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

P. Jean-Jacques Herings

Economic Theory, 1997, vol. 10, issue 2, 367 pages

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.

JEL-codes: C71 (search for similar items in EconPapers)
Date: 1997
Note: Received: January 22, 1996; revised version June 9, 1996
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Citations: View citations in EconPapers (13)

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