Yiping Ma (TIMC - Techniques de l’Ingénierie Médicale et de la Complexité - CNRS : UMR5525 - Université Joseph Fourier - Grenoble I) Sebastian Gonçalves (TIMC - Techniques de l’Ingénierie Médicale et de la Complexité - CNRS : UMR5525 - Université Joseph Fourier - Grenoble I, Instituto de Fisica, UFRGS - Universidade Federal do Rio Grande do Sul) Sylvain Mignot (TIMC - Techniques de l’Ingénierie Médicale et de la Complexité - 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 - Paris VI - Université Denis Diderot - Paris VII - Ecole Normale Supérieure de Paris - ENS Paris, CAMS - Centre d'analyse et de mathématique sociale - CNRS : UMR8557 - Ecole des Hautes Etudes en Sciences Sociales) Mirta B. Gordon (TIMC - Techniques de l’Ingénierie Médicale et de la Complexité - CNRS : UMR5525 - Université Joseph Fourier - Grenoble I)
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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_v1.
Length: Date of creation: 02 Jan 2009 Date of revision: Handle: RePEc:hal:wpaper:hal-00349642_v1
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