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Evolutionary Games and Periodic Fitness

Author

Listed:
  • Philippe Uyttendaele
  • Frank Thuijsman

  • Pieter Collins
  • Ralf Peeters
  • Gijs Schoenmakers
  • Ronald Westra

Abstract

One thing that nearly all stability concepts in evolutionary game theory have in common is that they use a time-independent fitness matrix. Although this is a reasonable assumption for mathematical purposes, in many situations in real life it seems to be too restrictive. We present a model of an evolutionary game, driven by replicator dynamics, where the fitness matrix is a variable rather than a constant, i.e., the fitness matrix is time-dependent. In particular, by considering periodically changing fitness matrices, we model seasonal effects in evolutionary games. We discuss a model with a continuously changing fitness matrix as well as a related model in which the changes occur periodically at discrete points in time. A numerical analysis shows stability of the periodic orbits that are observed. Moreover, trajectories leading to these orbits from arbitrary starting points synchronize their motion in time. Several examples are discussed. Copyright The Author(s) 2012

Suggested Citation

  • Philippe Uyttendaele & Frank Thuijsman & Pieter Collins & Ralf Peeters & Gijs Schoenmakers & Ronald Westra, 2012. "Evolutionary Games and Periodic Fitness," Dynamic Games and Applications, Springer, vol. 2(3), pages 335-345, September.
    • Handle: RePEc:spr:dyngam:v:2:y:2012:i:3:p:335-345
    DOI: 10.1007/s13235-012-0048-5
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    References listed on IDEAS

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    1. Gilboa, Itzhak & Matsui, Akihiko, 1991. "Social Stability and Equilibrium," Econometrica, Econometric Society, vol. 59(3), pages 859-867, May.
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    Cited by:

    1. Li, Cong & Lessard, Sabin, 2020. "Randomized matrix games in a finite population: Effect of stochastic fluctuations in the payoffs on the evolution of cooperation," Theoretical Population Biology, Elsevier, vol. 134(C), pages 77-91.

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