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The least core, kernel and bargaining sets of large games

Author

Listed:
  • Dov Monderer

    (Faculty of Industrial Engineering and Management, Technion-Israel Institute of Technology, Haifa, ISRAEL)

  • Ezra Einy

    (Departamento de Economía, Universidad Carlos III de Madrid, E-28903 Getafe, Madrid, SPAIN)

  • Diego Moreno

    (Departamento de Economía, Universidad Carlos III de Madrid, E-28903 Getafe, Madrid, SPAIN)

Abstract

We study the least core, the kernel and bargaining sets of coalitional games with a countable set of players. We show that the least core of a continuous superadditive game with a countable set of players is a non-empty (norm-compact) subset of the space of all countably additive measures. Then we show that in such games the intersection of the prekernel and the least core is non-empty. Finally, we show that the Aumann-Maschler and the Mas-Colell bargaining sets contain the set of all countably additive payoff measures in the prekernel.

Suggested Citation

  • Dov Monderer & Ezra Einy & Diego Moreno, 1998. "The least core, kernel and bargaining sets of large games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 11(3), pages 585-601.
    • Handle: RePEc:spr:joecth:v:11:y:1998:i:3:p:585-601
    Note: Received: June 6, 1996; revised version: March 1, 1997
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    References listed on IDEAS

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    1. Einy, Ezra & Holzman, Ron & Monderer, Dov & Shitovitz, Benyamin, 1996. "Core equivalence theorems for infinite convex games," UC3M Working papers. Economics 3965, Universidad Carlos III de Madrid. Departamento de Economía.
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    Cited by:

    1. Massimiliano Amarante & Luigi Montrucchio, 2010. "The bargaining set of a large game," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 43(3), pages 313-349, June.
    2. 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.
    3. Massimiliano Amarante & Luigi Montrucchio, 2007. "Mas-Colell Bargaining Set of Large Games," Carlo Alberto Notebooks 63, Collegio Carlo Alberto.
    4. Luigi Montrucchio & Patrizia Semeraro, 2006. "Refinement Derivatives and Values of Games," Carlo Alberto Notebooks 9, Collegio Carlo Alberto.
    5. Luigi Montrucchio & Patrizia Semeraro, 2008. "Refinement Derivatives and Values of Games," Mathematics of Operations Research, INFORMS, vol. 33(1), pages 97-118, February.

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    1. Einy, Ezra & Holzman, Ron & Monderer, Dov, 1999. "On the Least Core and the Mas-Colell Bargaining Set," Games and Economic Behavior, Elsevier, vol. 28(2), pages 181-188, August.

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