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Nonconvergence of the Mas-Colell and Zhou Bargaining Sets

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  • Robert M. Anderson
  • Walter Trockel
  • Lin Zhou

Abstract

In an nontransferable utility (NTU) exchange economy with a continuum of agents, the Mas- Colell bargaining set coincides with the set of Walrasian equilibria. In this paper, we show that the Mas-Colell bargaining set, as well as a smaller bargaining set due to Zhou, may fail to converge to competitive outcomes in large finite NTU exchange economies.
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Suggested Citation

  • Robert M. Anderson & Walter Trockel & Lin Zhou, 1997. "Nonconvergence of the Mas-Colell and Zhou Bargaining Sets," Econometrica, Econometric Society, vol. 65(5), pages 1227-1240, September.
    • Handle: RePEc:ecm:emetrp:v:65:y:1997:i:5:p:1227-1240
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    References listed on IDEAS

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    1. Gerard Debreu, 1963. "On a Theorem of Scarf," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 30(3), pages 177-180.
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    Citations

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    Cited by:

    1. Roberto Serrano & Rajiv Vohra & Oscar Volij, 2001. "On the Failure of Core Convergence in Economies with Asymmetric Information," Econometrica, Econometric Society, vol. 69(6), pages 1685-1696, November.
    2. Hara, Chiaki, 2005. "Bargaining set and anonymous core without the monotonicity assumption," Journal of Mathematical Economics, Elsevier, vol. 41(4-5), pages 545-556, August.
    3. Sun, Ning & Trockel, Walter & Yang, Zaifu, 2008. "Competitive outcomes and endogenous coalition formation in an n-person game," Journal of Mathematical Economics, Elsevier, vol. 44(7-8), pages 853-860, July.
    4. Elena Iñarra & Roberto Serrano & Ken-Ichi Shimomura, 2020. "The Nucleolus, the Kernel, and the Bargaining Set: An Update," Revue économique, Presses de Sciences-Po, vol. 71(2), pages 225-266.
    5. Federico Echenique & Sumit Goel & SangMok Lee, 2022. "Stable allocations in discrete exchange economies," Papers 2202.04706, arXiv.org, revised Feb 2024.
    6. Graziano, Maria Gabriella & Pesce, Marialaura & Urbinati, Niccolò, 2020. "Generalized coalitions and bargaining sets," Journal of Mathematical Economics, Elsevier, vol. 91(C), pages 80-89.
    7. Hervés-Beloso, Carlos & Hervés-Estévez, Javier & Moreno-García, Emma, 2018. "Bargaining sets in finite economies," Journal of Mathematical Economics, Elsevier, vol. 74(C), pages 93-98.
    8. Kovalenkov, Alexander, 2002. "Simple Strategy-Proof Approximately Walrasian Mechanisms," Journal of Economic Theory, Elsevier, vol. 103(2), pages 475-487, April.
    9. Hervés-Estévez, Javier & Moreno-García, Emma, 2015. "A bargaining-Walras approach for finite economies," MPRA Paper 69802, University Library of Munich, Germany.
    10. Hervés-Estévez, Javier & Moreno-García, Emma, 2014. "On bargaining sets for finite economies," MPRA Paper 62303, University Library of Munich, Germany, revised 18 Jul 2014.
    11. Niccolò Urbinati, 2020. "Walrasian objection mechanism and Mas Colell's bargaining set in economies with many commodities," Working Papers 07, Department of Management, Università Ca' Foscari Venezia.
    12. Hara, Chiaki, 2002. "The anonymous core of an exchange economy," Journal of Mathematical Economics, Elsevier, vol. 38(1-2), pages 91-116, September.
    13. Bhowmik, Anuj & Saha, Sandipan, 2023. "Bargaining-equilibrium equivalence," MPRA Paper 117194, University Library of Munich, Germany.
    14. Niccolò Urbinati, 2023. "The Walrasian objection mechanism and Mas-Colell’s bargaining set in economies with many commodities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 76(1), pages 45-68, July.
    15. Javier Hervés-Estévez & Emma Moreno-García, 2018. "A limit result on bargaining sets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 66(2), pages 327-341, August.
    16. Hervés-Estévez, Javier & Moreno-García, Emma, 2015. "A convergence result for a bargaining set," MPRA Paper 69813, University Library of Munich, Germany.
    17. Liu, Jiuqiang, 2017. "Equivalence of the Aubin bargaining set and the set of competitive equilibria in a finite coalition production economy," Journal of Mathematical Economics, Elsevier, vol. 68(C), pages 55-61.
    18. Hervés-Estévez, Javier & Moreno-García, Emma, 2018. "Bargaining set with endogenous leaders: A convergence result," Economics Letters, Elsevier, vol. 166(C), pages 10-13.
    19. Bhowmik, Anuj & Saha, Sandipan, 2023. "Restricted bargaining sets in a club economy," MPRA Paper 119210, University Library of Munich, Germany.

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    More about this item

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D8 - Microeconomics - - Information, Knowledge, and Uncertainty

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