Reducing the heterogeneity of payoffs: an effective way to promote cooperation in the prisoner's dilemma game.

In this paper, the accumulated payoff of each agent is regulated so as to reduce the heterogeneity of the distribution of all such payoffs. It is found that there exists an optimal regulation strength at which cooperation in the prisoner's dilemma game is optimally promoted. If the heterogeneity is regulated to be either too weak or too strong, the promotive effect disappears and the evolution of cooperation may even be impaired if compared to the absence of the proposed regulatory mechanism. An explanation of the observed results is provided. In particular, it is found that cooperators on the spatial grid are not isolated but form compact clusters and that the distribution of these clusters is crucial for the promotion of cooperation. Our work provides insights into relations between the distribution of payoffs and the evolution of cooperative behavior in situations constituting a social dilemma.