An elementary proof of the Knaster-Kuratowski-Mazurkiewicz-Shapley Theorem
نویسنده
چکیده
This note provides an elementary short proof of the Knas t e r 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 Ga le -N ika ido -Debreu Theorem can be proved by the same arguments.
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