Deterministic Equations for Stochastic Spatial Evolutionary Games
AbstractSpatial 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.
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Bibliographic InfoPaper provided by Research Institute for Market Economy, Sogang University in its series Working Papers with number 1004.
Length: 44 pages
Date of creation: Apr 2010
Date of revision:
Evolutionary games; mean-field interactions; deterministic approximation; Kac potentials; pattern formation; traveling wave solutions.;
Other versions of this item:
- Hwang, Sung-Ha & Katsoulakis, Markos & Rey-Bellet, Luc, 2013. "Deterministic equations for stochastic spatial evolutionary games," Theoretical Economics, Econometric Society, vol. 8(3), September.
- 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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