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A Stability Index for Local Effectivity Functions

  • Joseph Abdou


    (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS, EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics)

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.

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Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number halshs-00392508.

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Date of creation: Jan 2009
Date of revision:
Publication status: Published in Documents de travail du Centre d'Economie de la Sorbonne 2009.41 - ISSN : 1955-611X. 2009
Handle: RePEc:hal:cesptp:halshs-00392508
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  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, 2004. "Representation of effectivity functions by acceptable game forms: a complete characterization," Mathematical Social Sciences, Elsevier, vol. 47(3), pages 275-287, May.
  3. 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.
  4. Eyal Winter & Bezalel Peleg, 2002. "original papers : Constitutional implementation," Review of Economic Design, Springer, vol. 7(2), pages 187-204.
  5. Abdou, J, 1995. "Nash and Strongly Consistent Two-Player Game Forms," International Journal of Game Theory, Springer, vol. 24(4), pages 345-56.
  6. Rosenthal, Robert W., 1972. "Cooperative games in effectiveness form," Journal of Economic Theory, Elsevier, vol. 5(1), pages 88-101, August.
  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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