A stability index for local effectivity functions
AbstractWe 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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Bibliographic InfoPaper 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 b08056.
Length: 18 pages
Date of creation: Jul 2008
Date of revision:
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More information through EDIRC
Effectivity function; local effectivity function; acyclicity; stability index; Nakamura Number; acyclicity.;
Other versions of this item:
- 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.
- 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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- Rosenthal, Robert W., 1972. "Cooperative games in effectiveness form," Journal of Economic Theory, Elsevier, vol. 5(1), pages 88-101, August.
- 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.
- Moulin, H. & Peleg, B., 1982.
"Cores of effectivity functions and implementation theory,"
Journal of Mathematical Economics,
Elsevier, vol. 10(1), pages 115-145, June.
- Moulin, Hervé & Peleg, B., 1982. "Cores of effectivity functions and implementation theory," Economics Papers from University Paris Dauphine 123456789/13220, Paris Dauphine University.
- 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.
- Eyal Winter & Bezalel Peleg, 2002. "original papers : Constitutional implementation," Review of Economic Design, Springer, vol. 7(2), pages 187-204.
- Abdou, J., 2000. "Exact stability and its applications to strong solvability," Mathematical Social Sciences, Elsevier, vol. 39(3), pages 263-275, May.
- Abdou, J, 1995. "Nash and Strongly Consistent Two-Player Game Forms," International Journal of Game Theory, Springer, vol. 24(4), pages 345-56.
- repec:hal:cesptp:halshs-00633589 is not listed on IDEAS
- 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.
- repec:hal:wpaper:halshs-00633589 is not listed on IDEAS
- Joseph Abdou, 2012. "The structure of unstable power mechanisms," Economic Theory, Springer, vol. 50(2), pages 389-415, June.
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