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| HAL: hal-00711094, version 1 |
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| Uniqueness of equilibrium on rings |
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| Frédéric Meunier 1Thomas Pradeau 1 |
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| (2012-06-22) |
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| We consider congestion games on networks with nonatomic users and user-specific costs. We are interested in the uniqueness property defined by Milchtaich [Milchtaich, I. 2005. Topological conditions for uniqueness of equilibrium in networks. Math. Oper. Res. 30 225-244] as the uniqueness of equilibrium flows for all assignments of strictly increasing cost functions. He settled the case with two-terminal networks. In the present work we characterize completely bidirectional rings for which the uniqueness property holds. The main result is that it holds precisely for nine networks and those obtained from them by elementary operations. For other bidirectional rings, we exhibit affine cost functions yielding to two distinct equilibrium flows. Related results are also proven. |
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| 1: | Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique (CERMICS) |
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Ecole des Ponts ParisTech |
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| Subject | : | Computer Science/Computer Science and Game Theory Mathematics/Optimization and Control |
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| congestion externalities – nonatomic games – ring – transportation network – uniqueness property |
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| hal-00711094, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00711094 | |
| oai:hal.archives-ouvertes.fr:hal-00711094 | |
| From: Frédéric Meunier | |
| Submitted on: Friday, 22 June 2012 13:34:33 | |
| Updated on: Friday, 22 June 2012 14:15:55 | |
