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,
, when the set of feasible alternatives increases if a new member joins the group, and
, when a new member has an opposite effect and reduces the number of alternatives available for the enlarged group. We consider two notions,
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 dimensionality of feasible sets and the existence of stable structures.