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Nash-implementation of competitive equilibria via a bounded mechanism

Author

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  • Gaël Giraud

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

  • Hubert Stahn

    (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique)

Abstract

We deal with the problem of providing incentives for the implementation of competitive outcomes in a pure-exchange economy with finitely many households. We construct a feasible price-quantity mechanism, which fully implements Walras equilibria via Nash equilibria in fairly general environments. Traders' preferences need neither to be ordered nor continuous. In addition, the mechanism is such that no pure strategy is weakly dominated, hence is bounded (in the sense of Jackson 1992). In particular it makes no use of any integer game.

Suggested Citation

  • Gaël Giraud & Hubert Stahn, 2013. "Nash-implementation of competitive equilibria via a bounded mechanism," PSE-Ecole d'économie de Paris (Postprint) hal-01052680, HAL.
  • Handle: RePEc:hal:pseptp:hal-01052680
    DOI: 10.1007/s10058-012-0138-2
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    References listed on IDEAS

    as
    1. Peck, James & Shell, Karl & Spear, Stephen E., 1992. "The market game: existence and structure of equilibrium," Journal of Mathematical Economics, Elsevier, vol. 21(3), pages 271-299.
    2. Gaël Giraud & Céline Rochon, 2003. "Generic efficiency and collusion-proofness in exchange economies," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 20(3), pages 405-428, June.
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    9. Palfrey, Thomas R & Srivastava, Sanjay, 1991. "Nash Implementation Using Undominated Strategies," Econometrica, Econometric Society, vol. 59(2), pages 479-501, March.
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    11. Jackson Matthew O. & Palfrey Thomas R. & Srivastava Sanjay, 1994. "Undominated Nash Implementation in Bounded Mechanisms," Games and Economic Behavior, Elsevier, vol. 6(3), pages 474-501, May.
    12. Giraud, Gael & Rochon, Celine, 2002. "Consistent collusion-proofness and correlation in exchange economies," Journal of Mathematical Economics, Elsevier, vol. 38(4), pages 441-463, December.
    13. Koutsougeras, Leonidas C., 2003. "Non-Walrasian equilibria and the law of one price," Journal of Economic Theory, Elsevier, vol. 108(1), pages 169-175, January.
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    16. Sonia Weyers, 1999. "Uncertainty and insurance in strategic market games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 14(1), pages 181-201.
    17. Simon, Leo K & Stinchcombe, Maxwell B, 1995. "Equilibrium Refinement for Infinite Normal-Form Games," Econometrica, Econometric Society, vol. 63(6), pages 1421-1443, November.
    18. Schmeidler, David, 1980. "Walrasian Analysis via Strategic Outcome Functions," Econometrica, Econometric Society, vol. 48(7), pages 1585-1593, November.
    19. Giraud, Gael & Stahn, Hubert, 2003. "Efficiency and imperfect competition with incomplete markets," Journal of Mathematical Economics, Elsevier, vol. 39(5-6), pages 559-583, July.
    20. Stahn, Hubert, 1998. "On monopolistic equilibria with incomplete markets: the case of an exchange economy," Journal of Mathematical Economics, Elsevier, vol. 29(1), pages 83-107, January.
    21. Stahn, Hubert, 1999. "Monopolistic behaviors and general equilibrium: a generalization of Nikaido's work," Journal of Mathematical Economics, Elsevier, vol. 32(1), pages 87-112, August.
    22. Mertens, J. F., 2003. "The limit-price mechanism," Journal of Mathematical Economics, Elsevier, vol. 39(5-6), pages 433-528, July.
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    Cited by:

    1. Dutta, Bhaskar & Sen, Arunava, 2012. "Nash implementation with partially honest individuals," Games and Economic Behavior, Elsevier, vol. 74(1), pages 154-169.
    2. Dubey, Pradeep & Sondermann, Dieter, 2009. "Perfect competition in an oligopoly (including bilateral monopoly)," Games and Economic Behavior, Elsevier, vol. 65(1), pages 124-141, January.
    3. Gaël Giraud, 2007. "Walrasian non-tatonnement with incomplete and imperfectly competitive markets," Documents de travail du Centre d'Economie de la Sorbonne b07021, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.

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    More about this item

    Keywords

    Strategic boundedness; Weakly dominated strategy; Mechanism design;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General

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