Cycles of cooperation and free-riding in social systems

Yiping Ma (1) , Sebastian Gonçalves (1, 2) , Sylvain Mignot (1) , Jean-Pierre Nadal (3, 4) , Mirta B. Gordon (5)

1 TIMC-IMAG - Techniques de l'Ingénierie Médicale et de la Complexité - Informatique, Mathématiques et Applications, Grenoble - UMR 5525
2 Instituto de Fisica, UFRGS
3 LPS - Laboratoire de Physique Statistique de l'ENS
4 CAMS - Centre d'Analyse et de Mathématique sociales
5 AMA - Analyse de données, Modélisation et Apprentissage automatique [Grenoble]

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.

Domaines: Modélisation et simulation; Economies et finances; Physique et Société [physics.soc-ph]

Yiping Ma, Sebastian Gonçalves, Sylvain Mignot, Jean-Pierre Nadal, Mirta B. Gordon. Cycles of cooperation and free-riding in social systems. 2009. ⟨hal-00349642⟩