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

DOI10.1007/BF01210576zbMath0807.90141WikidataQ29307071 ScholiaQ29307071MaRDI QIDQ1338125

Rajiv Vohra, Lloyd S. Shapley

Publication date: 27 November 1994

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

zbMATH Keywords

Kakutani's fixed point theoremnon-emptiness of the core

Mathematics Subject Classification ID

Cooperative games (91A12) Fixed-point and coincidence theorems (topological aspects) (54H25) General equilibrium theory (91B50)

Related Items (19)

A simple proof of K-K-M-S theorem ⋮ 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 ⋮ Intersection theorems with a continuum of intersection points ⋮ KKM type theorems with boundary conditions ⋮ Rental harmony with roommates ⋮ Non-emptiness of the fuzzy core in a finite production economy with infinite-dimensional commodity space ⋮ Balanced 2-subsets ⋮ Stable sharing ⋮ A necessary and sufficient condition for an NTU fuzzy game to have a non-empty fuzzy core ⋮ Existence of fuzzy cores and generalizations of the K-K-M-S theorem ⋮ On the non-emptiness of the fuzzy core ⋮ Existence of Edgeworth and competitive equilibria and fuzzy cores in coalition production economies ⋮ Payoff-dependent balancedness and cores ⋮ Intermediate value theorem for simplices for simplicial approximation of fixed points and zeros ⋮ The unbinding core for coalitional form games ⋮ A direct proof of Shapley-Sperner's lemma based on the KKMS lemma ⋮ An extension of the KKMS theorem ⋮ Generalization of the Bolzano theorem for simplices

Cites Work

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• On the Knaster-Kuratowski-Mazurkiewicz-Shapley theorem
• Extensions of two fixed point theorems of F. E. Browder
• Non-cooperative games
• A generalization of Brouwer's fixed point theorem
• WELFARE ECONOMICS AND EXISTENCE OF AN EQUILIBRIUM FOR A COMPETITIVE ECONOMY
• Alternative Version of Shapley's Theorem on Closed Coverings of a Simplex
• The Core of an N Person Game
• Some theorems on the core of ann-Game without Side-Payments

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