On core solutions in economies with asymmetric information

In a scenario with a continuum of asymmetrically informed agents, we analyze how the initial information of a trader may be altered when she becomes a member of a coalition. In contrast to a perfect competition frame, we first show that neither arbitrarily small coalitions nor large coalitions are enough to block an allocation which is not in the core, due to the market failure produced by asymmetric information. However, under mild assumptions, we extend the characterizations of the core provided by Vind and Schmeidler (1972) to economies with asymmetrically informed traders. We then focus on information sharing rules based on the coalitions' size. Assuming the existence of coalitions to which the sharing rule associates an information finer than all the others, we show that the corresponding cores coincide with the one defined by this finest information. Finally, characterizations for the weak fine, the fine and the private core are obtained as particular cases of this equivalence theorem.