We study generalized Nash equilibrium problems (GNEPs) in Lebesgue spaces by means of a family of variational inequalities (VIs) parametrized by an L∞ vector r(t). The solutions of this family of VIs constitute a subset of the solution set of the GNEP. For each choice of r(t), the VI solutions thus obtained are solutions of the GNEP which can be characterized by a certain relationship among the Karush-Kuhn-Tucker (KKT) multipliers of the players. This result extends a previous one, where only the case in which the parameter r is a constant vector was investigated, and can be considered as a full generalization, to Lebesgue spaces, of a classical property proven by J. B. Rosen [Existence and uniqueness of equilibrium points for concave n person games, Econometrica 33 (1965) 520–534] in finite dimensional spaces.

Generalized Nash equilibrium problems and variational inequalities in Lebesgue spaces

Raciti F.
2020-01-01

Abstract

We study generalized Nash equilibrium problems (GNEPs) in Lebesgue spaces by means of a family of variational inequalities (VIs) parametrized by an L∞ vector r(t). The solutions of this family of VIs constitute a subset of the solution set of the GNEP. For each choice of r(t), the VI solutions thus obtained are solutions of the GNEP which can be characterized by a certain relationship among the Karush-Kuhn-Tucker (KKT) multipliers of the players. This result extends a previous one, where only the case in which the parameter r is a constant vector was investigated, and can be considered as a full generalization, to Lebesgue spaces, of a classical property proven by J. B. Rosen [Existence and uniqueness of equilibrium points for concave n person games, Econometrica 33 (1965) 520–534] in finite dimensional spaces.
2020
Generalized Nash equilibrium
Karush-Kuhn-Tucker conditions
Variational inequalities
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11769/498161
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