Stable sets for asymmetric information economies

An exchange economy with asymmetrically informed agents is considered with an exogenous rule that regulates the information sharing among agents. In this context, the notion of stable sets `a la von Neumann and Morgenstern is analyzed. Two different frameworks are taken into account as regards preferences: a model without expectations and a model with expected utilities. For the former, it is shown that the set V of all individually rational, Pareto optimal, symmetric allocations is the unique stable set of symmetric allocations. For the latter, an example is presented which shows that the same set V is not externally stable and a weaker result is proved.