Weak local Nash equilibrium
type: Item
instance of: scholarly article
title: Weak local Nash equilibrium
zbMATH Open document ID: 1298.91103
author: Carlos Biasi
author: Thaís F. M. Monis
published in: Topological Methods in Nonlinear Analysis
publication date: 2013-11-11T00:00:00Z
review text: Given metric spaces \((X_1,d_1),\dots, (X_n,d_n)\) and functions \(p_1,\dots,p_n:\) \(S_1\times\dots \times S_n\to\mathbb R\), the authors study the existence of a weak local equilibrium for \(p_1,\dots,p_n\), which is an \(\tilde s=(\tilde s_1,\dots,\tilde s_n)\in S_1\times\dots \times S_n\) such that for all \(\varepsilon>0\) there exists a \(\delta>0\) with \(p_i(\tilde s_1,\dots,\tilde s_{i-1},s_i,\tilde s_{i+1},\dots,\tilde s_n)\leq p_i(\tilde s)+\varepsilon d_i(s_i,\tilde s_i)\) whenever \(d_i(s_i,\tilde s_i)<\delta\) and \(1\leq i\leq n\).
Mathematics Subject Classification ID: 91B52
Mathematics Subject Classification ID: 55M20
Mathematics Subject Classification ID: 91A44
zbMATH DE Number: 6225523
zbMATH Keywords: fixed point
zbMATH Keywords: Nash equilibrium
zbMATH Keywords: weak local Nash equilibrium
zbMATH Keywords: proximative retract
reviewed by: Laszlo Zsilinszky
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 6225523