Deterministic equations for stochastic spatial evolutionary games
AbstractSpatial 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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Bibliographic InfoArticle provided by Econometric Society in its journal Theoretical Economics.
Volume (Year): 8 (2013)
Issue (Month): 3 (September)
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Web page: http://econtheory.org
Evolutionary games; mean-field interactions; deterministic approximation; Kac potentials; pattern formation; traveling wave solutions;
Other versions of this item:
- Sung-Ha Hwang & Markos Katsoulakis & Luc Rey-Bellet, 2010. "Deterministic Equations for Stochastic Spatial Evolutionary Games," Working Papers 1004, Research Institute for Market Economy, Sogang University.
- C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
- C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
- C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
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