Geodesic
Generalized Nash Equilibrium Problems and Variational Inequalities in Lebesgue Spaces
Minimax theory and its applications, Tome 5 (2020) no. 1
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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.
Mots-clés : Generalized Nash equilibrium, variational inequalities, Karush-Kuhn-Tucker condi tions 
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     author = {Giandomenico Mastroeni,Massimo Pappalardo and Fabio Raciti},
     title = {Generalized {Nash} {Equilibrium} {Problems} and {Variational} {Inequalities} in {Lebesgue} {Spaces}},
     journal = {Minimax theory and its applications},
     year = {2020},
     volume = {5},
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Giandomenico Mastroeni,Massimo Pappalardo; Fabio Raciti. Generalized Nash Equilibrium Problems and Variational Inequalities in Lebesgue Spaces. Minimax theory and its applications, Tome 5 (2020) no. 1. http://geodesic.mathdoc.fr/item/MTA_2020_5_1_a4/