Acyclic versions of the von Neumann and Nash equilibrium theorems
type: Item
instance of: scholarly article
title: Acyclic versions of the von Neumann and Nash equilibrium theorems
zbMATH Open document ID: 0947.47039
DOI: 10.1016/S0377-0427(99)00246-0
published in: Journal of Computational and Applied Mathematics
publication date: 2000-11-02T00:00:00Z
review text: The author rewrites earlier results of his [J. Korean Math. Soc. 35, No. 4, 803-829 (1998; Zbl 0923.47034)] for the case of compositions of acyclic-valued maps: For \(i=1,\dots,n\) let \(E_i\) be a topological vector space, \(X_i\subset E_i\) a convex set, \(K_i\subset X_i\) a nonempty compact set and \(T_i\) an upper semicontinuous map from \(X:=\prod_{j=1}^n X_j\) into the compact acyclic subsets of \(K_i\). If \(X\) is admissible in \(\prod_{i=1}^n E_i\) (i.e., if for every compact set \(K\subset X\) and each neighbourhood \(U\) of zero there is a finite dimensional map \(h:K\to X\) such that \(x-h(x)\in U\) for all \(x\in K\)) then there is an \(x\in\prod_{i=1}^nK_i\) such that \(x_i\in T_i(x)\) for \(i=1,\dots,n\). Standard arguments then yield the usual equilibrium theorems.
Mathematics Subject Classification ID: 47H04
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 54C60
zbMATH DE Number: 1398398
zbMATH Keywords: multivalued map
zbMATH Keywords: acyclic map
zbMATH Keywords: von Neumann intersection theorem
zbMATH Keywords: Nash equilibrium
author: Sehie Park
reviewed by: Christian Fenske
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1398398