# An extremely simple proof of the K-K-M-S Theorem

## Author Info

• P. Jean-Jacques Herings

(Department of Econometrics and CentER, Tilburg University, P.O. Box 90153, 5000 LE Tilburg, THE NETHERLANDS)

## 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.

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

as in new window
Handle: RePEc:spr:joecth:v:10:y:1997:i:2:p:361-367

Note: Received: January 22, 1996; revised version June 9, 1996
Contact details of provider:

Order Information:

## Related research

Keywords:

Other versions of this item:

Find related papers by JEL classification:
• C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

## References

No references listed on IDEAS
You 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.
as in new window

Cited by:
1. 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.
2. 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.
3. 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.
4. 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.

## Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

## Corrections

When requesting a correction, please mention this item's handle: RePEc:spr:joecth:v:10:y:1997:i:2:p:361-367. 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: (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.