Subgame Perfect Implementation and the Walrasian Correspondence

Consider a class of exchange,economies,in which,preferences,are continuous, convex and strongly monotonic. It is well known that the Walrasian correspondence, de…ned over such a class of economies, is not implementable in Nash Equilibrium. Monotonicity (Maskin (1999)), a necessary condition for Nash implementation, is violated for alloca- tions 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 implementa- tion. We …rst show,that the Walrasian correspondence,de…ned over this class of exchange,economies,is not implementable,in subgame,per- fect 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 di¤erentiability, we construct a sequential mecha- nism 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 an- nouncements,and …ts the very description of Walrasian Equilibrium. Keywords: Walrasian equilibrium, double implementation, subgame per-