Evolutionary Games and Periodic Fitness

Philippe Uyttendaele, Frank Thuijsman*, Pieter Collins, Ralf Peeters, Gijs Schoenmakers, Ronald Westra

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review


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.
Original languageEnglish
Pages (from-to)335-345
JournalDynamic Games and Applications
Issue number3
Publication statusPublished - Sept 2012


  • Evolutionary game
  • Replicator dynamics
  • Periodic fitness


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