An Extremely Simple Proof of the K-K-M-S Theorem

P. Jean-Jacques Herings

No 1996003, LIDAM Discussion Papers CORE from Université catholique de Louvain, Center for Operations Research and Econometrics (CORE)

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 1T-balancedness as introduced in Billera (1970). The proof makes clear that the conditions made with respect to [pi] by Billera can be even weakened.

Date: 1996-02-01
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Journal Article: An extremely simple proof of the K-K-M-S Theorem (1997)
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