Competitive equilibrium with asymmetric information: the arbitrage characterization

In a general equilibrium model of incomplete nominal-asset markets and adverse selection, Cornet-De Boisdeffre [3] introduced refined concepts of "no-arbitrage" prices and equilibria, which extended to the asymmetric information setting the classical concepts of symmetric information. In subsequent papers [4, 5], we generalized standard existence results of the symmetric information literature, as demonstrated by Cass [2], for nominal assets, or Geanakoplos-Polemarchakis [8], for numeraire assets, and showed that a no-arbitrage condition characterized the existence of equilibrium, in both asset structures, whether agents had symmetric or asymmetric information. We now introduce the model with arbitrary types of assets and a weaker concept of "pseudo-equilibrium" consistent with asymmetric information, to which we extend a classical theorem of symmetric information models with real assets. Namely, we show that the existence of a pseudo-equilibrium is still guaranteed by a no-arbitrage condition, under the same standard conditions with symmetric or asymmetric information.