Variational inequalities, Ky Fan minimax inequality, and strong nash equilibria in generalized games
Document Type
Article
Publication Date
2024
Department/School
Mathematics
Publication Title
Journal of Nonliear and Variational Analysis
Abstract
In this paper, we provide necessary and sufficient conditions for the existence of solutions for variational inequalities and sufficient conditions for the existence of solutions for quasi-Ky Fan minimax inequality, quasi-variational inequalities, and generalized variational inequalities. As applications, we apply these results to derive existence results for strong Nash equilibria in generalized games which generalize some existence theorems for Nash equilibria in generalized games in the literature and the existence theorem for strong Nash equilibria in normal-form games by Nessah and Tian [J. Math. Anal. Appl. 414 (2014), 871-885]. We also provide sufficient conditions for the uniqueness of strong Nash equilibria in certain generalized games.
Link to Published Version
Recommended Citation
Liu, J. (2024). Variational inequalities, Ky Fan minimax inequality, and strong nash equilibria in generalized games. Journal of Nonlinear and Variational Analysis, 8(2), 249–264. https://doi.org/10.23952/jnva.8.2024.2.04
Comments
J. Liu is a faculty member in EMU's Department of Mathematics and Statistics.