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Cycles of cooperation and free-riding in social systems

  • Yiping Ma

    (TIMC-IMAG - Techniques de l'Ingénierie Médicale et de la Complexité - Informatique, Mathématiques et Applications, Grenoble - CNRS : UMR5525 - Université Joseph Fourier - Grenoble I)

  • Sebastian Gonçalves

    (TIMC-IMAG - Techniques de l'Ingénierie Médicale et de la Complexité - Informatique, Mathématiques et Applications, Grenoble - CNRS : UMR5525 - Université Joseph Fourier - Grenoble I, Instituto de Fisica, UFRGS - Universidade Federal do Rio Grande do Sul)

  • Sylvain Mignot

    (TIMC-IMAG - Techniques de l'Ingénierie Médicale et de la Complexité - Informatique, Mathématiques et Applications, Grenoble - CNRS : UMR5525 - Université Joseph Fourier - Grenoble I)

  • Jean-Pierre Nadal

    (LPS - Laboratoire de Physique Statistique de l'ENS - CNRS : UMR8550 - Université Pierre et Marie Curie (UPMC) - Paris VI - Université Paris VII - Paris Diderot - École normale supérieure [ENS] - Paris, CAMS - Centre d'analyse et de mathématique sociale - CNRS : UMR8557 - École des Hautes Études en Sciences Sociales (EHESS))

  • Mirta B. Gordon

    ()

    (TIMC-IMAG - Techniques de l'Ingénierie Médicale et de la Complexité - Informatique, Mathématiques et Applications, Grenoble - CNRS : UMR5525 - Université Joseph Fourier - Grenoble I)

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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Paper provided by HAL in its series Working Papers with number hal-00349642.

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Date of creation: 02 Jan 2009
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Handle: RePEc:hal:wpaper:hal-00349642
Note: View the original document on HAL open archive server: http://hal.archives-ouvertes.fr/hal-00349642
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  1. Ernst Fehr & Simon Gaechter, 2003. "Altruistic Punishment in Humans," Microeconomics 0305006, EconWPA.
  2. 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.
  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. 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.
  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. Mirta B. Gordon & Jean-Pierre Nadal & Denis Phan & Viktoriya Semeshenko, 2007. "Discrete Choices under Social Influence: Generic Properties," Working Papers halshs-00135405, HAL.
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