How Much Interconnected Should Networks be for Cooperation to Thrive?

While the consensus is that interconnectivity between networks does promote cooperation by means of organizational complexity and enhanced reciprocity that is out of reach on isolated networks, we here address the question just how much interconnectivity there should be. The more the better according to naive intuition, yet we show that in fact only an intermediate density of sufficiently strong interactions between networks is optimal for the evolution of cooperation. This is due to an intricate interplay between the heterogeneity that causes an asymmetric strategy flow because of the additional links between the networks, and the independent formation of cooperative patterns on each individual network. Presented results are robust to variations of the strategy updating rule, the topology of interconnected networks, and the governing social dilemma, and thus indicate a high degree of universality. We also outline future directions for research based on coevolutionary games and survey existing work.