Béal, Sylvain () (Sonderforschungsbereich 504) Durieu, Jacques (CREUSET, University of Saint-Etienne) Solal, Philippe (CREUSET, University of Saint-Etienne)
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We study farsighted coalitional stability in the context of TUgames. Chwe (1994, p.318) notes that, in this context, it is difficult to prove nonemptiness of the largest consistent set. We show that every TU-game has a nonempty largest consistent set. Moreover, the proof of this result points out that each TU-game has a farsighted stable set. We go further by providing a characterization of the collection of farsighted stable sets in TU-games. We also show that the farsighted core of a TU-game is empty or is equal to the set of imputations of the game. Next, the relationships between the core and the largest consistent set are studied in superadditive TU-games and in clan games. In the last section, we explore the stability of the Shapley value. It is proved that the Shapley value of a superadditive TU-game is always a stable imputation: it is a core imputation or it constitutes a farsighted stable set. A necessary and sufficient condition for a superadditive TU-game to have the Shapley value in the largest consistent set is given.
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Paper provided by Sonderforschungsbereich 504, Universität Mannheim & Sonderforschungsbereich 504, University of Mannheim in its series Sonderforschungsbereich 504 Publications with number
07-57.
Length: 40 pages Date of creation: 06 Aug 2007 Date of revision: Handle: RePEc:xrs:sfbmaa:07-57
Note: Financial support from the Deutsche Forschungsgemeinschaft, SFB 504, at the University of Mannheim, is gratefully acknowledged. Contact details of provider: Postal: D-68131 Mannheim Phone: (49) (0) 621-292-2547 Fax: (49) (0) 621-292-5594 Email: Web page: http://www.sfb504.uni-mannheim.de/ More information through EDIRC
References listed on IDEAS Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
Branzei, Rodica & Dimitrov, Dinko & Tijs, Stef, 2006.
"Convex games versus clan games,"
Discussion Paper
58, Tilburg University, Center for Economic Research.
[Downloadable!]
Other versions:
Rodica Branzei & Dinko Dimitrov & Stef Tijs, 2006.
"Convex games versus clan games,"
Working Papers
381, Bielefeld University, Institute of Mathematical Economics.
[Downloadable!]