(Near) Substitute Preferences and Equilibria with Indivisibilities

An obstacle to using market mechanisms to allocate indivisible goods is the non-existence 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.