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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.

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File URL: ftp://mse.univ-paris1.fr/pub/mse/CES2009/09041.pdf
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Paper provided by Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne in its series Documents de travail du Centre d'Economie de la Sorbonne with number 09041.

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Length: 22 pages
Date of creation: Jan 2009
Date of revision: Oct 2009
Handle: RePEc:mse:cesdoc:09041

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Keywords: Stability index; acyclicity; strong Nash equilibrium; core; solvability; consistency; simple game; effectivity function.;

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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. Abdou, J, 1995. "Nash and Strongly Consistent Two-Player Game Forms," International Journal of Game Theory, Springer, vol. 24(4), pages 345-56.
  3. Rosenthal, Robert W., 1972. "Cooperative games in effectiveness form," Journal of Economic Theory, Elsevier, vol. 5(1), pages 88-101, August.
  4. Abdou, J., 2000. "Exact stability and its applications to strong solvability," Mathematical Social Sciences, Elsevier, vol. 39(3), pages 263-275, May.
  5. 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.
  6. 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.
  7. Eyal Winter & Bezalel Peleg, 2002. "original papers : Constitutional implementation," Review of Economic Design, Springer, vol. 7(2), pages 187-204.
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Cited by:
  1. Joseph Abdou, 2010. "Stability and Index of the Meet Game on a Lattice," Documents de travail du Centre d'Economie de la Sorbonne 10050, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  2. Joseph Abdou, 2012. "The structure of unstable power mechanisms," Economic Theory, Springer, vol. 50(2), pages 389-415, June.
  3. repec:hal:wpaper:halshs-00633589 is not listed on IDEAS

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