An extremely simple proof of the K-K-M-S Theorem
Abstract
An extremely simple proof of the K-K-M-S Theorem is given involving only Brouwer's fixed point theorem and some elementary calculus. A function is explicitly given such that a fixed point of it yields an intersection point of a balanced collection of sets together with balancing weights. Moreover, any intersection point of a balanced collection of sets together with balancing weights corresponds to a fixed point of the function. Furthermore, the proof can be used to show $\pi $-balanced versions of the K-K-M-S Theorem, with $\pi $-balancedness as introduced in Billera (1970). The proof makes clear that the conditions made with respect to $\pi $ by Billera can be even weakened.Download Info
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.
Bibliographic Info
Article provided by Springer in its journal Economic Theory.
Volume (Year): 10 (1997)
Issue (Month): 2 ()
Pages: 361-367
Note: Received: January 22, 1996; revised version June 9, 1996
Contact details of provider:
Web page: http://link.springer.de/link/service/journals/00199/index.htm
Order Information:
Web: http://link.springer.de/orders.htm
Related research
Keywords:Other versions of this item:
- HERINGS , P.Jean-Jacques, 1996. "An Extremely Simple Proof of the K-K-M-S Theorem," CORE Discussion Papers 1996003, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Herings, P.J.J., 1997. "An Extremely Simple Proof of the K-K-M-S Theorem," Open Access publications from Maastricht University urn:nbn:nl:ui:27-5942, Maastricht University.
- C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
References
No references listed on IDEASYou can help add them by filling out this form.
Citations
Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.Cited by:
- Herings, P.J.J. & Laan, G. van der & Talman, A.J.J., 2003.
"Socially Structured Games and their Applications,"
Discussion Paper
2003-40, Tilburg University, Center for Economic Research.
- Herings,P. Jean-Jacques & Laan, van der,Gerard & Talman,Dolf, 2003. "Socially Structured Games and Their Applications," Research Memoranda 024, Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization.
- Herings, P.J.J. & Laan, G. van der & Talman, A.J.J., 2007.
"Socially structured games,"
Open Access publications from Tilburg University
urn:nbn:nl:ui:12-195975, Tilburg University.
- P. Herings & Gerard Laan & Dolf Talman, 2007. "Socially Structured Games," Theory and Decision, Springer, vol. 62(1), pages 1-29, February.
- Herings, P. Jean-Jacques & Laan, Gerard van der & Talman, Dolf, 2007. "Socially structured games," Open Access publications from Maastricht University urn:nbn:nl:ui:27-22840, Maastricht University.
- Herings, P.J.J. & Laan, G. van der & Talman, A.J.J., 2000.
"Cooperative Games in Graph Structure,"
Discussion Paper
2000-90, Tilburg University, Center for Economic Research.
- Herings,P. Jean-Jacques & Laan,Gerard,van der & Talman,Dolf, 2000. "Cooperative Games in Graph Structure," Research Memoranda 011, Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization.
- Herings,P. Jean-Jacques & Laan,Gerard,van der & Talman,Dolf, 2002. "Cooperative Games in Graph Structure," Research Memoranda 011, Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization.
- Herings,P. Jean-Jacques & Predtetchinski,Arkadi, 2002.
"A Necessary and Sufficient Condition for Non--emptiness of the Core of a Non--transferable Utility Game,"
Research Memoranda
016, Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization.
- Predtetchinski, Arkadi & Jean-Jacques Herings, P., 2004. "A necessary and sufficient condition for non-emptiness of the core of a non-transferable utility game," Journal of Economic Theory, Elsevier, vol. 116(1), pages 84-92, May.
- Predtetchinski, Arkadi & Herings, P. Jean-Jacques, 2004. "A necessary and sufficient condition for nonemptiness of the core of a non-transferable utility game," Open Access publications from Maastricht University urn:nbn:nl:ui:27-12168, Maastricht University.
Lists
This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.Statistics
Access and download statisticsCorrections
When requesting a correction, please mention this item's handle: RePEc:spr:joecth:v:10:y:1997:i:2:p:361-367For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Guenther Eichhorn) or (Christopher F Baum).
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.