Existence of Edgeworth equilibria for economies with asymmetric information

We analyze a general equilibrium model with asymmetrically informed agents. A basic and well-known consequence of asymmetric information is the failure of equal treatment property. Despite of this, we show that in every replica economy a private core allocation, which treats agents of the same type equally, exists. This result is provided in the framework of two different models, with and without expectations, and it suffices to guarantee in both cases the existence of a private Edgeworth equilibrium.