Cooperation and free-riding with moral costs

International audienceWe study social organizations with possible coexistence at equilibrium of cooperating individuals and pure consumers (free-riders). We investigate this polymorphic equilibrium using a game-theoretic approach and a statistical physics analysis of a simple model. The agents face a binary decision problem: whether to contribute or not to the public good, through the maximization of an additive utility that has two competing terms, a fixed cost for cooperating and an idiosyncratic moral cost for free-riding proportional to the fraction of cooperators. We study the equilibria regimes of this model. We show that there is a fraction of expected cooperators below which cooperation fails to emerge. Besides the homogeneous stable equilibria (everybody cooperates or everybody free-rides), it exists a solution in which cooperators coexist with free-riders. This polymorphic equilibrium is a consequence of the heterogeneous (idiosyncratic) perceptions of the social reproval by the different individuals. We provide analytic results in the case of a simple distribution of the idiosyncratic moral weights, and discuss them on the basis of concepts of game theory