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.

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Bibliographic Info

Article provided by Springer & Society for the Advancement of Economic Theory (SAET) in its journal Economic Theory.

Volume (Year): 10 (1997)
Issue (Month): 2 ()
Pages: 361-367

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 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: Web page: http://www.springer.com Order Information: Web: http://www.springer.com/economics/economic+theory/journal/199/PS2

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