Nonsymmetric variants of the prekernel and the prenucleolus
A solution on a class of TU games that satisfies the axioms of the pre-nucleolus or -kernel except the equal treatment property and is single valued for two-person games, is a nonsymmetric pre-nucleolus (NSPN) or -kernel (NSPK). We investigate the NSPKs and NSPNs and their relations to the positive prekernel and to the positive core. It turns out that any NSPK is a subsolution of the positive prekernel. Moreover, we show that an arbitrary NSPK, when applied to a TU game, intersects the set of preimputations whose dissatisfactions coincide with the dissatisfactions of an arbitrary element of any other NSPK applied to this game. This result also provides a new proof of sufficiency of the characterizing conditions for NSPKs introduced by Orshan (Non-symmetric prekernels, discussion paper 60. Center for Rationality, The Hebrew University of Jerusalem, 1994 ). Any NSPN belongs to “its” NSPK. Several classes of NSPNs are presented, all of them being subsolutions of the positive core. We show that any NSPN is a subsolution of the positive core provided that it satisfies the equal treatment property on an infinite subset of the universe of potential players. Moreover, we prove that, for any game whose prenucleolus is in its anticore, any NSPN coincides with the prenucleolus. Copyright Springer-Verlag 2012
If 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.
Volume (Year): 41 (2012)
Issue (Month): 4 (November)
|Contact details of provider:|| Web page: http://link.springer.de/link/service/journals/00182/index.htm|
|Order Information:||Web: http://link.springer.de/orders.htm|
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.:
- Peleg, B, 1986. "On the Reduced Game Property and Its Converse," International Journal of Game Theory, Springer, vol. 15(3), pages 187-200.
- Bezalel Peleg & Peter Sudhölter, 1998. "The Positive Prekernel of a Cooperative Game," Center for Mathematical Economics Working Papers 292, Center for Mathematical Economics, Bielefeld University.
- Peter Sudhölter & Yan-An Hwang, 2001. "Axiomatizations of the core on the universal domain and other natural domains," International Journal of Game Theory, Springer, vol. 29(4), pages 597-623.
- Guni Orshan & Peter Sudhölter, 2010.
"The positive core of a cooperative game,"
International Journal of Game Theory,
Springer, vol. 39(1), pages 113-136, March.
- Aumann, Robert J. & Maschler, Michael, 1985. "Game theoretic analysis of a bankruptcy problem from the Talmud," Journal of Economic Theory, Elsevier, vol. 36(2), pages 195-213, August.
- Orshan, Gooni, 1993. "The Prenucleolus and the Reduced Game Property: Equal Treatment Replaces Anonymity," International Journal of Game Theory, Springer, vol. 22(3), pages 241-48.
When requesting a correction, please mention this item's handle: RePEc:spr:jogath:v:41:y:2012:i:4:p:809-828. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Sonal Shukla)or (Christopher F Baum)
If references are entirely missing, you can add them using this form.