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Agglomeration, Segregation, and Social Welfare in Group Formation Games

We consider a non cooperative game in which a continuum of heterogeneous individuals partition themselves into groups. A player's payoff depends on the group she chooses and the set of players who choose the same group as her.In the case of anonymous group externalities, we show that free mobility equilibria are socially optimal when group externalities vary logarithmically with community size. When they increase less (more) than logarithmically, the equilibrium partition exhibits excessive agglomeration (excessive fragmentation). In the case of nonanonymous group externalities, free mobility affects the size, but also the composition of groups. We characterize conditions under which free mobility equilibria are excessively or insufficiently segregated.When applied to local public goods economies, these results provide insights on the social welfare effect of free mobility as a function of the local public good technology, the income distribution, and the tax scheme.