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

  • HERINGS , P.Jean-Jacques

    (Department of Economics and IRES, Université catholique de Louvain ( UCL), Louvain-la-Neuve, Belgium)

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.

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Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 1996003.

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Date of creation: 01 Feb 1996
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Handle: RePEc:cor:louvco:1996003
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