Generalized Nash Equilibrium Problems and Variational Inequalities in Lebesgue Spaces
Keywords:
Generalized Nash equilibrium, variational inequalities, Karush-Kuhn-Tucker condi tionsAbstract
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.
Downloads
Downloads
Published
Issue
Section
License
You are free to:
- Share — copy and redistribute the material in any medium or format for any purpose, even commercially.
- Adapt — remix, transform, and build upon the material for any purpose, even commercially.
- The licensor cannot revoke these freedoms as long as you follow the license terms.
Under the following terms:
- Attribution — You must give appropriate credit , provide a link to the license, and indicate if changes were made . You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.
Notices:
You do not have to comply with the license for elements of the material in the public domain or where your use is permitted by an applicable exception or limitation .
No warranties are given. The license may not give you all of the permissions necessary for your intended use. For example, other rights such as publicity, privacy, or moral rights may limit how you use the material.
