Deterministic equations for stochastic spatial evolutionary games
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 gener...
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| Veröffentlicht in: | Theoretical economics 2013-09, Vol.8 (3), p.829-874 |
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| container_end_page | 874 |
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| container_title | Theoretical economics |
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| creator | Hwang, Sung-Ha Katsoulakis, Markos Rey-Bellet, Luc |
| description | 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. |
| doi_str_mv | 10.3982/TE829 |
| format | Article |
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| subjects | C70 C72 C73 deterministic approximation Economic theory equilibrium selection Evolutionary games Games Kac potentials long‐range interactions mean-field interactions Ordinary differential equations pattern formation Spatial evolutionary games Stochastic models Stochastic processes Studies traveling front solutions traveling wave solutions |
| title | Deterministic equations for stochastic spatial evolutionary games |
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