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 such a class of economies, is not implementable in Nash Equilibrium. Monotonicity (Maskin (1999)), a necessary condition for Nash implementation, is violated for allocations at the boundary of the feasible set. However, we know since the seminal work of Moore-Repullo (1988) and Abreu-Sen (1990) that monotonicity is no longer necessary for subgame perfect implementation. We first show that the Walrasian correspondence defined over this class of exchange economies is not implementable in subgame perfect equilibrium. Indeed, the assumption of di¤erentiability cannot be relaxed unless one imposes parametric restrictions on the environment, like assumption EE.3 in Moore-Repullo (1988). Next, assuming differentiability, we construct a sequential mechanism that fully implements the Walrasian correspondence in subgame perfect and strong subgame perfect equilibrium.. We take care 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