k-Balanced games and capacities
AbstractIn this paper, we present a generalization of the concept of balanced game for finite games. Balanced games are those having a nonempty core, and this core is usually considered as the solution of the game. Based on the concept of k-additivity, we define the so-called k-balanced games and the corresponding generalization of core, the k-additive core, whose elements are not directly imputations but k-additive games. We show that any game is k-balanced for a suitable choice of k, so that the corresponding k-additive core is not empty. For the games in the k-additive core, we propose a sharing procedure to get an imputation and a representative value for the expectations of the players based on the pessimistic criterion. Moreover, we look for necessary and sufficient conditions for a game to be k-balanced. For the general case, it is shown that any game is either balanced or 2-balanced. Finally, we treat the special case of capacities.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Bibliographic InfoArticle provided by Elsevier in its journal European Journal of Operational Research.
Volume (Year): 200 (2010)
Issue (Month): 2 (January)
Contact details of provider:
Web page: http://www.elsevier.com/locate/eor
Cooperative games k-Additivity Balanced games Capacities Core;
Other versions of this item:
- Pedro Miranda & Michel Grabisch, 2008. "K-balanced games and capacities," Documents de travail du Centre d'Economie de la Sorbonne b08079, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
- C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
- D7 - Microeconomics - - Analysis of Collective Decision-Making
You can help add them by filling out this form.
CitEc Project, subscribe to its RSS feed for this item.
- Stéphane Gonzalez & Michel Grabisch, 2012.
"Preserving coalitional rationality for non-balanced games,"
UniversitÃ© Paris1 PanthÃ©on-Sorbonne (Post-Print and Working Papers)
- Stéphane Gonzalez & Michel Grabisch, 2012. "Preserving coalitional rationality for non-balanced games," Documents de travail du Centre d'Economie de la Sorbonne 12022, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
- Stéphane Gonzalez & Michel Grabisch, 2012. "Preserving coalitional rationality for non-balanced games," Documents de travail du Centre d'Economie de la Sorbonne 12022r, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Apr 2013.
- repec:hal:journl:halshs-00718358 is not listed on IDEAS
- repec:hal:cesptp:hal-00625339 is not listed on IDEAS
- Grabisch, Michel & Li, Tong, 2011.
"On the set of imputations induced by the k-additive core,"
European Journal of Operational Research,
Elsevier, vol. 214(3), pages 697-702, November.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei).
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.