On Kakutani's fixed point theorem, the K-K-M-S theorem and the core of a balanced game

Shapley, Lloyd; Vohra, Rajiv
January 1991
Economic Theory;1991, Vol. 1 Issue 1, p108
Academic Journal
We provide elementary proofs of Scarfs theorem on the non-emptiness of the core and of the K-K-M-S thoerem, 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.


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