Mutual synchronization of oscillations in a system of coupled evolutionary games

The purpose of this study is to investigate collective dynamics of coupled communities that evolve according to the population game "Battle of the Sexes". A separate community includes two interacting populations of players of opposite sex, where each player has one of two possible competing behavior strategies. It is necessary to determine the possibility of mutual synchronization of oscillations in the number of players adhering to a particular strategy, build a synchronization region, and also evaluate the dependence of the properties of oscillations on the coupling strength. Methods. In this paper, we study the system of evolutionary games "Battle of the Sexes" interacting through migration. To simulate the evolutionary game dynamics we make use of the stochastic Moran process, as well as the Monte Carlo method to sample game trajectories. Mutual synchronization is defined by the appropriately generalized criteria of frequency and phase locking. Results. It is shown that the system of coupled evolutionary games "Battle of the Sexes" demonstrates mutual synchronization of oscillations under sufficiently strong coupling. In particular, oscillation frequencies of two communities get adjusted to each other and begin to coincide at some interaction parameter, while the oscillations themselves become almost identical. A similar result was also observed for an ensemble of more than two communities. Conclusion. The dependence of the average frequencies of community oscillations on the coupling strength was determined, the adjustment of oscillations with an increase in the coupling strength was demonstrated, thereby showing the possibility of mutual synchronization in the model of coupled evolutionary games "Battle of the Sexes". The region of frequency synchronization was numerically found.