Journal article
An Elementary Proof of the Knaster-Kuratowski-Mazurkiewicz-Shapley Theorem
Economic theory, Vol.4(3), pp.467-471
05/1994
DOI: 10.1007/BF01215384
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.
Details
- Title: Subtitle
- An Elementary Proof of the Knaster-Kuratowski-Mazurkiewicz-Shapley Theorem
- Creators
- Stefan Krasa - University of Illinois Urbana-ChampaignNicholas C. Yannelis - University of Illinois Urbana-Champaign
- Resource Type
- Journal article
- Publication Details
- Economic theory, Vol.4(3), pp.467-471
- Publisher
- Springer-Verlag
- DOI
- 10.1007/BF01215384
- ISSN
- 0938-2259
- eISSN
- 1432-0479
- Language
- English
- Date published
- 05/1994
- Academic Unit
- Economics
- Record Identifier
- 9984380484902771
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