Alternative version of Shapley’s theorem on closed coverings of a simplex
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- by Tatsuro Ichiishi PDF
- Proc. Amer. Math. Soc. 104 (1988), 759-763 Request permission
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
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Additional Information
- © Copyright 1988 American Mathematical Society
- 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