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Jiuqiang Liu, Variational inequalities, Ky Fan minimax inequality, and strong Nash equilibria in generalized games

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DOI: 10.23952/jnva.8.2024.2.04

Volume 8, Issue 2, 1 April 2024, Pages 249-264

 

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.

 

How to Cite this Article:
J. Liu, Variational inequalities, Ky Fan minimax inequality, and strong Nash equilibria in generalized games, J. Nonlinear Var. Anal. 8 (2024), 249-264.