Role of recommendation in spatial public goods games

We study the role of recommendation in a co-evolutionary public goods game in which groups can recommend their members for establishment of new relationships with individuals outside the current group according to group quality. Intriguingly, for square lattices and ER graphs there exists optimal group quality for recommendation that induces positive feedback between cooperation and recommendation. Snapshots of spatial patterns of cooperators, defectors, recommended cooperators and recommended defectors show that if group quality is appropriate for recommendation, cooperation and recommendation can simultaneously emerge. Moreover, we find that local recommendation improves cooperation more than global recommendation. As an extension, we also present results for Barabási–Albert networks. The positive effect of recommendation on cooperation for Barabási–Albert networks is independent of group quality. Our results provide an insight into the evolution of cooperation in real social systems.