https://doi.org/10.1140/epjb/e2009-00325-x
Cycles of cooperation and free-riding in social systems
1
Laboratoire TIMC-IMAG (UMR 5525 CNRS-UJF-INPG), Domaine de la Merci, Jean Roget, 38710 La Tronche, France
2
Centre d'Analyse et Mathématique Sociales (UMR 8557 CNRS-EHESS), École des Hautes Études en Sciences Sociales, Paris, France
3
Laboratoire de Physique Statistique (UMR 8550 CNRS-ENS-Paris 6-Paris 7), École Normale Supérieure, Paris, France
Corresponding author: a mirta.gordon@imag.fr
Received:
2
January
2009
Revised:
7
July
2009
Published online:
7
October
2009
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.
PACS: 89.65.-s – Social and economic systems / 89.65.Ef – Social organizations; anthropology / 89.75.Fb – Structures and organization in complex systems
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2009