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
Mastroeni G.;Pappalardo M.
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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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
