The purpose of this paper is to establish general existence of equilibria for noncompact generalized games (respectively, noncompact abstract economics) under general setting of noncompact conditions and in which the L-majorized preference mappings may not have lower semicontinuity, and constraint correspondences are only lower or upper semicontinuous. In our model, strategic (respectively, commodity) spaces are not compact, the set of players (respectively, agents) are countable or uncountable, and underlying spaces are either finite- or infinite-dimensional locally topological vector spaces. Our results might be regarded as a unified theory for the corresponding results in the existing literatures in the study of generalized games (respectively, abstract economics) theory.