Majorized correspondences and equilibrium existence in discontinuous games

This paper is aimed at widening the scope of applications of majorized correspondences. A new class of majorized correspondences -- domain U-majorized correspondences -- is introduced. For them, a maximal element existence theorem is established. Then, sufficient conditions for the existence of an equilibrium in qualitative games are provided. They are used to show the existence of a pure strategy Nash equilibrium in compact quasiconcave games that are either correspondence secure or correspondence transfer continuous.