Evolution Of Prisoner's Dilemma Strategies On Scale Free Networks

Evolutionary game theory, a successful combination of game theory and biology as a common mathematical framework, plays an important role in understanding the emergence of cooperation in the context of Darwinian evolution. It has been extended to the cooperation found in some phenomena existing in many different fields of natural and social sciences.Meanwhile, many natural and artificial systems in the real world can be described as complex networks. Since most topological structures of complex networks were found to show a small-world or a scale-free feature, complex networks have attracted growing interest among the physical community.Here, in this paper, using evolutionary game theory and complex networks, we incorporate the topological structure of individuals into the study of cooperation behaviors, by adopting the prisoner's dilemma game as metaphors of cooperation between unrelated individuals, under the assumption that individuals on scale free networks only play games with their neighbors. It is found that cooperation behaviors not only depend on the strategy taken by players but also depends on the topological structure of the network. The smaller the average degree is, the easier it is to promote cooperation through natural selection. Cooperation on scale free networks built upon big clustering coefficients is enhanced and maintained at a high level. The introduction of punishment strategy for unsatisfied agents also increases cooperation and improves its persistence on scale-free networks.