboardview.do?cu ... eId=econ&pkid=893103 First version, 2010 (application/pdf)

Related works:
Journal Article: Deterministic equations for stochastic spatial evolutionary games (2013)
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Persistent link: https://EconPapers.repec.org/RePEc:sgo:wpaper:1004

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