Summary.We study the core and competitive allocations in exchange economies with a continuum of traders and differential information. We show that if the economy is "irreducible", then a competitive equilibrium, in the sense of Radner (1968Radner ( , 1982, exists. Moreover, the set of competitive equilibrium allocations coincides with the "private core" (Yannelis, 1991). We also show that the "weak fine core" of an economy coincides with the set of competitive allocations of an associated symmetric information economy in which the traders information is the joint information of all the traders in the original economy.

_We characterize the set of agreements that the players of a non-cooperative game may reach when they have the opportunity to communicate prior to play. We show that communication allows the players to correlate their actions. Therefore, we take the set of correlated strategies as the space of agreements. Since we consider situations where agreements are non-binding, they must not be subject to profitable self-enforcing deviations by coalitions of players. A coalition-proof equilibrium is a correlated strategy from which no coalition has an improving and self-enforcing deviation. A coalition-proof equilibrium exists when there is a correlated strategy which (i) has a support contained in the set of actions that survive the iterated elimination of strictly dominated strategies, and (H) weakly Pareto dominates every other correlated strategy whose support is contained in that set. Consequently, the unique equilibrium of a dominance solvable game is coalition-proof.

We study the relationship between the set of rational expectations equilibrium allocations and the ex-post core of exchange economies with asymmetric information.

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In markets with adverse selection, only low-quality units trade in the competitive equilibrium when the average quality of the good held by sellers is low. Under decentralized trade, however, both high and lowquality units trade, although with delay. Moreover, when frictions are small the surplus realized is greater than the (static) competitive surplus. Thus, decentralized trade mitigates the lemons problem. Remarkably, payoffs are competitive as frictions vanish, even though both high and low-quality units continue to trade and there is trade at several prices.