Quasi-Equilibrium Problems with Non-Self Constraint Maps in Topological Spaces. Necessary and Sufficient Conditions for the Existence of Solutions

Quasi-equilibrium problems represent a general framework covering, in many situations, quasivariational inequalities, complementarity problems and generalized Nash equilibrium problems. In this work, we provide necessary and sufficient conditions guaranteeing the existence of a new kind of solution for quasi-equilibrium problems defined on Hausdorff topological spaces with non-self constraint maps. The main machineries for proving our results are a Tian’s fixed point theorem for the convex case, and the finite intersection property for the non-convex case. Furthermore, quasi-variational inequality problems and generalized Nash equilibrium problems are considered as applications.