Switching from Complete to Incomplete Information

ABSTRACT:We construct an elementary mechanism (Dutta-Sen-Vohra (1995)) that Nash implements the Constrained Walrasian correspondence. We extend it to incomplete and non-exclusive information economies by en-larging the message space of agents. We characterize the set of Bayesian equilibrium outcomes of the mechanism, and thus characterize an exten-sion of the Constrained Walrasian correspondence when one switches from complete to incomplete information. First, measurability restrictions on al-locations do not emerge from the strategic behavior of agents: there exist simple economies for which the set of Constrained Rational Expectations equilibrium allocations is not contained in the set of equilibrium outcomes of the mechanism. Next, by imposing measurability restrictions on allocations, the mechanism globally implements the Constrained Rational Expectations Equilibrium correspondence. This result shows game-theoretic connections between these two market equilibrium concepts. However, it is obtained at the price of strong restrictions on the behavior of agents