Dynamic Games and Applications

, 1:440

Stochasticity and Time Delays in Evolutionary Games

Open AccessArticle

DOI: 10.1007/s13235-011-0028-1

Cite this article as:
Miȩkisz, J. & Wesołowski, S. Dyn Games Appl (2011) 1: 440. doi:10.1007/s13235-011-0028-1


We discuss combined effects of stochasticity and time delays in simple evolutionary games with a unique mixed evolutionarily stable strategy. We present three models of time-delay stochastic dynamics of finite well-mixed or random-matching populations. We show that in the first two models the evolutionarily stable strategy loses its stability and there appears a stable cycle around it with the time period and the amplitude proportional to the delay. In the third model, only one randomly chosen individual can update his strategy at a time. This slows down the dynamics and makes the evolutionarily stable strategy stable with respect to both time delay and stochastic perturbations.


Evolutionary game theoryTime delayStochastic dynamicsStochastic stabilityStable cycles
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© The Author(s) 2011

Authors and Affiliations

  1. 1.Institute of Applied Mathematics and MechanicsUniversity of WarsawWarsawPoland