Synergistic effects of global exclusion and mutation on replicator dynamics of public cooperation

Global exclusion represents an effective mechanism for the evolution of cooperation, even within an infinitely well-mixed population. However, it remains unknown how global exclusion performs when faced with the evolutionary challenges posed by both defection and neutral mutation in the public goods game. Here, we report that global exclusion is able to resist or even have a positive interplay with unbiased mutations in the replicator dynamics of public cooperation. In the limit of an infinite population size, we find that the replicator-mutation dynamics can result in either a global stable coexistence or two local stable coexistences, whose attraction basins are separated by an unstable fixed point, between global exclusion and defection, as well as several types of bifurcations. Interestingly, there is an optimal mutation rate that leads to the largest enhancement of the emergent level for cooperation by global exclusion when the exclusion cost is reasonably low. Our results thus indicate that random exploration of strategies by mutation can enhance the beneficial effects of global exclusion on the evolution of public cooperation.