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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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File URL: http://hdl.handle.net/10.1140/epjb/e2009-00325-x
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Article provided by Springer in its journal The European Physical Journal B.

Volume (Year): 71 (2009)
Issue (Month): 4 (October)
Pages: 597-610

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Handle: RePEc:spr:eurphb:v:71:y:2009:i:4:p:597-610
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  1. Ernst Fehr & Simon Gaechter, 2003. "Altruistic Punishment in Humans," Microeconomics 0305006, EconWPA.
  2. Mirta B. Gordon & Jean-Pierre Nadal & Denis Phan & Viktoriya Semeshenko, 2007. "Discrete Choices under Social Influence: Generic Properties," Working Papers halshs-00135405, HAL.
  3. Gachter, Simon & Fehr, Ernst, 1999. "Collective action as a social exchange," Journal of Economic Behavior & Organization, Elsevier, vol. 39(4), pages 341-369, July.
  4. Walid Hichri & Alan Kirman, 2007. "The Emergence of Coordination in Public Good Games," Post-Print halshs-00161572, HAL.
  5. Ernst Fehr & Urs Fischbacher, 2004. "Social norms and human cooperation," Macroeconomics 0409026, EconWPA.
  6. 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.
  7. W. Hichri & A. Kirman, 2007. "The emergence of coordination in public good games," The European Physical Journal B - Condensed Matter and Complex Systems, Springer, vol. 55(2), pages 149-159, 01.
  8. Ben Greiner & Maria Vittoria Levati, 2003. "Indirect Reciprocity in Cyclical Networks - An Experimental Study -," Papers on Strategic Interaction 2003-15, Max Planck Institute of Economics, Strategic Interaction Group.
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