Stable Partitions in a Model with Group-Dependent Feasible Sets.

In this paper we consider a model of group formation where group of individuals may have different feasible sets. We focus on two polar cases, increasing returns, when the set of feasible alternatives increases if a new member joins thegroup, and decreasing returns, when a new member has an opposite effect and reduces the number of alternatives available for the enlarged group. We consider two notions, stability and strong stability of group structures, that correspond to Nash and Strong Nash equilibrium of the associated non-cooperative game. We prove existence results for various classes of environments and also investigate the link between the dimensionality of the set of alternatives and the existence of stable structures.