Evolutionary Games in Interacting Communities

In this paper, we extend the evolutionary games framework by considering a population composed of communities with each having its set of strategies and payoff functions. Assuming that the interactions among the communities occur with different probabilities, we define new evolutionarily stable strategies (ESS) with different levels of stability against mutations. In particular, through the analysis of two-community two-strategy model, we derive the conditions of existence of ESSs under different levels of stability. We also study the evolutionary game dynamics both in its classic form and with delays. The delays may be strategic, i.e., associated with the strategies, spatial, i.e., associated with the communities, or spatial strategic. We apply our model to the Hawk–Dove game played in two communities with an asymmetric level of aggressiveness, and we characterize the regions of ESSs as function of the interaction probabilities and the parameters of the model. We also show through numerical examples how the delays and the game parameters affect the stability of the mixed ESS.