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A simple rule for the evolution of cooperation on graphs and social networks

Naturevolume 441pages502505 (2006) | Download Citation



A fundamental aspect of all biological systems is cooperation. Cooperative interactions are required for many levels of biological organization ranging from single cells to groups of animals1,2,3,4. Human society is based to a large extent on mechanisms that promote cooperation5,6,7. It is well known that in unstructured populations, natural selection favours defectors over cooperators. There is much current interest, however, in studying evolutionary games in structured populations and on graphs8,9,10,11,12,13,14,15,16,17. These efforts recognize the fact that who-meets-whom is not random, but determined by spatial relationships or social networks18,19,20,21,22,23,24. Here we describe a surprisingly simple rule that is a good approximation for all graphs that we have analysed, including cycles, spatial lattices, random regular graphs, random graphs and scale-free networks25,26: natural selection favours cooperation, if the benefit of the altruistic act, b, divided by the cost, c, exceeds the average number of neighbours, k, which means b/c > k. In this case, cooperation can evolve as a consequence of ‘social viscosity’ even in the absence of reputation effects or strategic complexity.

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Support from the John Templeton Foundation, JSPS, NDSEG and Harvard-MIT HST is gratefully acknowledged. The Program for Evolutionary Dynamics at Harvard University is sponsored by Jeffrey Epstein.

Author information


  1. Department of Biology, Kyushu University, 812-8581, Fukuoka, Japan

    • Hisashi Ohtsuki
  2. Program for Evolutionary Dynamics, Department of Organismic and Evolutionary Biology, Department of Mathematics

    • Hisashi Ohtsuki
    • , Christoph Hauert
    • , Erez Lieberman
    •  & Martin A. Nowak
  3. Department of Applied Mathematics, Harvard University, Cambridge, Massachusetts, 02138, USA

    • Erez Lieberman


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Competing interests

Reprints and permissions information is available at npg.nature.com/reprintsandpermissions. The authors declare no competing financial interests.

Corresponding author

Correspondence to Martin A. Nowak.

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  1. Supplementary Notes

    This file contains the Supplementary Discussion, Supplementary Figure 4 and additional references. (PDF 248 kb)

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