Role of collective influence in promoting cooperation

The collective influence on the individuals' behavior have attracted much attention, and interesting phenomena such as social facilitation and social loafing have been studied. In this paper, we consider how the collective influence affects the evolution of cooperation in a structured population of individuals who nourish and benefit from public goods in groups. Individuals are supposed to distribute endowments to different groups to nourish the corresponding public goods. The collective influence is indicated by a tunable parameter α, with larger α corresponding to the players' higher preference to contribute more to the larger groups, which is similar to the social-facilitation effect in the real world, whereas, with smaller α corresponding to individuals' contrary preference, i.e., the social-loafing effect. Interestingly, we find that the heterogeneity of public-goods setting favors cooperation. Furthermore, the system where social loafing occurs performs better than that with social facilitation, in the case of heterogeneous formation.