A note on Berge equilibrium

This work is a contribution on the problem of the existence of Berge equilibrium. Abalo and Kostreva give an existence theorem for this equilibrium that appears in the papers [K.Y. Abalo, M.M. Kostreva, Berge equilibrium: Some recent results from fixed-point theorems, Appl. Math. Comput. 169 (2005)...

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Main Authors:	Nessaha, Rabia, Larbani, Moussa, Tazdait, Tarik
Format:	Article
Language:	English
Published:	Taylor and Francis 2007
Subjects:	QA75 Electronic computers. Computer science
Online Access:	http://irep.iium.edu.my/695/ http://irep.iium.edu.my/695/ http://irep.iium.edu.my/695/1/moussa_1-s2.0-S0893965907000080-main.pdf

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recordtype	eprints
spelling	iium-6952013-06-25T02:35:36Z http://irep.iium.edu.my/695/ A note on Berge equilibrium Nessaha, Rabia Larbani, Moussa Tazdait, Tarik QA75 Electronic computers. Computer science This work is a contribution on the problem of the existence of Berge equilibrium. Abalo and Kostreva give an existence theorem for this equilibrium that appears in the papers [K.Y. Abalo, M.M. Kostreva, Berge equilibrium: Some recent results from fixed-point theorems, Appl. Math. Comput. 169 (2005) 624–638; K.Y. Abalo, M.M. Kostreva, Some existence theorems of Nash and Berge equilibria, Appl. Math. Lett. 17 (2004) 569–573]. We found that the assumptions of these theorems are not sufficient for the existence of Berge equilibrium. Indeed, we construct a game that verifies Abalo and Kostreva’s assumptions, but has no Berge equilibrium. Then we provide a condition that overcomes the problem in these theorems. Our conclusion is also valid for Radjef’s theorem, which is the basic reference for [K.Y. Abalo, M.M. Kostreva, Berge equilibrium: Some recent results from fixed-point theorems, Appl. Math. Comput. 169 (2005) 624–638; K.Y. Abalo, M.M. Kostreva, Some existence theorems of Nash and Berge equilibria, Appl. Math. Lett. 17 (2004) 569–573; K.Y. Abalo, M.M. Kostreva, Fixed points, Nash games and their organizations, Topol. Methods Nonlinear Anal. 8 (1996) 205–215; K.Y. Abalo, M.M. Kostreva, Equi-well-posed games, J. Optim. Theory Appl. 89 (1996) 89–99]. Taylor and Francis 2007-08 Article PeerReviewed application/pdf en http://irep.iium.edu.my/695/1/moussa_1-s2.0-S0893965907000080-main.pdf Nessaha, Rabia and Larbani, Moussa and Tazdait, Tarik (2007) A note on Berge equilibrium. Applied Mathematics Letters, 20 (8). pp. 926-932. ISSN 1350-4851 10.1016/j.aml.2006.09.005
repository_type	Digital Repository
institution_category	Local University
institution	International Islamic University Malaysia
building	IIUM Repository
collection	Online Access
language	English
topic	QA75 Electronic computers. Computer science
spellingShingle	QA75 Electronic computers. Computer science Nessaha, Rabia Larbani, Moussa Tazdait, Tarik A note on Berge equilibrium
description	This work is a contribution on the problem of the existence of Berge equilibrium. Abalo and Kostreva give an existence theorem for this equilibrium that appears in the papers [K.Y. Abalo, M.M. Kostreva, Berge equilibrium: Some recent results from fixed-point theorems, Appl. Math. Comput. 169 (2005) 624–638; K.Y. Abalo, M.M. Kostreva, Some existence theorems of Nash and Berge equilibria, Appl. Math. Lett. 17 (2004) 569–573]. We found that the assumptions of these theorems are not sufficient for the existence of Berge equilibrium. Indeed, we construct a game that verifies Abalo and Kostreva’s assumptions, but has no Berge equilibrium. Then we provide a condition that overcomes the problem in these theorems. Our conclusion is also valid for Radjef’s theorem, which is the basic reference for [K.Y. Abalo, M.M. Kostreva, Berge equilibrium: Some recent results from fixed-point theorems, Appl. Math. Comput. 169 (2005) 624–638; K.Y. Abalo, M.M. Kostreva, Some existence theorems of Nash and Berge equilibria, Appl. Math. Lett. 17 (2004) 569–573; K.Y. Abalo, M.M. Kostreva, Fixed points, Nash games and their organizations, Topol. Methods Nonlinear Anal. 8 (1996) 205–215; K.Y. Abalo, M.M. Kostreva, Equi-well-posed games, J. Optim. Theory Appl. 89 (1996) 89–99].
format	Article
author	Nessaha, Rabia Larbani, Moussa Tazdait, Tarik
author_facet	Nessaha, Rabia Larbani, Moussa Tazdait, Tarik
author_sort	Nessaha, Rabia
title	A note on Berge equilibrium
title_short	A note on Berge equilibrium
title_full	A note on Berge equilibrium
title_fullStr	A note on Berge equilibrium
title_full_unstemmed	A note on Berge equilibrium
title_sort	note on berge equilibrium
publisher	Taylor and Francis
publishDate	2007
url	http://irep.iium.edu.my/695/ http://irep.iium.edu.my/695/ http://irep.iium.edu.my/695/1/moussa_1-s2.0-S0893965907000080-main.pdf
first_indexed	2023-09-18T20:07:51Z
last_indexed	2023-09-18T20:07:51Z
_version_	1777407278858633216

A note on Berge equilibrium

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