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Cooperation in Networks Where the Learning Environment Differs from the Interaction Environment

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  • Jianlei Zhang
  • Chunyan Zhang
  • Tianguang Chu
  • Franz J Weissing

Abstract

We study the evolution of cooperation in a structured population, combining insights from evolutionary game theory and the study of interaction networks. In earlier studies it has been shown that cooperation is difficult to achieve in homogeneous networks, but that cooperation can get established relatively easily when individuals differ largely concerning the number of their interaction partners, such as in scale-free networks. Most of these studies do, however, assume that individuals change their behaviour in response to information they receive on the payoffs of their interaction partners. In real-world situations, subjects do not only learn from their interaction partners, but also from other individuals (e.g. teachers, parents, or friends). Here we investigate the implications of such incongruences between the ‘interaction network’ and the ‘learning network’ for the evolution of cooperation in two paradigm examples, the Prisoner's Dilemma game (PDG) and the Snowdrift game (SDG). Individual-based simulations and an analysis based on pair approximation both reveal that cooperation will be severely inhibited if the learning network is very different from the interaction network. If the two networks overlap, however, cooperation can get established even in case of considerable incongruence between the networks. The simulations confirm that cooperation gets established much more easily if the interaction network is scale-free rather than random-regular. The structure of the learning network has a similar but much weaker effect. Overall we conclude that the distinction between interaction and learning networks deserves more attention since incongruences between these networks can strongly affect both the course and outcome of the evolution of cooperation.

Suggested Citation

  • Jianlei Zhang & Chunyan Zhang & Tianguang Chu & Franz J Weissing, 2014. "Cooperation in Networks Where the Learning Environment Differs from the Interaction Environment," PLOS ONE, Public Library of Science, vol. 9(3), pages 1-8, March.
  • Handle: RePEc:plo:pone00:0090288
    DOI: 10.1371/journal.pone.0090288
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    References listed on IDEAS

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    1. Zhang, Jianlei & Zhang, Chunyan & Chu, Tianguang, 2011. "The evolution of cooperation in spatial groups," Chaos, Solitons & Fractals, Elsevier, vol. 44(1), pages 131-136.
    2. Zhang, Chunyan & Zhang, Jianlei & Xie, Guangming & Wang, Long, 2011. "Effects of encounter in a population of spatial prisoner’s dilemma players," Theoretical Population Biology, Elsevier, vol. 80(3), pages 226-231.
    3. Christoph Hauert & Michael Doebeli, 2004. "Spatial structure often inhibits the evolution of cooperation in the snowdrift game," Nature, Nature, vol. 428(6983), pages 643-646, April.
    4. Ding, Fei & Liu, Yun & Shen, Bo & Si, Xia-Meng, 2010. "An evolutionary game theory model of binary opinion formation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(8), pages 1745-1752.
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    Cited by:

    1. Tian, Lin-Lin & Li, Ming-Chu & Wang, Zhen, 2016. "Cooperation enhanced by indirect reciprocity in spatial prisoner’s dilemma games for social P2P systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 1252-1260.
    2. Chen, Wei & Yang, Zhihu & Wu, Te, 2021. "Evolution of cooperation driven by collective interdependence on multilayer networks," Applied Mathematics and Computation, Elsevier, vol. 388(C).
    3. Wu, Yu’e & Zhang, Zhipeng & Chang, Shuhua, 2019. "Reciprocal reward promotes the evolution of cooperation in structured populations," Chaos, Solitons & Fractals, Elsevier, vol. 119(C), pages 230-236.
    4. Amnon Rapoport & Darryl A Seale & Andrew M Colman, 2015. "Is Tit-for-Tat the Answer? On the Conclusions Drawn from Axelrod's Tournaments," PLOS ONE, Public Library of Science, vol. 10(7), pages 1-11, July.

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