Effects of time delay on an evolutionary game

Social and biological processes are usually modelled by ordinary or partial differential equations or by Markov processes if one takes into account stochastic perturbations. However, interactions between individuals, players or molecules, naturally take time. In social models, individuals respond to information of events that took place in the past. In biological models, results of interactions, that is payoffs, appear in some future time. It is therefore important to study effects of time-delayed interactions on evolution of populations. In particular, joint effects of time delays and stochasticity will be explored. We expect changes in the number and stability of stationary states. This deliverable ties in very nicely deliverables D1.4 and D1.5 of WP1, and here we will resort to bifurcation theory of delay differential equations to explore dynamical properties, such as linear and nonlinear stability, of the models