Journal Home Page

Cumulative Index

List of all Volumes

Complete Contents
of this Volume

Previous Article

Next Article

Minimax Theory and its Applications 05 (2020), No. 1, 047--064
Copyright Heldermann Verlag 2020

Generalized Nash Equilibrium Problems and Variational Inequalities in Lebesgue Spaces

Giandomenico Mastroeni
Dip. di Informatica, UniversitÓ di Pisa, 56127 Pisa, Italy

Massimo Pappalardo
Dip. di Informatica, UniversitÓ di Pisa, 56127 Pisa, Italy

Fabio Raciti
Dip. di Matematica e Informatica, UniversitÓ di Catania, 95125 Catania, Italy

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.

Keywords: Generalized Nash equilibrium, variational inequalities, Karush-Kuhn-Tucker conditions.

MSC: 90C33, 58E35, 90C30.

[ Fulltext-pdf  (140  KB)] for subscribers only.