Implementation of the Walrasian correspondence

The boundary problem

Olivier Bochet

    Research output: Contribution to journalArticle

    Abstract

    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.

    Original languageEnglish (US)
    Pages (from-to)301-316
    Number of pages16
    JournalInternational Journal of Game Theory
    Volume36
    Issue number2
    DOIs
    StatePublished - Oct 1 2007

    Fingerprint

    Boundary Problem
    Correspondence
    Walrasian Equilibrium
    Subgame Perfect Equilibrium
    Exchange Economy
    Solution Concepts
    Monotonic
    economy
    Monotonicity
    Restriction
    literature

    Keywords

    • Double implementation
    • Implementability
    • Justified sensitivity
    • Strong subgame perfect equilibrium
    • Subgame perfect equilibrium
    • Walrasian equilibrium

    ASJC Scopus subject areas

    • Statistics and Probability
    • Mathematics (miscellaneous)
    • Social Sciences (miscellaneous)
    • Economics and Econometrics
    • Statistics, Probability and Uncertainty

    Cite this

    Implementation of the Walrasian correspondence : The boundary problem. / Bochet, Olivier.

    In: International Journal of Game Theory, Vol. 36, No. 2, 01.10.2007, p. 301-316.

    Research output: Contribution to journalArticle

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