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Social diversity promotes the emergence of cooperation in public goods games

Nature volume 454, pages 213–216 (2008)Cite this article

Abstract

Humans often cooperate in public goods games1,2,3 and situations ranging from family issues to global warming4,5. However, evolutionary game theory predicts4,6 that the temptation to forgo the public good mostly wins over collective cooperative action, and this is often also seen in economic experiments7. Here we show how social diversity provides an escape from this apparent paradox. Up to now, individuals have been treated as equivalent in all respects4,8, in sharp contrast with real-life situations, where diversity is ubiquitous. We introduce social diversity by means of heterogeneous graphs and show that cooperation is promoted by the diversity associated with the number and size of the public goods game in which each individual participates and with the individual contribution to each such game. When social ties follow a scale-free distribution9, cooperation is enhanced whenever all individuals are expected to contribute a fixed amount irrespective of the plethora of public goods games in which they engage. Our results may help to explain the emergence of cooperation in the absence of mechanisms based on individual reputation and punishment10,11,12. Combining social diversity with reputation and punishment will provide instrumental clues on the self-organization of social communities and their economical implications.

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Figure 1: Population structure and local neighbourhoods.
Figure 2: Evolution of cooperation in networked PGGs.
Figure 3: Dynamics on the double star.
Figure 4: Wealth distribution.

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References

  1. Hardin, G. The tragedy of the commons. Science 162, 1243–1248 (1968)

    Article  ADS  CAS  Google Scholar 

  2. Binmore, K. G. Game Theory and the Social Contract Vol. 1, Playing Fair (MIT Press, Cambridge, MA, 1994)

    MATH  Google Scholar 

  3. Kollock, P. Social dilemmas: The anatomy of cooperation. Annu. Rev. Sociol. 24, 183–214 (1998)

    Article  Google Scholar 

  4. Hauert, C., De Monte, S., Hofbauer, J. & Sigmund, K. Volunteering as Red Queen mechanism for cooperation in public goods games. Science 296, 1129–1132 (2002)

    Article  ADS  CAS  Google Scholar 

  5. Milinski, M., Semmann, D., Krambeck, H. J. & Marotzke, J. Stabilizing the Earth’s climate is not a losing game: Supporting evidence from public goods experiments. Proc. Natl Acad. Sci. USA 103, 3994–3998 (2006)

    Article  ADS  CAS  Google Scholar 

  6. Hofbauer, J. & Sigmund, K. Evolutionary Games and Population Dynamics (Cambridge Univ. Press, Cambridge, 1998)

    Book  Google Scholar 

  7. Fehr, E. & Gachter, S. Altruistic punishment in humans. Nature 415, 137–140 (2002)

    Article  ADS  CAS  Google Scholar 

  8. Szabo, G. & Hauert, C. Phase transitions and volunteering in spatial public goods games. Phys. Rev. Lett. 89, 118101 (2002)

    Article  ADS  Google Scholar 

  9. Barabási, A. L. & Albert, R. Emergence of scaling in random networks. Science 286, 509–512 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  10. Ohtsuki, H. & Iwasa, Y. How should we define goodness?—reputation dynamics in indirect reciprocity. J. Theor. Biol. 231, 107–120 (2004)

    Article  MathSciNet  Google Scholar 

  11. Nowak, M. A. & Sigmund, K. Evolution of indirect reciprocity. Nature 437, 1291–1298 (2005)

    Article  ADS  CAS  Google Scholar 

  12. Pacheco, J. M., Santos, F. C. & Chalub, F. A. Stern-judging: A simple, successful norm which promotes cooperation under indirect reciprocity. PLoS Comput. Biol. 2, e178 (2006)

    Article  ADS  Google Scholar 

  13. Hauert, C., Traulsen, A., Brandt, H., Nowak, M. A. & Sigmund, K. Via freedom to coercion: the emergence of costly punishment. Science 316, 1905–1907 (2007)

    Article  ADS  MathSciNet  CAS  Google Scholar 

  14. Boyd, R. & Mathew, S. Behavior. A narrow road to cooperation. Science 316, 1858–1859 (2007)

    Article  CAS  Google Scholar 

  15. Szabo, G. & Hauert, C. Evolutionary prisoner’s dilemma games with voluntary participation. Phys. Rev. E 66, 062903 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  16. Santos, F. C. & Pacheco, J. M. Scale-free networks provide a unifying framework for the emergence of cooperation. Phys. Rev. Lett. 95, 098104 (2005)

