The rules of multiplayer cooperation in networks of communities

Community organization permeates both social and biological complex systems. To study its interplay with behavior emergence, we model mobile structured populations with multiplayer interactions. We derive general analytical methods for evolutionary dynamics under high home fidelity when populations self-organize into networks of asymptotically isolated communities. In this limit, community organization dominates over the network structure and emerging behavior is independent of network topology. We obtain the rules of multiplayer cooperation in networks of communities for different types of social dilemmas. The success of cooperation is a result of the benefits shared amongst communal cooperators outperforming the benefits reaped by defectors in mixed communities. Under weak selection, cooperation can evolve and be stable for any size (Q) and number (M) of communities if the reward-to-cost ratio (V/K) of public goods is higher than a critical value. Community organization is a solid mechanism for sustaining the evolution of cooperation under public goods dilemmas, particularly when populations are organized into a higher number of smaller communities. Contrary to public goods dilemmas relating to production, the multiplayer Hawk-Dove (HD) dilemma is a commons dilemma focusing on the fair consumption of preexisting resources. This game holds mixed results but tends to favour cooperation under larger communities, highlighting that the two types of social dilemmas might lead to solid differences in the behaviour adopted under community structure.