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Implementation of the Walrasian Correspondence without Continuous, Convex, and Ordered Preferences

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  • Tian, Guoqiang

Abstract

This paper consideres the problem of designing better mechanisms whose Nash allocations coincide with constrained Walrasian allocations for non-neoclassical economies under the minimal possible assumptions. We show that no assumprions on preferences are needed for feasible and continuous implementation of the constrained Walraisan correspondence. Further, under the monotonicity assumption, we present a mechanism that is completely feasible and continuous. Hence, no continuity and convexity assumptions on preferences are required, and preferences may be nontotal or nontransitive. Thus, this paper gives a somewhat positive answer to the question raised in the literature by showing that, even for non-neoclassical economies, there are incentive-compatible, privacy preserving, and well-behaved mechanisms which yield Pareto-efficient and individually rational allocations at Nash equilibria.

Suggested Citation

  • Tian, Guoqiang, 1991. "Implementation of the Walrasian Correspondence without Continuous, Convex, and Ordered Preferences," MPRA Paper 41298, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:41298
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    File URL: https://mpra.ub.uni-muenchen.de/41298/1/MPRA_paper_41298.pdf
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    References listed on IDEAS

    as
    1. Mas-Colell,Andreu, 1990. "The Theory of General Economic Equilibrium," Cambridge Books, Cambridge University Press, number 9780521388702.
    2. Walker, Mark, 1981. "A Simple Incentive Compatible Scheme for Attaining Lindahl Allocations," Econometrica, Econometric Society, vol. 49(1), pages 65-71, January.
    3. Hurwicz, Leonid, 1979. "On allocations attainable through Nash equilibria," Journal of Economic Theory, Elsevier, vol. 21(1), pages 140-165, August.
    4. Tian, Guoqiang, 1991. "Implementation of Lindahl allocations with nontotal--nontransitive preferences," Journal of Public Economics, Elsevier, vol. 46(2), pages 247-259, November.
    5. Shafer, Wayne & Sonnenschein, Hugo, 1975. "Equilibrium in abstract economies without ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 2(3), pages 345-348, December.
    6. Schmeidler, David, 1980. "Walrasian Analysis via Strategic Outcome Functions," Econometrica, Econometric Society, vol. 48(7), pages 1585-1593, November.
    7. Frederick Mosteller & Philip Nogee, 1951. "An Experimental Measurement of Utility," Journal of Political Economy, University of Chicago Press, vol. 59, pages 371-371.
    8. L. Hurwicz, 1979. "Outcome Functions Yielding Walrasian and Lindahl Allocations at Nash Equilibrium Points," Review of Economic Studies, Oxford University Press, vol. 46(2), pages 217-225.
    9. Palfrey, Thomas R & Srivastava, Sanjay, 1991. "Nash Implementation Using Undominated Strategies," Econometrica, Econometric Society, vol. 59(2), pages 479-501, March.
    10. Tian, Guoqiang, 1988. "On the constrained Walrasian and Lindahl correspondences," Economics Letters, Elsevier, vol. 26(4), pages 299-303.
    11. Guoqiang Tian, 1989. "Implementation of the Lindahl Correspondence by a Single-Valued, Feasible, and Continuous Mechanism," Review of Economic Studies, Oxford University Press, vol. 56(4), pages 613-621.
    12. Mas-Colell, Andrew, 1974. "An equilibrium existence theorem without complete or transitive preferences," Journal of Mathematical Economics, Elsevier, vol. 1(3), pages 237-246, December.
    13. Tian, Guoqiang & Li, Qi, 1991. "Completely feasible and continuous implementation of the Lindahl correspondence with any number of goods," Mathematical Social Sciences, Elsevier, vol. 21(1), pages 67-79, February.
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    More about this item

    Keywords

    Walrasian Correspondence; Convex; Ordered Preferences;

    JEL classification:

    • D5 - Microeconomics - - General Equilibrium and Disequilibrium

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