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In the evolutionary games based on a heterogeneous population, recent researches has shown that the degree of each player in the network plays an important role and often determines the level of cooperation. Yet, the individual influence described by centralities remain inadequate in quantifying the effect of promoting cooperation. In this paper, how the representative centralities impact the fate of cooperation on different levels of heterogeneous populations has been comprehensively investigated. Simulation results show that on the whole, centrality characteristic is efficient to facilitate cooperation in social dilemmas except the clustering, and degree is neither the sole nor the best one. Meanwhile, there is an optimal level of heterogeneity that maximizes the cooperators regardless of the influence of centralities.

The Role of Heterogeneity and Centrality for Promoting Cooperation in Prisoner’s Dilemma Games