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Evolution of Cooperation on Stochastic Dynamical Networks

Author

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  • 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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    Cited by:

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    5. Changbing Tang & Zhen Wang & Xiang Li, 2014. "Moderate Intra-Group Bias Maximizes Cooperation on Interdependent Populations," PLOS ONE, Public Library of Science, vol. 9(2), pages 1-7, February.
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    8. Jianlei Zhang & Chunyan Zhang & Tianguang Chu & Matjaž Perc, 2011. "Resolution of the Stochastic Strategy Spatial Prisoner's Dilemma by Means of Particle Swarm Optimization," PLOS ONE, Public Library of Science, vol. 6(7), pages 1-7, July.
    9. Adam Lee Miles & Matteo Cavaliere, 2021. "Opinion Diversity and the Resilience of Cooperation in Dynamical Networks," Mathematics, MDPI, vol. 9(15), pages 1-18, July.
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    11. Li, Zhi & Deng, Chuang & Suh, Il Hong, 2015. "Network topology control strategy based on spatial evolutionary public goods game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 432(C), pages 16-23.
    12. Yang, Zhihu & Li, Zhi & Wang, Long, 2020. "Evolution of cooperation in a conformity-driven evolving dynamic social network," Applied Mathematics and Computation, Elsevier, vol. 379(C).
    13. Jinming Du, 2018. "Insurance optimizes complex interactive and cooperative behaviors in public goods games," PLOS ONE, Public Library of Science, vol. 13(5), pages 1-9, May.
    14. Guo, Yujie & Zhang, Liming & Li, Haihong & Dai, Qionglin & Yang, Junzhong, 2023. "Network adaption based on environment feedback promotes cooperation in co-evolutionary games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 617(C).
    15. Luciano Miranda & Adauto J F de Souza & Fernando F Ferreira & Paulo R A Campos, 2012. "Complex Transition to Cooperative Behavior in a Structured Population Model," PLOS ONE, Public Library of Science, vol. 7(6), pages 1-9, June.
    16. José M Galán & Maciej M Łatek & Seyed M Mussavi Rizi, 2011. "Axelrod's Metanorm Games on Networks," PLOS ONE, Public Library of Science, vol. 6(5), pages 1-11, May.
    17. Chunyan Zhang & Jianlei Zhang & Guangming Xie & Long Wang & Matjaž Perc, 2011. "Evolution of Interactions and Cooperation in the Spatial Prisoner's Dilemma Game," PLOS ONE, Public Library of Science, vol. 6(10), pages 1-7, October.
    18. Su, Qi & Li, Aming & Wang, Long, 2017. "Spatial structure favors cooperative behavior in the snowdrift game with multiple interactive dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 299-306.
    19. Kokubo, Satoshi & Wang, Zhen & Tanimoto, Jun, 2015. "Spatial reciprocity for discrete, continuous and mixed strategy setups," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 552-568.
    20. Michael Foley & Rory Smead & Patrick Forber & Christoph Riedl, 2021. "Avoiding the bullies: The resilience of cooperation among unequals," PLOS Computational Biology, Public Library of Science, vol. 17(4), pages 1-18, April.
    21. Yang, Guoli & Zhu, Cheng & Zhang, Weiming, 2019. "Adaptive and probabilistic strategy evolution in dynamical networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 518(C), pages 99-110.
    22. Faqi Du & Feng Fu, 2011. "Partner Selection Shapes the Strategic and Topological Evolution of Cooperation," Dynamic Games and Applications, Springer, vol. 1(3), pages 354-369, September.
    23. Amado, André & Huang, Weini & Campos, Paulo R.A. & Ferreira, Fernando Fagundes, 2015. "Learning process in public goods games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 430(C), pages 21-31.
    24. Qu, Xinglong & Zhou, Changli & Cao, Zhigang & Yang, Xiaoguang, 2016. "Conditional dissociation as a punishment mechanism in the evolution of cooperation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 449(C), pages 215-223.

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