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Evolution of Cooperation on Stochastic Dynamical Networks

Author

Listed:
  • Bin Wu
  • Da Zhou
  • Feng Fu
  • Qingjun Luo
  • Long Wang
  • Arne Traulsen

Abstract

Cooperative behavior that increases the fitness of others at a cost to oneself can be promoted by natural selection only in the presence of an additional mechanism. One such mechanism is based on population structure, which can lead to clustering of cooperating agents. Recently, the focus has turned to complex dynamical population structures such as social networks, where the nodes represent individuals and links represent social relationships. We investigate how the dynamics of a social network can change the level of cooperation in the network. Individuals either update their strategies by imitating their partners or adjust their social ties. For the dynamics of the network structure, a random link is selected and breaks with a probability determined by the adjacent individuals. Once it is broken, a new one is established. This linking dynamics can be conveniently characterized by a Markov chain in the configuration space of an ever-changing network of interacting agents. Our model can be analytically solved provided the dynamics of links proceeds much faster than the dynamics of strategies. This leads to a simple rule for the evolution of cooperation: The more fragile links between cooperating players and non-cooperating players are (or the more robust links between cooperators are), the more likely cooperation prevails. Our approach may pave the way for analytically investigating coevolution of strategy and structure.

Suggested Citation

  • Bin Wu & Da Zhou & Feng Fu & Qingjun Luo & Long Wang & Arne Traulsen, 2010. "Evolution of Cooperation on Stochastic Dynamical Networks," PLOS ONE, Public Library of Science, vol. 5(6), pages 1-7, June.
    • Handle: RePEc:plo:pone00:0011187
    DOI: 10.1371/journal.pone.0011187
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    References listed on IDEAS

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    1. Blume Lawrence E., 1993. "The Statistical Mechanics of Strategic Interaction," Games and Economic Behavior, Elsevier, vol. 5(3), pages 387-424, July.
    2. Nobuyuki Hanaki & Alexander Peterhansl & Peter S. Dodds & Duncan J. Watts, 2007. "Cooperation in Evolving Social Networks," Management Science, INFORMS, vol. 53(7), pages 1036-1050, July.
    3. Francisco C Santos & Jorge M Pacheco & Tom Lenaerts, 2006. "Cooperation Prevails When Individuals Adjust Their Social Ties," PLOS Computational Biology, Public Library of Science, vol. 2(10), pages 1-8, October.
    4. Chen, Xiaojie & Fu, Feng & Wang, Long, 2008. "Promoting cooperation by local contribution under stochastic win-stay-lose-shift mechanism," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(22), pages 5609-5615.
    5. Martin A. Nowak & Karl Sigmund, 2005. "Evolution of indirect reciprocity," Nature, Nature, vol. 437(7063), pages 1291-1298, October.
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