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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| Format: | Article |
| Language: | English |
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Taylor and Francis
2007
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| Online Access: | http://irep.iium.edu.my/695/ http://irep.iium.edu.my/695/1/moussa_1-s2.0-S0893965907000080-main.pdf |
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| author | Nessaha, Rabia Larbani, Moussa Tazdait, Tarik |
| author_facet | Nessaha, Rabia Larbani, Moussa Tazdait, Tarik |
| author_sort | Nessaha, Rabia |
| building | IIUM Repository |
| collection | Online Access |
| 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].
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| first_indexed | 2025-11-14T14:19:03Z |
| format | Article |
| id | iium-695 |
| institution | International Islamic University Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T14:19:03Z |
| publishDate | 2007 |
| publisher | Taylor and Francis |
| recordtype | eprints |
| repository_type | Digital Repository |
| 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 |
| spellingShingle | QA75 Electronic computers. Computer science Nessaha, Rabia Larbani, Moussa Tazdait, Tarik A note on Berge equilibrium |
| title | 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_short | A note on Berge equilibrium |
| title_sort | note on berge equilibrium |
| topic | QA75 Electronic computers. Computer science |
| 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 |