On Kakutani's Fixed Point Theorem, the K-K-M-S Theorem and the Core of a Balanced Game

Lloyd Shapley and Rajiv Vohra

Economic Theory, 1991, vol. 1, issue 1, 108-16

Abstract: We provide elementary proofs of Scarf's theorem on the non-emptiness of the core and of the K-K-M-S theorem, based.on Kakutani's fixed point theorem. We also show how these proofs can be modified to apply a coincidence theorem of Fan instead of Kakutani's fixed point theorem, for some additional simplicity.

Date: 1991
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