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Coincidence of the Mas-Colell bargaining set and the set of competitive equilibria in a continuum coalition production economy

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  • Jiuqiang Liu

    (Xi’an University of Finance and Economics
    Eastern Michigan University)

  • Huihui Zhang

    (Central China Normal University)

Abstract

Mas-Colell (J Math Econ 18:129–139, 1989) proved that the bargaining set and the set of competitive allocations coincide in an exchange economy with a continuum of traders under some standard assumptions. We extend this result to continuum coalition production economies and prove that the bargaining set and the set of competitive allocations coincide in a coalition production economy with a continuum of traders under some standard assumptions. As a consequence, we obtain a coincidence theorem for the core and the set of competitive allocations in a coalition production economy which extends the well-known coincidence theorem by Aumann (Econometrica 32:39–50, 1964).

Suggested Citation

  • Jiuqiang Liu & Huihui Zhang, 2016. "Coincidence of the Mas-Colell bargaining set and the set of competitive equilibria in a continuum coalition production economy," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(4), pages 1095-1109, November.
    • Handle: RePEc:spr:jogath:v:45:y:2016:i:4:d:10.1007_s00182-015-0511-9
    DOI: 10.1007/s00182-015-0511-9
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    References listed on IDEAS

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    Cited by:

    1. Avishay Aiche, 2019. "On the equal treatment imputations subset in the bargaining set for smooth vector-measure games with a mixed measure space of players," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(2), pages 411-421, June.
    2. Graziano, Maria Gabriella & Pesce, Marialaura & Urbinati, Niccolò, 2020. "Generalized coalitions and bargaining sets," Journal of Mathematical Economics, Elsevier, vol. 91(C), pages 80-89.
    3. Jiuqiang Liu, 2022. "Equivalence of Competitive Equilibria, Fuzzy Cores, and Fuzzy Bargaining Sets in Finite Production Economies," Mathematics, MDPI, vol. 10(18), pages 1-16, September.
    4. Chiara Donnini & Marialaura Pesce, 2021. "Fairness and fuzzy coalitions," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(4), pages 1033-1052, December.
    5. Bhowmik, Anuj & Saha, Sandipan, 2023. "Bargaining-equilibrium equivalence," MPRA Paper 117194, University Library of Munich, Germany.
    6. 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.
    7. 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.
    8. Cui Li & Doudou Wu & Tengfei Shao, 2023. "Research on Sustainable Cooperation Strategies for Cross-Regional Supply Chain Enterprises in Uncertain Environments," Sustainability, MDPI, vol. 15(22), pages 1-31, November.
    9. Bhowmik, Anuj & Saha, Sandipan, 2023. "Restricted bargaining sets in a club economy," MPRA Paper 119210, University Library of Munich, Germany.

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