Reducing the Heterogeneity of Payoffs: an Effective Way to Promote Cooperation in Prisoner's Dilemma Game

In this paper, the total payoff of each agent is regulated to reduce the heterogeneity of the distribution of the total payoffs. It is found there is an optimal regulation strength where the fraction of cooperation is prominently promoted, too weak or too strong of the strength will have little effects or result in the disappearance of the cooperators. It is also found that most of the cooperators are not distributed in isolation but form the cooperator clusters, and to promote the cooperation the only way is to enlarge the size of the cooperator clusters. Finally, we try to explain the emergence of larger clusters and prove the existence of the optimal regulation strength. Our works provide insight into the understanding of the relations between the distribution of payoffs and the cooperative behaviors.