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Deterministic Equations for Stochastic Spatial Evolutionary Games


  • 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.)


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, Research Institute for Market Economy, Sogang University.
  • Handle: RePEc:sgo:wpaper:1004

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    References listed on IDEAS

    1. John C. Harsanyi & Reinhard Selten, 1988. "A General Theory of Equilibrium Selection in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582384, January.
    2. Bergin, James & Bernhardt, Dan, 2009. "Cooperation through imitation," Games and Economic Behavior, Elsevier, vol. 67(2), pages 376-388, November.
    3. H. Peyton Young & Mary A. Burke, 2001. "Competition and Custom in Economic Contracts: A Case Study of Illinois Agriculture," American Economic Review, American Economic Association, vol. 91(3), pages 559-573, June.
    4. Schelling, Thomas C, 1969. "Models of Segregation," American Economic Review, American Economic Association, vol. 59(2), pages 488-493, May.
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    Cited by:

    1. Sandholm, William H., 2015. "Population Games and Deterministic Evolutionary Dynamics," Handbook of Game Theory with Economic Applications, Elsevier.

    More about this item


    Evolutionary games; mean-field interactions; deterministic approximation; Kac potentials; pattern formation; traveling wave solutions.;

    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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