On the existence of equilibria in economies with infinitely many commodities and without ordered preferences

Abstract

The present paper deals with the existence of equilibria in economies whose commodity space is L ∞( M, M, μ) and where the agents' preferences need not be complete or transitive. Applying a fixed point theorem of Browder, an equilibrium existence theorem for abstract economies (generalized qualitative games) is proven where each agent's choice set is contained in an arbitrary topological vector space. With the help of this theorem the existence of Walrasian general equilibrium for a suitably specified economic model is obtained. The final result is a generalization of T. F. Bewley's ( J. Econ. Theory 4 (1972), 514–540) equilibrium existence theorem to the case of non-ordered preferences.