Competitive Equilibrium with Asymmetric Information: an Existence Theorem for Numeraire Assets

In [2], we had extended the classical concepts and arbitrage theory of symmetric information, to an asymmetric information model, which dropped Radner's (1979) rational expectations' assumption. In [3], we showed how agents could infer enough information, in this model, to rule out arbitrage from markets. In [4], we extended to that model Cass' (1984) classical existence Theorem for nominal assets. Namely, we showed that existence of equilibrium was characterized by the generalized no-arbitrage condition introduced in [2], whether agents had symmetric or asymmetric information. We now display the same characteristic property for numeraire asset markets, and, thus, extend Geanakoplos-Polemarchakis' (1986) existence Theorem to the asymmetric information setting. Contrasting with Radner's, these results show that symmetric and asymmetric information economies can be embedded into a common general equilibrium model, where they share similar properties.