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.
Original language | English (US) |
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Pages (from-to) | 467-471 |
Number of pages | 5 |
Journal | Economic Theory |
Volume | 4 |
Issue number | 3 |
DOIs | |
State | Published - May 1994 |
ASJC Scopus subject areas
- Economics and Econometrics