Cycles of cooperation and free-riding in social systems

Yiping Ma, Sebastian Gonçalves, Sylvain Mignot, Jean-Pierre Nadal () and Mirta B. Gordon ()
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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]
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

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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.

Date: 2009-01-02
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Journal Article: Cycles of cooperation and free-riding in social systems (2009)
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