Dresden 2006 – scientific programme

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AKSOE: Physik sozio-ökonomischer Systeme

AKSOE 10: Poster Session (posters are expected to be displayed the full day 8:30-18:00)

AKSOE 10.59: Poster

Wednesday, March 29, 2006, 16:00–18:00, P2

Dynamics of Social Systems: Cooperation and Free-Riding — •Yiping Ma^1,2, Mirta B. Gordon¹, and Jean-Pierre Nadal³ — ¹Laboratoire Leibniz-IMAG, Grenoble, France — ²Department of Physics, Hong Kong University of Science and Technology, Hong Kong — ³Laboratoire de Physique Statistique, Ecole Normale Supérieure, Paris.

We study the mean field dynamics of a model introduced in [1] of a social community. The N agents may choose between three strategies: either to join the community or not, and in the case of joining it, either to cooperate or to behave as a free-rider. Individuals’ preferences have an idiosyncratic willingness to join, and a social component that depends on the fractions of cooperators and free-riders. Cooperators bear a fixed cost whereas free-riders support an idiosyncratically weighted cost proportional to the number of cooperators. We study the dynamics of this model analytically in the large N limit for both parallel and sequential updating. The resulting 2-d map in parallel updating, and 2-d flow in sequential updating, are analyzed within the framework of dynamical systems. As one varies one of the parameters, the phase diagram experiences a rich class of bifurcations. Noticeably, a stable limit cycle is shown to exist in both parallel and sequential updating, under certain parameter settings. We illustrate these results by computer simulations exhibiting examples of fixed points and of limit cycles, reached both through parallel and sequential updating. Comparison with the analytical predictions reveals however strong finite size effects.

[1] D. Phan, R. Waldeck, M. B. Gordon and J.-P. Nadal, WEHIA 2005 [http://perso.univ-rennes1.fr/denis.phan/papers/pgnw2005.pdf]