Article

Dynamic Games and Applications

, Volume 2, Issue 3, pp 335-345

Open Access This content is freely available online to anyone, anywhere at any time.

Evolutionary Games and Periodic Fitness

  • Philippe UyttendaeleAffiliated withDepartment of Knowledge Engineering, Maastricht University
  • , Frank ThuijsmanAffiliated withDepartment of Knowledge Engineering, Maastricht University Email author 
  • , Pieter CollinsAffiliated withDepartment of Knowledge Engineering, Maastricht University
  • , Ralf PeetersAffiliated withDepartment of Knowledge Engineering, Maastricht University
  • , Gijs SchoenmakersAffiliated withDepartment of Knowledge Engineering, Maastricht University
  • , Ronald WestraAffiliated withDepartment of Knowledge Engineering, Maastricht University

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.

Keywords

Evolutionary game Replicator dynamics Periodic fitness