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Stability and index of the meet game on a lattice

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  • Joseph Abdou

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. Copyright Springer-Verlag 2012

Suggested Citation

  • Joseph Abdou, 2012. "Stability and index of the meet game on a lattice," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(4), pages 775-789, November.
    • Handle: RePEc:spr:jogath:v:41:y:2012:i:4:p:775-789
    DOI: 10.1007/s00182-012-0339-5
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    References listed on IDEAS

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    1. Abdou, Joseph, 2010. "A stability index for local effectivity functions," Mathematical Social Sciences, Elsevier, vol. 59(3), pages 306-313, May.
    2. Moulin, H. & Peleg, B., 1982. "Cores of effectivity functions and implementation theory," Journal of Mathematical Economics, Elsevier, vol. 10(1), pages 115-145, June.
    3. Peleg,Bezalel, 2008. "Game Theoretic Analysis of Voting in Committees," Cambridge Books, Cambridge University Press, number 9780521074650, October.
    4. 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.
    5. Abdou, J., 2000. "Exact stability and its applications to strong solvability," Mathematical Social Sciences, Elsevier, vol. 39(3), pages 263-275, May.
    6. 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.
    7. repec:dau:papers:123456789/13220 is not listed on IDEAS
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    More about this item

    Keywords

    Effectivity function; Lattice; Stability index; Equilibrium; Nakamura number; C70; D71; 91A44;
    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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