Evolutionary Games and Periodic Fitness

Philippe Uyttendaele, Frank Thuijsman (), Pieter Collins, Ralf Peeters, Gijs Schoenmakers and Ronald Westra

Dynamic Games and Applications, 2012, vol. 2, issue 3, 335-345

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

Keywords: Evolutionary game; Replicator dynamics; Periodic fitness (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s13235-012-0048-5

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