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.