Subgame Perfect Implementation and the Walrasian Correspondence

Abstract

Consider a class of exchange economies in which preferences are continuous, convex and strongly monotonic. It is well known that the Walrasian correspondence defined over this class violates Maskin Monotonicity (Maskin, 1999) and is thus not Nash implementable. However, contrary to a result in Moore-Repullo (1988), it is not implementable in subgame perfect equilibrium (and, in fact, in any solution concept). Indeed, the assumption of differentiability cannot be relaxed unless one imposes parametric restrictions on the environment, like assumption EE.3 in Moore-Repullo (1988). Nest, assuming differentiability, we construct a sequential mechanism that fully implements the Walrasian correspondence in subgame perfect and strong subgame perfect equilibrium. We take of the boundary problem that was prominent in the Nash implementation literature. Moreover, our mechanism is based on price-allocation announcements and fits the very description of Walrasian equilibrium.