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Cycles of cooperation and free-riding in social systems

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  • Yiping Ma

    (TIMC-IMAG - Techniques de l'Ingénierie Médicale et de la Complexité - Informatique, Mathématiques et Applications, Grenoble - UMR 5525 - UJF - Université Joseph Fourier - Grenoble 1 - Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology - VAS - VetAgro Sup - Institut national d'enseignement supérieur et de recherche en alimentation, santé animale, sciences agronomiques et de l'environnement - CNRS - Centre National de la Recherche Scientifique)

  • Sebastian Gonçalves

    (TIMC-IMAG - Techniques de l'Ingénierie Médicale et de la Complexité - Informatique, Mathématiques et Applications, Grenoble - UMR 5525 - UJF - Université Joseph Fourier - Grenoble 1 - Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology - VAS - VetAgro Sup - Institut national d'enseignement supérieur et de recherche en alimentation, santé animale, sciences agronomiques et de l'environnement - CNRS - Centre National de la Recherche Scientifique, Instituto de Fisica, UFRGS - UFRGS - Universidade Federal do Rio Grande do Sul [Porto Alegre])

  • Sylvain Mignot

    (TIMC-IMAG - Techniques de l'Ingénierie Médicale et de la Complexité - Informatique, Mathématiques et Applications, Grenoble - UMR 5525 - UJF - Université Joseph Fourier - Grenoble 1 - Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology - VAS - VetAgro Sup - Institut national d'enseignement supérieur et de recherche en alimentation, santé animale, sciences agronomiques et de l'environnement - CNRS - Centre National de la Recherche Scientifique)

  • Jean-Pierre Nadal

    (LPS - Laboratoire de Physique Statistique de l'ENS - FRDPENS - Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - CNRS - Centre National de la Recherche Scientifique - UPMC - Université Pierre et Marie Curie - Paris 6 - UPD7 - Université Paris Diderot - Paris 7 - CNRS - Centre National de la Recherche Scientifique, CAMS - Centre d'Analyse et de Mathématique sociales - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique)

  • Mirta B. Gordon

    (AMA - Analyse de données, Modélisation et Apprentissage automatique [Grenoble] - LIG - Laboratoire d'Informatique de Grenoble - UPMF - Université Pierre Mendès France - Grenoble 2 - UJF - Université Joseph Fourier - Grenoble 1 - Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology - INPG - Institut National Polytechnique de Grenoble - CNRS - Centre National de la Recherche Scientifique)

Abstract

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.

Suggested Citation

  • Yiping Ma & Sebastian Gonçalves & Sylvain Mignot & Jean-Pierre Nadal & Mirta B. Gordon, 2009. "Cycles of cooperation and free-riding in social systems," Working Papers hal-00349642, HAL.
    • Handle: RePEc:hal:wpaper:hal-00349642
    Note: View the original document on HAL open archive server: https://hal.science/hal-00349642
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    References listed on IDEAS

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    1. 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.
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    5. 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.
    6. Mirta B. Gordon & Jean-Pierre Nadal & Denis Phan & Viktoriya Semeshenko, 2007. "Discrete Choices under Social Influence: Generic Properties," Working Papers halshs-00135405, HAL.
    7. Gachter, Simon & Fehr, Ernst, 1999. "Collective action as a social exchange," Journal of Economic Behavior & Organization, Elsevier, vol. 39(4), pages 341-369, July.
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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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