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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
DOI: https://doi.org/10.1090/S0002-9939-1988-0964853-5
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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DOI: https://doi.org/10.1090/S0002-9939-1988-0964853-5
Article copyright: © Copyright 1988 American Mathematical Society

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