An elementary proof of the Knaster-Kuratowski-Mazurkiewicz-Shapley Theorem |
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Authors: | Stefan Krasa Nicholas C Yannelis |
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Institution: | (1) Department of Economics, University of Illinois at Urbana-Champaign, 61820 Champaign, IL, USA |
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Abstract: | Summary 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.We wish to thank Roko Aliprantis for useful comments. |
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