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Implementation of the Walrasian correspondence: the boundary problem

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  • Bochet, O.L.A.

    (Microeconomics & Public Economics)

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, 1999) is violated for allocations at the boundary of the feasible set. We derive an impossibility result showing that it is in fact not implementable in any solution concept. Next, we construct a sequential mechanism based on price-allocation announcements that fits the very description of Walrasian Equilibrium. Imposing an additional domain restriction, we show that it fully implements the Walrasian correspondence in subgame perfect and strong subgame perfect equilibrium. We thus take care of the boundary problem that was prominent in the Nash implementation literature.
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  • Bochet, O.L.A., 2005. "Implementation of the Walrasian correspondence: the boundary problem," Research Memorandum 039, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    • Handle: RePEc:unm:umamet:2005039
    DOI: 10.26481/umamet.2005039
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    Cited by:

    1. Michele Lombardi & Naoki Yoshihara, 2017. "Natural implementation with semi-responsible agents in pure exchange economies," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(4), pages 1015-1036, November.
    2. Bochet, Olivier & Maniquet, François, 2010. "Virtual Nash implementation with admissible support," Journal of Mathematical Economics, Elsevier, vol. 46(1), pages 99-108, January.
    3. Muller, Rudolf & Perea, Andres & Wolf, Sascha, 2007. "Weak monotonicity and Bayes-Nash incentive compatibility," Games and Economic Behavior, Elsevier, vol. 61(2), pages 344-358, November.
    4. Bochet, O.L.A., 2006. "Equal-budget choice equivalent solutions in exchange economies," Research Memorandum 025, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    5. Lombardi, Michele & Yoshihara, Naoki & 吉原, 直毅, 2016. "Natural Implementation with Semi-responsible-sincere Agents in Pure Exchange Economies," Discussion Paper Series 649, Institute of Economic Research, Hitotsubashi University.

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