Equilibria of lower semicontinuous games ☆ ☆☆

In this paper, we first introduce the notion of θ*-majorized (θπi*-majorized) correspondences which generalize θ-majorized correspondences and differs from L-majorized correspondences, and then, we give a new existence theorem of a maximal element. As its applications, we obtain some new existence theorems of an equilibrium for a qualitative game and an abstract economy.