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Deterministic equations for stochastic spatial evolutionary games

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Author Info

  • Hwang, Sung-Ha

    ()
    (Department of Mathematics and Statistics, University of Massachusetts at Amherst)

  • Katsoulakis, Markos

    ()
    (Department of Mathematics and Statistics, University of Massachusetts at Amherst)

  • Rey-Bellet, Luc

    ()
    (Department of Mathematics and Statistics, University of Massachusetts at Amherst)

Abstract

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.

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Bibliographic Info

Article provided by Econometric Society in its journal Theoretical Economics.

Volume (Year): 8 (2013)
Issue (Month): 3 (September)
Pages:

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Handle: RePEc:the:publsh:829

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Web page: http://econtheory.org

Related research

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

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  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, December.
  2. 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.
  3. Schelling, Thomas C, 1969. "Models of Segregation," American Economic Review, American Economic Association, vol. 59(2), pages 488-93, May.
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