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Feasible and Continuous Double Implementation of Constrained Walrasian Allocations

Author

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  • Guoqiang Tian

    (Department of Economics, Texas A&M University)

Abstract

This paper provides a simple, feasible, and continuous mechanism whose Nash allocations and strong Nash allocations coincide with constrained Walrasian allocations for pure exchange economies. This mechanism allows not only references and initial endowments but also coalition patterns to be privately observed, a feature missing from much recent work in implementation theory. Unlike most mechanisms proposed in the literature, our mechanism works not only for three or more agents, but also for two-agent economies, and thus it is a unified mechanism which is irrespective of the number of agents. In addition, our implementation result is obtained without modifying individuals' preferences and thus it improves the mechanism proposed in Peleg (1996) without having to define artificial preference relations on price messages announced by individuals.

Suggested Citation

  • Guoqiang Tian, 2000. "Feasible and Continuous Double Implementation of Constrained Walrasian Allocations," Annals of Economics and Finance, Society for AEF, vol. 1(1), pages 19-32, May.
  • Handle: RePEc:cuf:journl:y:2000:v:1:i:1:p:19-32
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    References listed on IDEAS

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    1. Bevia, Carmen & Quinzii, Martine & Silva, Jose A., 1999. "Buying several indivisible goods," Mathematical Social Sciences, Elsevier, pages 1-23.
    2. Roth, Alvin E. & Sotomayor, Marilda, 1992. "Two-sided matching," Handbook of Game Theory with Economic Applications,in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 16, pages 485-541 Elsevier.
    3. van der Laan, Gerard & Talman, Dolf & Yang, Zaifu, 1997. "Existence of an equilibrium in a competitive economy with indivisibilities and money," Journal of Mathematical Economics, Elsevier, vol. 28(1), pages 101-109, August.
    4. Kaneko, Mamoru & Yamamoto, Yoshitsugu, 1986. "The existence and computation of competitive equilibria in markets with an indivisible commodity," Journal of Economic Theory, Elsevier, vol. 38(1), pages 118-136, February.
    5. Herbert Scarf, 1994. "The Allocation of Resources in the Presence of Indivisibilities," Journal of Economic Perspectives, American Economic Association, pages 111-128.
    6. Scarf, Herbert E, 1986. "Neighborhood Systems for Production Sets with Indivisibilities," Econometrica, Econometric Society, pages 507-532.
    7. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
    8. Bikhchandani, Sushil & Mamer, John W., 1997. "Competitive Equilibrium in an Exchange Economy with Indivisibilities," Journal of Economic Theory, Elsevier, vol. 74(2), pages 385-413, June.
    9. Gul, Faruk & Stacchetti, Ennio, 1999. "Walrasian Equilibrium with Gross Substitutes," Journal of Economic Theory, Elsevier, vol. 87(1), pages 95-124, July.
    10. Kelso, Alexander S, Jr & Crawford, Vincent P, 1982. "Job Matching, Coalition Formation, and Gross Substitutes," Econometrica, Econometric Society, vol. 50(6), pages 1483-1504, November.
    11. Danilov, V. & Koshevoy, G. & Lang, C., 2013. "Equilibria in Markets with Indivisible Goods," Journal of the New Economic Association, New Economic Association, vol. 18(2), pages 10-34.
    12. Roth, Alvin E. & Sotomayor, Marilda, 1992. "Two-sided matching," Handbook of Game Theory with Economic Applications,in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 16, pages 485-541 Elsevier.
    13. Yang, Zaifu, 2000. "Equilibrium in an exchange economy with multiple indivisible commodities and money," Journal of Mathematical Economics, Elsevier, vol. 33(3), pages 353-365, April.
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    Citations

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    Cited by:

    1. Olivier Bochet, 2007. "Implementation of the Walrasian correspondence: the boundary problem," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(2), pages 301-316, October.

    More about this item

    Keywords

    Incentive mechanism design; Walrasian allocations; Implementation;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis
    • D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy Formulation and Implementation

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