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Clustering in Large Networks Does Not Promote Upstream Reciprocity

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  • Naoki Masuda

Abstract

Upstream reciprocity (also called generalized reciprocity) is a putative mechanism for cooperation in social dilemma situations with which players help others when they are helped by somebody else. It is a type of indirect reciprocity. Although upstream reciprocity is often observed in experiments, most theories suggest that it is operative only when players form short cycles such as triangles, implying a small population size, or when it is combined with other mechanisms that promote cooperation on their own. An expectation is that real social networks, which are known to be full of triangles and other short cycles, may accommodate upstream reciprocity. In this study, I extend the upstream reciprocity game proposed for a directed cycle by Boyd and Richerson to the case of general networks. The model is not evolutionary and concerns the conditions under which the unanimity of cooperative players is a Nash equilibrium. I show that an abundance of triangles or other short cycles in a network does little to promote upstream reciprocity. Cooperation is less likely for a larger population size even if triangles are abundant in the network. In addition, in contrast to the results for evolutionary social dilemma games on networks, scale-free networks lead to less cooperation than networks with a homogeneous degree distribution.

Suggested Citation

  • Naoki Masuda, 2011. "Clustering in Large Networks Does Not Promote Upstream Reciprocity," PLOS ONE, Public Library of Science, vol. 6(10), pages 1-8, October.
  • Handle: RePEc:plo:pone00:0025190
    DOI: 10.1371/journal.pone.0025190
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    References listed on IDEAS

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    1. Martin A. Nowak & Karl Sigmund, 2005. "Evolution of indirect reciprocity," Nature, Nature, vol. 437(7063), pages 1291-1298, October.
    2. Greiner, Ben & Vittoria Levati, M., 2005. "Indirect reciprocity in cyclical networks: An experimental study," Journal of Economic Psychology, Elsevier, vol. 26(5), pages 711-731, October.
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    Cited by:

    1. Wang, Zi-Yi & Han, Jing-Ti & Zhao, Jun, 2017. "Identifying node spreading influence for tunable clustering coefficient networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 242-250.
    2. Hisashi Ohtsuki & Yoh Iwasa & Martin A Nowak, 2015. "Reputation Effects in Public and Private Interactions," PLOS Computational Biology, Public Library of Science, vol. 11(11), pages 1-11, November.
    3. Duan-Bing Chen & Hui Gao & Linyuan Lü & Tao Zhou, 2013. "Identifying Influential Nodes in Large-Scale Directed Networks: The Role of Clustering," PLOS ONE, Public Library of Science, vol. 8(10), pages 1-10, October.

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