    Article  ADS  CAS  Google Scholar 

  17. Santos, F. C., Pacheco, J. M. & Lenaerts, T. Evolutionary dynamics of social dilemmas in structured heterogeneous populations. Proc. Natl Acad. Sci. USA 103, 3490–3494 (2006)

    Article  ADS  CAS  Google Scholar 

  18. Ohtsuki, H., Hauert, C., Lieberman, E. & Nowak, M. A. A simple rule for the evolution of cooperation on graphs and social networks. Nature 441, 502–505 (2006)

    Article  ADS  CAS  Google Scholar 

  19. Amaral, L. A., Scala, A., Barthelemy, M. & Stanley, H. E. Classes of small-world networks. Proc. Natl Acad. Sci. USA 97, 11149–11152 (2000)

    Article  ADS  CAS  Google Scholar 

  20. Albert, R. & Barabási, A. L. Statistical mechanics of complex networks. Rev. Mod. Phys. 74, 47–97 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  21. Dorogotsev, S. N. & Mendes, J. F. F. Evolution of Networks: From Biological Nets to the Internet and WWW. (Oxford Univ. Press, Oxford, 2003)

    Book  Google Scholar 

  22. Lieberman, E., Hauert, C. & Nowak, M. A. Evolutionary dynamics on graphs. Nature 433, 312–316 (2005)

    Article  ADS  CAS  Google Scholar 

  23. Nowak, M. A. & May, R. M. Evolutionary games and spatial chaos. Nature 359, 826–829 (1992)

    Article  ADS  Google Scholar 

  24. Nowak, M. A. Five rules for the evolution of cooperation. Science 314, 1560–1563 (2006)

    Article  ADS  CAS  Google Scholar 

  25. Boehm, C. Hierarchy in the Forest: The Evolution of Egalitarian Behavior (Harvard Univ. Press, Cambridge, MA, 1999)

    Google Scholar 

  26. Skyrms, B. The Stag Hunt and the Evolution of Social Structure (Cambridge Univ. Press, Cambridge, 2004)

    Google Scholar 

  27. Santos, F. C. & Pacheco, J. M. A new route to the evolution of cooperation. J. Evol. Biol. 19, 726–733 (2006)

    Article  CAS  Google Scholar 

  28. Traulsen, A., Nowak, M. A. & Pacheco, J. M. Stochastic dynamics of invasion and fixation. Phys. Rev. E 74, 011909 (2006)

    Article  ADS  Google Scholar 

  29. Hauert, C. & Doebeli, M. Spatial structure often inhibits the evolution of cooperation in the snowdrift game. Nature 428, 643–646 (2004)

    Article  ADS  CAS  Google Scholar 

  30. Ohtsuki, H., Nowak, M. A. & Pacheco, J. M. Breaking the symmetry between interaction and replacement in evolutionary dynamics on graphs. Phys. Rev. Lett. 98, 108106 (2007)

    Article  ADS  Google Scholar 

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Acknowledgements

F.C.S. acknowledges support from Fonds de la Recherche Scientifique, Belgium. M.D.S. and J.M.P. acknowledge financial support from Fundação para a Ciência e Tecnologia, Portugal.

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Authors and Affiliations

  1. Computer and Decision Engineering Department, Institut de Recherches Interdisciplinaires et de Développements en Intelligence Artificielle (IRIDIA), Université Libre de Bruxelles, B-1050 Brussels, Belgium

    Francisco C. Santos

  2. Centro de Fisica Teórica e Computacional (CFTC) and Departamento de Física da Universidade de Lisboa, ATP-group, Complexo Interdisciplinar, Av. Prof. Gama Pinto 2, 1649-003 Lisboa, Portugal,

    Marta D. Santos & Jorge M. Pacheco

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  1. Francisco C. Santos
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  2. Marta D. Santos
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  3. Jorge M. Pacheco
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Correspondence to Jorge M. Pacheco.

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Santos, F., Santos, M. & Pacheco, J. Social diversity promotes the emergence of cooperation in public goods games. Nature 454, 213–216 (2008). https://doi.org/10.1038/nature06940

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