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Cycles of cooperation and free-riding in social systems


  • Y. P. Ma
  • S. Gonçalves
  • S. Mignot
  • J.-P. Nadal
  • M. B. Gordon



Basic evidences on non-profit making and other forms of benevolent-based organizations reveal a rough partition of members between somepure consumers of the public good (free-riders) and benevolent individuals (cooperators). We study the relationship between the community size and the level of cooperation in a simple model where the utility of joining the community is proportional to its size. We assume an idiosyncratic willingness to join the community ; cooperation bears a fixed cost while free-riding bears a (moral) idiosyncratic cost proportional to the fraction of cooperators. We show that the system presents two types of equilibria: fixed points (Nash equilibria) with a mixture of cooperators and free-riders and cycles where the size of the community, as well as the proportion of cooperators and free-riders, vary periodically.
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Suggested Citation

  • Y. P. Ma & S. Gonçalves & S. Mignot & J.-P. Nadal & M. B. Gordon, 2009. "Cycles of cooperation and free-riding in social systems," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 71(4), pages 597-610, October.
  • Handle: RePEc:spr:eurphb:v:71:y:2009:i:4:p:597-610
    DOI: 10.1140/epjb/e2009-00325-x

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    References listed on IDEAS

    1. 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.
    2. Denis Phan, 2006. "Discrete Choices under Social Influence:Generic Properties," Post-Print halshs-00105857, HAL.
    3. W. Hichri & A. Kirman, 2007. "The emergence of coordination in public good games," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 55(2), pages 149-159, January.
    4. Gachter, Simon & Fehr, Ernst, 1999. "Collective action as a social exchange," Journal of Economic Behavior & Organization, Elsevier, vol. 39(4), pages 341-369, July.
    5. Jean-Pierre Nadal & Denis Phan & Mirta Gordon & Jean Vannimenus, 2005. "Multiple equilibria in a monopoly market with heterogeneous agents and externalities," Quantitative Finance, Taylor & Francis Journals, vol. 5(6), pages 557-568.
    6. Ernst Fehr & Urs Fischbacher, 2004. "Social norms and human cooperation," Macroeconomics 0409026, EconWPA.
    7. Ernst Fehr & Simon Gaechter, 2003. "Altruistic Punishment in Humans," Microeconomics 0305006, EconWPA.
    8. Denis Phan, 2005. "Cooperation and free riding with moral cost," Post-Print halshs-00105849, HAL.
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    Cited by:

    1. Leahy, Eimear & Devitt, Conor & Lyons, Seán & Tol, Richard S.J., 2012. "The cost of natural gas shortages in Ireland," Energy Policy, Elsevier, vol. 46(C), pages 153-169.


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