CK-Equilibria and Informational E±ciency in a Competitive Economy

We consider a very simple competitive economy with in ̄nitesimal agents and asymmetric information. We de ̄ne a Common Knowledge (CK hereafter) Equilibrium as a price distribution compatible with CK of market clearing and rationality. At equilibrium, expectational mistakes and incorrect information revelation by price are possible. But, whenever unique, the CK equilibrium is a fully revealing Rational Expectations Equilibrium. Hence uniqueness of equilibrium means market informational e±ciency. We give di®erent conditions of uniqueness of equilibrium bearing on the information structure. The ̄rst ones emphasize that many informed agents are required for market e±ciency. Agents need not be perfectly informed, but each "piece" of information has to be known by a large enough proportion of the population. The main result is a characterization of the information structures allowing for local uniqueness: multiplicity of equilibria obtains when all the agents have to extract information from the price to obtain information about the same event. We show that this result holds in an exchange economy with ̄nitely many goods and generic preferences. Finally, we provide a simple market game in which the CK-equilibria obtain through in ̄nitely repeated elimination of weakly dominated strategies.