Abstract
In this paper, we will introduce the concept of L S {L_S} -majorized correspondence and prove a new maximal element existence theorem on nonparacompact sets. As applications, we prove a new existence theorem of equilibrium for a nonparacompact 1 1 -person game with L S {L_S} -majorized preference correspondences, and then we prove that a nonparacompact N-person game with preference correspondences of class L L can be reduced to a 1 1 -person game with L S {L_S} -majorized preference correspondences.
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