Minimal Exact Balancedness
AbstractTo verify whether a transferable utility game is exact, one has to check a linear inequality for each exact balanced collection of coalitions. This paper studies the structure and properties of the class of exact balanced collections. Comparing the definition of exact balanced collections with the definition of balanced collections, the weight vector of a balanced collection must be positive whereas the weight vector for an exact balanced collection may contain one negative weight. We investigate minimal exact balanced collections, and show that only these collections are needed to obtain exactness. The relation between minimality of an exact balanced collection and uniqueness of the corresponding weight vector is analyzed. We show how the class of minimal exact balanced collections can be partitioned into three basic types each of which can be systematically generated.
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.
Bibliographic InfoPaper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2011-012.
Date of creation: 2011
Date of revision:
Contact details of provider:
Web page: http://center.uvt.nl
Cooperative games; exact games; exact balanced collections;
Other versions of this item:
- C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
This paper has been announced in the following NEP Reports:
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.:
- Péter Csóka & P. Jean-Jacques Herings & László Á. Kóczy, 2007.
"Balancedness Conditions for Exact Games,"
Working Paper Series
0805, Óbuda University, Keleti Faculty of Business and Management, revised May 2008.
- Csóka, Péter & Herings, P. Jean-Jacques & Kóczy, László Á,, 2007.
"Stable Allocations of Risk,"
040, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
- Peter Csoka & P. Jean-Jacques Herings, & Laszlo A. Koczy, 2007. "Stable Allocations of Risk," IEHAS Discussion Papers 0704, Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences.
- Péter Csóka & P. Jean-Jacques Herings & László Á. Kóczy, 2007. "Stable Allocations of Risk," Working Paper Series 0802, Óbuda University, Keleti Faculty of Business and Management, revised Apr 2008.
- Hans Haller & Jean Derks, 1999. "Weighted nucleoli," International Journal of Game Theory, Springer, vol. 28(2), pages 173-187.
- Calleja, Pedro & Borm, Peter & Hendrickx, Ruud, 2005. "Multi-issue allocation situations," European Journal of Operational Research, Elsevier, vol. 164(3), pages 730-747, August.
- Branzei, R. & Tijs, S. & Zarzuelo, J., 2009. "Convex multi-choice games: Characterizations and monotonic allocation schemes," European Journal of Operational Research, Elsevier, vol. 198(2), pages 571-575, October.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Richard Broekman).
If references are entirely missing, you can add them using this form.