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Deterministic Equations for Stochastic Spatial Evolutionary Games

Author

Listed:
  • Sung-Ha Hwang

    (Department of Economics, Sogang University, Seoul)

  • 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.)

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.

Suggested Citation

  • Sung-Ha Hwang & Markos Katsoulakis & Luc Rey-Bellet, 2010. "Deterministic Equations for Stochastic Spatial Evolutionary Games," Working Papers 1004, Nam Duck-Woo Economic Research Institute, Sogang University (Former Research Institute for Market Economy).
    • Handle: RePEc:sgo:wpaper:1004
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    References listed on IDEAS

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    2. Dai Zusai, 2023. "Evolutionary dynamics in heterogeneous populations: a general framework for an arbitrary type distribution," International Journal of Game Theory, Springer;Game Theory Society, vol. 52(4), pages 1215-1260, December.
    3. Sandholm, William H., 2015. "Population Games and Deterministic Evolutionary Dynamics," Handbook of Game Theory with Economic Applications,, Elsevier.
    4. Ozgur Aydogmus & Yun Kang, 2024. "Deterministic Approximation of a Stochastic Imitation Dynamics with Memory," Dynamic Games and Applications, Springer, vol. 14(3), pages 525-548, July.

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    Keywords

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    JEL classification:

    • 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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