Generalized Nash equilibrium problems and Newton methods

Authors:
Francisco Facchinei;Andreas Fischer;Veronica Piccialli
Affiliations:
“Sapienza” Università di Roma, Department of Computer and System Sciences “A. Ruberti”, via Ariosto 25, 00185, Roma, Italy;Technische Universität Dresden, Institute of Numerical Mathematics, via Ariosto 25, 01062, Dresden, Germany;“Sapienza” Università di Roma, Department of Computer and System Sciences “A. Ruberti”, via Ariosto 25, 00185, Roma, Italy
Venue:
Mathematical Programming: Series A and B
Year:
2008

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Abstract

The generalized Nash equilibrium problem, where the feasible sets of the players may depend on the other players’ strategies, is emerging as an important modeling tool. However, its use is limited by its great analytical complexity. We consider several Newton methods, analyze their features and compare their range of applicability. We illustrate in detail the results obtained by applying them to a model for internet switching.