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

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.

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Year of publication:	1994
Authors:	Krasa, Stefan ; Yannelis, Nicholas C
Published in:	Economic Theory. - Springer. - Vol. 4.1994, 3, p. 467-71
Publisher:	Springer

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10005370687