Agglomeration and Segregation in Group Formation Games

We consider a game in which a continuum of heterogeneous individuals partition themselves into communities. Communities can be of any size and group externalities can display any type of economies of scale or congestion effects. When group externalities are anonymous, we show that free mobility equilibria are socially optimal when group externalities increase or decrease logarithmically with community size. When they increase less (resp. more) than logarithmically, the equilibrium exhibits excessive agglomeration (resp. excessive fragmentation). These results hold irrespective of the distribution of preferences and the set of available communities. When group externalities are not anonymous, the optimality of free mobility equilibria requires an additional symmetry condition. We characterize conditions under which free mobility equilibria are excessively or ine