Implementation of the Walrasian Correspondence: the Boundary Problem

Bochet, Olivier (2007). Implementation of the Walrasian Correspondence: the Boundary Problem. International journal of game theory, 36(2), pp. 301-316. Berlin: Springer 10.1007/s00182-007-0103-4

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Consider exchange economies in which preferences are continuous, convex and strongly monotonic. It is well known that the Walrasian correspondence is not Nash implementable: Maskin monotonicity (Maskin in Rev Econ Stud 66:23–38, 1999) is violated for Walrasian allocations on the boundary of the feasible set. We derive an impossibility result showing that the Walrasian correspondence is in fact not implementable in any of the solution concepts considered in the implementation literature. Next, imposing an additional domain restriction, we construct a sequential mechanism that doubly implements the Walrasian correspondence in subgame perfect and strong subgame perfect equilibrium. The mechanism is based on price-allocation announcements, and it fits the very description of Walrasian equilibrium. We thus take care of the boundary problem that was prominent in the Nash implementation literature.

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