(Near) Substitute Preferences and Equilibria with Indivisibilities

Abstract

An obstacle to using market mechanisms to allocate indivisible goods is the nonexistence of competitive equilibria (CE). To surmount this Arrow and Hahn proposed the notion of social-approximate equilibria: a price vector and corresponding excess demands that are ‘small’. We identify social approximate equilibria where the excess demand, good-by-good, is bounded by a parameter that depends on preferences only and not the size of the economy. This parameter measures the degree of departure from substitute preferences. As a special case, we identify a class called geometric substitutes that guarantees the existence of competitive equilibria in non-quasi-linear settings. It strictly generalizes prior conditions such as single improvement, no complementarities, gross substitutes and net substitutes.