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

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Author Info
P. Jean-Jacques Herings (Department of Econometrics and CentER, Tilburg University, P.O. Box 90153, 5000 LE Tilburg, THE NETHERLANDS)

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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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Publisher Info
Article provided by Springer 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
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Find related papers by JEL classification:
C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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  1. Herings, P.J.J. & Laan, G. van der & Talman, D., 2000. "Cooperative games in graph structure," Discussion Paper 90, Tilburg University, Center for Economic Research. [Downloadable!]
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  2. Talman, D. & Herings, P.J. & Laan, G. van der, 2003. "Socially structured games and their applications," Discussion Paper 40, Tilburg University, Center for Economic Research. [Downloadable!]
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  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. [Downloadable!]
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  4. P. Herings & Gerard Laan & Dolf Talman, 2007. "Socially Structured Games," Theory and Decision, Springer, vol. 62(1), pages 1-29, February. [Downloadable!] (restricted)
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