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Deterministic Equations for Stochastic Spatial Evolutionary Games

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Author Info

  • 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.

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File URL: ftp://163.239.165.41/RePEc/sgo/wpaper/HSH_RIME_2010-04.pdf
File Function: First version, 2010
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Bibliographic Info

Paper provided by Research Institute for Market Economy, Sogang University in its series Working Papers with number 1004.

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Length: 44 pages
Date of creation: Apr 2010
Date of revision:
Handle: RePEc:sgo:wpaper:1004

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Related research

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

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  1. 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.
  2. Schelling, Thomas C, 1969. "Models of Segregation," American Economic Review, American Economic Association, vol. 59(2), pages 488-93, May.
  3. 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.
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