Cycles of cooperation and free-riding in social systems

Yi-Ping Ma, S. Gonçalves, S. Mignot, J.-P. Nadal, M. B. Gordon

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


Basic evidences on non-profit making and other forms of benevolent-based organizations reveal a rough partition of members between some pure 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.
Original languageEnglish
Pages (from-to)597-610
JournalThe European Physical Journal B
Issue number4
Publication statusPublished - 2009


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