Equilibrium theory with asymmetric information and with infinitely many commodities

The traditional deterministic general equilibrium theory with infinitely many commodities cannot cover economies with private information constraints on the consumption sets. We bring the level of asymmetric information equilibrium theory at least at par with that of the deterministic. In particular, we establish results on equilibrium existence for exchange economies with asymmetric (differential) information and with an infinite dimensional commodity space. Two settings are treated. In the first, the commodity space is an ordered normed space whose positive cone has a non-empty interior, while in the second it is a locally convex-solid Riesz space whose positive cone may have empty interior. Preferences are not assumed to be monotone, complete, or transitive. Our new equilibrium existence theorems for asymmetric information economies not only include, as a special case, classical results, e.g. Bewley (1972), Mas-Colell (1986), among others, but also complement and extend the techniques and some results in Aliprantis, Tourky, and Yannelis (2001). Furthermore, they imply new existence results for the core of an economy with asymmetric information.