A Stability Index for Local Effectivity Functions
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.
|Date of creation:||Jul 2008|
|Date of revision:|
|Publication status:||Published in Documents de travail du Centre d'Economie de la Sorbonne 2008.56 - ISSN : 1955-611X. 2008|
|Note:||View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-00331223|
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- Eyal Winter & Bezalel Peleg, 2002. "original papers : Constitutional implementation," Review of Economic Design, Springer, vol. 7(2), pages 187-204.
- 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, Hervé & Peleg, B., 1982.
"Cores of effectivity functions and implementation theory,"
Economics Papers from University Paris Dauphine
123456789/13220, Paris Dauphine University.
- Moulin, H. & Peleg, B., 1982. "Cores of effectivity functions and implementation theory," Journal of Mathematical Economics, Elsevier, vol. 10(1), pages 115-145, June.
- 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.
- Rosenthal, Robert W., 1972. "Cooperative games in effectiveness form," Journal of Economic Theory, Elsevier, vol. 5(1), pages 88-101, August.
- Abdou, J, 1995. "Nash and Strongly Consistent Two-Player Game Forms," International Journal of Game Theory, Springer, vol. 24(4), pages 345-56.
- 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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