Existence of equilibria for generalized games and generalized social systems with coordination

The general existence of equilibria for non-compact generalized games in which the L-majorized preference mappings may not have lower semicontinuity is established. It is shown that the constraint mappings may only be either lower of upper semicontinuous and the set of players may not be countable. The underlying spaces are also shown to be either infinite dimensional locally convex topological vector spaces.