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Stability and Index of the Meet Game on a Lattice

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  • Joseph M. Abdou

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

Abstract

We study the stability and the stability index of the meet game form defined on a meet-semilattice. Given any active coalition structure, we show that the stability index relative to the equilibrium, to the beta core and to the exact core is a function of the Nakamura number, the depth of the semilattice and its gap function.

Suggested Citation

  • Joseph M. Abdou, 2010. "Stability and Index of the Meet Game on a Lattice," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00497447, HAL.
    • Handle: RePEc:hal:cesptp:halshs-00497447
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00497447
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    References listed on IDEAS

    as
    1. Moulin, H. & Peleg, B., 1982. "Cores of effectivity functions and implementation theory," Journal of Mathematical Economics, Elsevier, vol. 10(1), pages 115-145, June.
    2. Peleg,Bezalel, 2008. "Game Theoretic Analysis of Voting in Committees," Cambridge Books, Cambridge University Press, number 9780521074650, September.
    3. Abdou, Joseph, 2010. "A stability index for local effectivity functions," Mathematical Social Sciences, Elsevier, vol. 59(3), pages 306-313, May.
    4. Abdou, Joseph & Keiding, Hans, 2003. "On necessary and sufficient conditions for solvability of game forms," Mathematical Social Sciences, Elsevier, vol. 46(3), pages 243-260, December.
    5. repec:dau:papers:123456789/13220 is not listed on IDEAS
    6. Joseph Abdou, 2012. "The structure of unstable power mechanisms," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 50(2), pages 389-415, June.
    7. Abdou, J., 2000. "Exact stability and its applications to strong solvability," Mathematical Social Sciences, Elsevier, vol. 39(3), pages 263-275, May.
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    More about this item

    Keywords

    Effectivity function; lattice; stability index; equilibrium; Nakamura number; Fonction d'effectivité; treillis; stabilité; coeur; équilibre;
    All these keywords.

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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