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Bargaining Sets with Small Coalitions

Author

Listed:
  • Ulla Schjødt

    (Institute of Mathematics, University of Copenhagen)

  • Birgitte Sloth

    (Institute of Economics, University of Copenhagen)

Abstract

The paper considers various cooperative equilibrium/solution concepts for atomless exchange economies. A famous result states that in such economies the core is equal to the set of Walrasian equilibria. We consider two arguments against using the core as solution concept in large economies: (1) A coalition will not block an allocation, if the agents fear that this will imply counterobjections from other coalitions, and there by result in an allocation which is worse than the original allocation. (2) A coalition will not block an allocation, if the coalition is too large to form. Each argument leads to definition of new solution concepts. (1) leads to the 'bargaining set' (two different definitions are considered in the paper) and (2) leads to 'the e-core'. We discuss these solution concepts and their relation to the core and the Walrasian equilibria. Then we try to define solution concepts taking both arguments into consideration. The results show that the bargaining set is not an equilibrium concept, but a concept demanding either equilibrium or 'no equilibria one step away', and that the bargaining set, in contrast to the core, is very sensible to the exact definition.

Suggested Citation

  • Ulla Schjødt & Birgitte Sloth, 1990. "Bargaining Sets with Small Coalitions," Discussion Papers 90-18, University of Copenhagen. Department of Economics.
    • Handle: RePEc:kud:kuiedp:9018
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    Cited by:

    1. Hervés-Estévez, Javier & Moreno-García, Emma, 2015. "A bargaining-Walras approach for finite economies," MPRA Paper 69802, University Library of Munich, Germany.
    2. 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.
    3. 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.
    4. Javier Hervés-Estévez & Emma Moreno-García, 2015. "On restricted bargaining sets," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(3), pages 631-645, August.
    5. 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.
    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. 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.
    8. Bhowmik, Anuj & Saha, Sandipan, 2023. "Restricted bargaining sets in a club economy," MPRA Paper 119210, University Library of Munich, Germany.
    9. Hervés-Estévez, Javier & Moreno-García, Emma, 2012. "Some remarks on restricted bargaining sets," MPRA Paper 39385, University Library of Munich, Germany, revised 10 Jun 2012.

    More about this item

    Keywords

    bargaining; coalition; game theory and bargaining theory;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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