A Generalized $$\Gamma $$-Convergence Concept for a Class of Equilibrium Problems

Abstract

A novel generalization of $$\Gamma $$ Γ -convergence applicable to a class of equilibrium problems is studied. After the introduction of the latter, a variety of its applications is discussed. The existence of equilibria with emphasis on Nash equilibrium problems is investigated. Subsequently, our $$\Gamma $$ Γ -convergence notion for equilibrium problems is introduced and discussed as well as applied to a class of penalized generalized Nash equilibrium problems and quasi-variational inequalities. The work ends with a comparison of our results to previous generalizations in the literature.