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An Elementary Proof of the Knaster-Kuratowski-Mazurkiewicz-Shapley Theorem
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An Elementary Proof of the Knaster-Kuratowski-Mazurkiewicz-Shapley Theorem

Stefan Krasa and Nicholas C. Yannelis
Economic theory, Vol.4(3), pp.467-471
05/1994
DOI: 10.1007/BF01215384

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Abstract

This note provides an elementary short proof of the Knaster-Kuratowski-Mazurkiewicz-Shapley (K-K-M-S) Theorem based on Brouwer's fixed point theorem. The usefulness of the K-K-M-S Theorem lies in the fact that it can be applied to prove directly Scarf's (1967) Theorem, i.e. any balanced game has a non-empty core. We also show that the K-K-M-S Theorem and the Gale-Nikaido-Debreu Theorem can be proved by the same arguments.
Brouwer fixed point theorem Coincidence Continuous functions Diagonal lemma Economic theory Existence theorems Exposita Notes Mathematical functions Mathematical sets Mathematical theorems

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