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The Equitable Bargaining Set

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Abstract

We define the equitable bargaining set for exchange economies. Our definition differs from that in Mas-Colell (1989) because it requires that objections and counterobjections must satisfy some equitability conditions. We show that the equitable bargaining set coincides with that of Mas-Colell when the underlying economy is atomless, but not in general. Then we provide two sets of conditions for economies with market imperfections that apply to finite economies and to mixed market economies. In the first case our conditions imply that the equitable bargaining set is a subset of the core, and so it converges to the set of competitive allocations if the economy is replicated. In the second case, we show that all allocations in the equitable bargaining set are competitive, extending the Walras-bargaining equivalence of Mas-Colell (1989) to the framework of mixed markets. All the conditions we use follow from well-established assumptions from the literature in finite and mixed market economies.

Suggested Citation

  • Maria Gabriella Graziano & Marialaura Pesce & Niccolo Urbinati, 2023. "The Equitable Bargaining Set," CSEF Working Papers 676, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.
    • Handle: RePEc:sef:csefwp:676
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    References listed on IDEAS

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    1. Schjodt, Ulla & Sloth, Birgitte, 1994. "Bargaining Sets with Small Coalitions," International Journal of Game Theory, Springer;Game Theory Society, vol. 23(1), pages 49-55.
    2. Greenberg, Joseph & Shitovitz, Benyamin, 1986. "A simple proof of the equivalence theorem for oligopolistic mixed markets," Journal of Mathematical Economics, Elsevier, vol. 15(2), pages 79-83, April.
    3. Mas-Colell,Andreu, 1990. "The Theory of General Economic Equilibrium," Cambridge Books, Cambridge University Press, number 9780521388702.
    4. Busetto, Francesca & Codognato, Giulio & Ghosal, Sayantan & Julien, Ludovic & Tonin, Simone, 2018. "Noncooperative oligopoly in markets with a continuum of traders and a strongly connected set of commodities," Games and Economic Behavior, Elsevier, vol. 108(C), pages 478-485.
    5. Gerard Debreu, 1963. "On a Theorem of Scarf," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 30(3), pages 177-180.
    6. Green, Jerry R., 1972. "On the inequitable nature of core allocations," Journal of Economic Theory, Elsevier, vol. 4(2), pages 132-143, April.
    7. 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.
    8. Mas-Colell, Andreu, 1989. "An equivalence theorem for a bargaining set," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 129-139, April.
    9. Maschler, Michael, 1976. "An advantage of the bargaining set over the core," Journal of Economic Theory, Elsevier, vol. 13(2), pages 184-192, October.
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    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Bargaining set; Core; Equal treatment property; Walrasian objections.;
    All these keywords.

    JEL classification:

    • D62 - Microeconomics - - Welfare Economics - - - Externalities
    • D85 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Network Formation
    • I12 - Health, Education, and Welfare - - Health - - - Health Behavior
    • I18 - Health, Education, and Welfare - - Health - - - Government Policy; Regulation; Public Health

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