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Alternative version of Shapley's theorem on closed coverings of a simplex

Author: Tatsuro Ichiishi
Journal: Proc. Amer. Math. Soc. 104 (1988), 759-763
MSC: Primary 47H10; Secondary 54B99, 90D12
MathSciNet review: 964853
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Abstract: Sperner's theorem as formulated by Ky Fan is dual to the KnasterKuratowski-Mazurkiewicz theorem. Shapley's theorem is a generalization of the Knaster-Kuratowski-Mazurkiewicz theorem. This paper points out that Shapley's theorem is a generalization of Sperner's theorem as well, by establishing an alternative version of Shapley's theorem. Applications to the multiperson cooperative game theory are also discussed.

References [Enhancements On Off] (What's this?)

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Article copyright: © Copyright 1988 American Mathematical Society

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