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The least core, kernel, and bargaining sets of large games

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  • Einy, Ezra
  • Monderer, Dov
  • Moreno, Diego

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 countable additive measures. Then we show that in such games the intersection of the prekernel and least core is non-empty. Finally, we show that this intersection is contained in the Aumann-Maschler and the Mas-Colell bargaining sets.

Suggested Citation

  • Einy, Ezra & Monderer, Dov & Moreno, Diego, 1996. "The least core, kernel, and bargaining sets of large games," UC3M Working papers. Economics 4097, Universidad Carlos III de Madrid. Departamento de Economía.
    • Handle: RePEc:cte:werepe:4097
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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. Luigi Montrucchio & Patrizia Semeraro, 2006. "Refinement Derivatives and Values of Games," Carlo Alberto Notebooks 9, Collegio Carlo Alberto.
    4. Luigi Montrucchio & Patrizia Semeraro, 2008. "Refinement Derivatives and Values of Games," Mathematics of Operations Research, INFORMS, vol. 33(1), pages 97-118, February.
    5. Massimiliano Amarante & Luigi Montrucchio, 2007. "Mas-Colell Bargaining Set of Large Games," Carlo Alberto Notebooks 63, Collegio Carlo Alberto.

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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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    Keywords

    Coalitional games;

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