title: Impact of heterogeneous activity and community structure on the evolutionary success of cooperators in social networks.
abstract: Recent empirical studies suggest that heavy-tailed distributions of human activities are universal in real social dynamics [L. Muchnik, S. Pei, L. C. Parra, S. D. S. Reis, J. S. Andrade Jr., S. Havlin, and H. A. Makse, Sci. Rep. 3, 1783 (2013)]. On the other hand, community structure is ubiquitous in biological and social networks [M. E. J. Newman, Nat. Phys. 8, 25 (2012)]. Motivated by these facts, we here consider the evolutionary prisoner's dilemma game taking place on top of a real social network to investigate how the community structure and the heterogeneity in activity of individuals affect the evolution of cooperation. In particular, we account for a variation of the birth-death process (which can also be regarded as a proportional imitation rule from a social point of view) for the strategy updating under both weak and strong selection (meaning the payoffs harvested from games contribute either slightly or heavily to the individuals' performance). By implementing comparative studies, where the players are selected either randomly or in terms of their actual activities to play games with their immediate neighbors, we figure out that heterogeneous activity benefits the emergence of collective cooperation in a harsh environment (the action for cooperation is costly) under strong selection, whereas it impairs the formation of altruism under weak selection. Moreover, we find that the abundance of communities in the social network can evidently foster the formation of cooperation under strong selection, in contrast to the games evolving on randomized counterparts. Our results are therefore helpful for us to better understand the evolution of cooperation in real social systems.
authors: Institute of Computational Physics and Complex Systems, Lanzhou University, Lanzhou, Gansu 730000, China.
authors: Zhi-Xi
authors: ZX
authors: Wu
authors: CompleX Lab, Web Sciences Center, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, China and Department of Electronic and Information Engineering, The Hong Kong Polytechnic University, Kowloon, Hong Kong.
authors: Zhihai
authors: Z
authors: Rong
authors: Department of Physics, Fuzhou University, Fuzhou 350108, China.
authors: Han-Xin
authors: HX
authors: Yang
mesh_terms: D005075:Biological Evolution; D003299:Cooperative Behavior; D006801:Humans; D008962:Models, Theoretical; D000068956:Prisoner Dilemma; D012111:Residence Characteristics; D012944:Social Support