This paper has two central aims: first, to provide simple conditions under
which the generalized games in choice form and, consequently, the abstract
economies, admit equilibrium; second, to study the solvability of several types
of systems of vector quasi-equilibrium problems as an application. Our work
outlines that there still is much to be gained from using the results
concerning the existence of equilibrium of games as tools of research for other
optimization problems.Comment: 20 page