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

✍ Scribed by Lloyd Shapley; Rajiv Vohra


Publisher
Springer
Year
1991
Tongue
English
Weight
551 KB
Volume
1
Category
Article
ISSN
0938-2259

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We give two combinatorial proofs of Franks' Theorem, that an area preserving torus homeomorphism with mean rotation zero has a fixed point. The first proof uses Lax's version of the Marriage Theorem. The second proof uses Euler's Theorem on circuits in graphs and an explicit method of Alpern for dec