Diversity-optimized cooperation on complex networks

Han-Xin Yang, Wen-Xu Wang, Zhi-Xi Wu, Ying-Cheng Lai, Bing-Hong Wang

Research output: Contribution to journalArticlepeer-review

137 Citations (Scopus)


We propose a strategy for achieving maximum cooperation in evolutionary games on complex networks. Each individual is assigned a weight that is proportional to the power of its degree, where the exponent alpha is an adjustable parameter that controls the level of diversity among individuals in the network. During the evolution, every individual chooses one of its neighbors as a reference with a probability proportional to the weight of the neighbor, and updates its strategy depending on their payoff difference. It is found that there exists an optimal value of alpha, for which the level of cooperation reaches maximum. This phenomenon indicates that, although high-degree individuals play a prominent role in maintaining the cooperation, too strong influences from the hubs may counterintuitively inhibit the diffusion of cooperation. Other pertinent quantities such as the payoff, the cooperator density as a function of the degree, and the payoff distribution are also investigated computationally and theoretically. Our results suggest that in order to achieve strong cooperation on a complex network, individuals should learn more frequently from neighbors with higher degrees, but only to a certain extent.

Original languageEnglish
Article number056107
Number of pages7
JournalPhysical Review. E, Statistical, Nonlinear and Soft Matter Physics
Issue number5
Publication statusPublished - May 2009


  • complex networks
  • cooperative systems
  • game theory
  • prisoners-dilemma game
  • public-goods games
  • snowdrift game
  • stochastic resonance
  • indirect reciprocity
  • dynamics
  • emergence
  • evolution


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