, Volume 1, Issue 3, pp 440-448,
Open Access This content is freely available online to anyone, anywhere at any time.
Date: 01 Sep 2011

Stochasticity and Time Delays in Evolutionary Games


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.