The First will be the Last and the Last First: Segregation in Societies with Positional Externalities

This paper studies coalition formation among individuals who differ in productivity. The output of a coalition is determined by the sum of productivities if the coalition exceeds a minimal threshold of members. We consider competitive societies in which the surplus of a coalition is split according to productivity and egalitarian societies in which coalitions split their surplus equally. Preferences of coalition members depend on their material payoffs, but are also influenced by positional concerns, which relate their material payoffs to the average material payoff in the coalition. Our analysis uses two stability notions, the Core and the Myopic Stable Set. Both competitive and egalitarian societies lead to segregated partition structures. For competitive societies, all stable allocations are based on bottom-up segregation, i.e., individuals with adjacent productivities form coalitions and if some individuals are not part of a productive coalition, then these are the most productive ones. For egalitarian societies, we obtain top-down segregation in all stable allocations. Again it holds that individuals with adjacent productivities form coalitions, but now the least productive individuals may not be part of any productive coalition. If all individuals have different productivity levels, then the material efficiency of competitive societies is below that of egalitarian societies.