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A Stability Index for Local Effectivity Functions

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Abstract

We study the structure of unstable local effectivity functions defined for n players and p alternatives. A stability index based on the notion of cycle is introduced. In the particular case of simple games, the stability index is closely related to the Nakamura Number. In general it may be any integer between 2 and p. We prove that the stability index for maximal effectivity functions and for maximal local effectivity functions is either 2 or 3

Suggested Citation

  • Joseph Abdou, 2009. "A Stability Index for Local Effectivity Functions," Documents de travail du Centre d'Economie de la Sorbonne 09041, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Oct 2009.
    • Handle: RePEc:mse:cesdoc:09041
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    File URL: ftp://mse.univ-paris1.fr/pub/mse/CES2009/09041.pdf
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    Cited by:

    1. is not listed on IDEAS
    2. 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.
    3. Joseph M. Abdou, 2009. "The Structure of Unstable Power Systems," Post-Print halshs-00392515, HAL.
    4. repec:hal:wpaper:halshs-00633589 is not listed on IDEAS
    5. 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.

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    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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