Existence of Competitive Equilibria in Markets with a Continuum of Traders - Aumann, Robert J. (Econometrica, 1966)
Abstract : It is well known, and easy to establish, that there exist markets that do not have competitive equilibria, provided the traders do not have convex preferences–that is, that the set of commodity bundles preferred or indifferent to a given bundle is not always convex. It is proved, nevertheless, that in a market consisting of a continuum of traders, each one individually insignificant, there is always a competitive equilibrium, even when the preferences are not convex. (Author)