On generalized equilibrium points
type: Item
instance of: scholarly article
title: On generalized equilibrium points
zbMATH Open document ID: 1063.90061
author: Peter Kas
author: Zehra Boratas Sensoy
author: Gábor Kassay
published in: Journal of Mathematical Analysis and Applications
publication date: 2004-08-19T00:00:00Z
review text: Let \(X=X_{1}\times X_{2}\times\cdots\times X_{n}\) be a product of Euclidean spaces and \(\varphi:X\times X\rightarrow\mathbb{R}\) be a function. This paper introduces the notion of \(\varepsilon\)-equilibrium point of \(f\), where \(\varepsilon=(\varepsilon_{1},\varepsilon_{2},\ldots\varepsilon_{n} )\in\mathbb{R}^{n}\), as follows: \(x=(x_{1},x_{2},\ldots x_{n})\in X\) is an \(\varepsilon\)-equilibrium point if for all \(y=(y_{1},y_{2},\ldots y_{n})\in X\), \(\varphi(x,y)\geq\sum_{i=1}^{n}\varepsilon_{i}\left\| x_{i} -y_{i}\right\| ^{2}\). The main result of the paper is an existence theorem for \(\varepsilon\)-equilibrium points. As an application, the particular cases of \(\varepsilon\)-saddle points and \(\varepsilon\)-Nash equilibria are examined and corresponding existence theorems are established.
Mathematics Subject Classification ID: 90C47
Mathematics Subject Classification ID: 91B50
Mathematics Subject Classification ID: 26B25
zbMATH DE Number: 2092951
zbMATH Keywords: equilibrium problem
zbMATH Keywords: Nash equilibria
zbMATH Keywords: approximate saddle point
reviewed by: Nicolas Hadjisavvas
MaRDI profile type: Publication
full work available at URL: j.jmaa.2004.04.030
OpenAlex ID: W2039856002
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DOI: 10.1016/J.JMAA.2004.04.030
description: scientific article; zbMATH DE number 2092951