TY - JOUR
T1 - Evolutionary Games and Periodic Fitness
AU - Uyttendaele, Philippe
AU - Thuijsman, Frank
AU - Collins, Pieter
AU - Peeters, Ralf
AU - Schoenmakers, Gijs
AU - Westra, Ronald
PY - 2012/9
Y1 - 2012/9
N2 - 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.
AB - 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.
KW - Evolutionary game
KW - Replicator dynamics
KW - Periodic fitness
U2 - 10.1007/s13235-012-0048-5
DO - 10.1007/s13235-012-0048-5
M3 - Article
SN - 2153-0785
VL - 2
SP - 335
EP - 345
JO - Dynamic Games and Applications
JF - Dynamic Games and Applications
IS - 3
ER -