A flexible minimax theorem
type: Item
instance of: scholarly article
title: A flexible minimax theorem
zbMATH Open document ID: 0818.49007
DOI: 10.1007/BF01874944
published in: Acta Mathematica Hungarica
publication date: 1995-07-18T00:00:00Z
review text: The paper deals with a generalization of the von Neumann's minimax theorem in topological spaces, i.e., some sufficient conditions are suggested for the equality of minimax and maximin. The conditions are given in an abstract form that is also specified in the paper. Namely, the conditions assume compactness of any Lebesgue set of the pay-off function with respect to \(y\) for any \(x\), pseudoconnectedness of such set intersection, and their jointness for different \(x\). For any of the latter two conditions, the author proves other sufficient conditions and compaires them with the previous results. Thus, there are unified various minimax theorems, including one for quasiconcave functions (with respect to \(x\)) in the sense of interval spaces.
Mathematics Subject Classification ID: 49J35
zbMATH DE Number: 556296
zbMATH Keywords: von Neumann's minimax theorem
zbMATH Keywords: compactness
zbMATH Keywords: Lebesgue set
zbMATH Keywords: pay-off function
zbMATH Keywords: pseudoconnectedness
zbMATH Keywords: quasiconcave functions
zbMATH Keywords: interval spaces
author: Stephen Simons
reviewed by: N. M. Novikova
MaRDI profile type: Publication
cites work: Minimax Theorems
cites work: Q3670035
cites work: Topological Minimax Theorems
cites work: Minimax theorems without linear structure
cites work: Q3723194
cites work: A general minimax theorem
cites work: Note on my paper ''A simple proof for von Neumann's minimax theorem''
cites work: A note on Ky Fan's minimax theorem
cites work: Minimax theorems for interval spaces
cites work: Q3834585
cites work: Elementary proof for Sion's minimax theorem
cites work: Minimax theorems for upper semicontinuous functions
cites work: Über das von-Neumannsche Minimax-Theorem
cites work: A symmetric minimax theorem without linear structure
cites work: Bemerkungen zum von Neumannschen Minimaxtheorem
cites work: An upward-downward minimax theorem
cites work: Q3200113
cites work: Minimax theorems with staircases
cites work: Q3976097
cites work: On general minimax theorems
cites work: Q3876570
cites work: Some Minimax Theorems.
cites work: Q4074698
cites work: On the general minimax theorem
cites work: Q5724368
description: scientific article; zbMATH DE number 556296