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Generalized Nash equilibrium problems and Newton methods

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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.

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Authors and Affiliations

  1. Department of Computer and System Sciences “A. Ruberti”, “Sapienza” Università di Roma, via Ariosto 25, 00185, Roma, Italy

    Francisco Facchinei & Veronica Piccialli

  2. Institute of Numerical Mathematics, Technische Universität Dresden, 01062, Dresden, Germany

    Andreas Fischer

Authors
  1. Francisco Facchinei
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  2. Andreas Fischer
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  3. Veronica Piccialli
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Correspondence to Francisco Facchinei.

Additional information

Dedicated to Stephen M. Robinson on the occasion of his 65th birthday, in honor of his fundamental contributions to mathematical programming.

The work of the first and third authors has been partially supported by MIUR-PRIN 2005 Research Program n.2005017083 “Innovative Problems and Methods in Nonlinear Optimization”.

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Facchinei, F., Fischer, A. & Piccialli, V. Generalized Nash equilibrium problems and Newton methods. Math. Program. 117, 163–194 (2009). https://doi.org/10.1007/s10107-007-0160-2

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  • DOI: https://doi.org/10.1007/s10107-007-0160-2

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