A simple proof of K-K-M-S theorem

DOI10.1007/BF01215383zbMath0858.54041WikidataQ30047867 ScholiaQ30047867MaRDI QIDQ1341505

Hidetoshi Komiya

Publication date: 25 March 1997

Published in: Economic Theory (Search for Journal in Brave)

zbMATH Keywords

Kakutani fixed point theoremBerge maximum theoremK-K-M-S theoremKnaster-Kuratowski-Mazurkiewicz and Shapley theorem

Mathematics Subject Classification ID

Cooperative games (91A12) Fixed-point and coincidence theorems (topological aspects) (54H25)

Related Items (14)

An elementary proof of the Knaster-Kuratowski-Mazurkiewicz-Shapley theorem ⋮ A theorem on open coverings of a simplex and Scarf's core existence theorem through Brouwer's fixed point theorem ⋮ Fair distributions for more participants than allocations ⋮ Intersection theorems with a continuum of intersection points ⋮ KKM type theorems with boundary conditions ⋮ Rental harmony with roommates ⋮ Fair division with multiple pieces ⋮ A sparse colorful polytopal KKM theorem ⋮ Existence of fuzzy cores and generalizations of the K-K-M-S theorem ⋮ The \((p, q)\) property in families of \(d\)-intervals and \(d\)-trees ⋮ Intermediate value theorem for simplices for simplicial approximation of fixed points and zeros ⋮ Fractional covers and matchings in families of weighted \(d\)-intervals ⋮ A direct proof of Shapley-Sperner's lemma based on the KKMS lemma ⋮ Generalization of the Bolzano theorem for simplices

Cites Work

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• On the Knaster-Kuratowski-Mazurkiewicz-Shapley theorem
• On Kakutani's fixed point theorem, the K-K-M-S theorem and the core of a balanced game
• An elementary proof of the Knaster-Kuratowski-Mazurkiewicz-Shapley theorem
• Extensions of two fixed point theorems of F. E. Browder
• A generalization of Brouwer's fixed point theorem
• The Core of an N Person Game
• Some theorems on the core of ann-Game without Side-Payments

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