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- Title
An elementary proof of the Knaster-Kuratowski-Mazurkiewicz-Shapley Theorem.
- Authors
Krasa, Stefan; Yannelis, Nicholas C.
- 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.
- Subjects
FIXED point theory; NONLINEAR operators; UTILITY functions; OPERATOR theory; FUNCTIONAL analysis; MATHEMATICAL economics; GAME theory
- Publication
Economic Theory, 1994, Vol 4, Issue 3, p467
- ISSN
0938-2259
- Publication type
Article
- DOI
10.1007/BF01215384