Abstract: A new class of system of generalized vector quasi-equilibrium problems (SGVQEP) is introduced and studied in generalized convex spaces. By using an existence theorem of maximal elements for a family of set-valued mappings due to the author, a new equilibriu existence theorem for generalized games is proved. As applications, some new existence theorems of solutions for the SGVQEP are established in noncompact product G-convex spaces.

Key words: Maximal element, Generalized game, System of generalized vector quasi-equilibrium problems, Product G-convex spaces