  We provide a unified variational inequality framework for the study of
fundamental properties of the Nash equilibrium in network games. We identify
several conditions on the underlying network (in terms of spectral norm,
infinity norm and minimum eigenvalue of its adjacency matrix) that guarantee
existence, uniqueness, convergence and continuity of equilibrium in general
network games with multidimensional and possibly constrained strategy sets. We
delineate the relations between these conditions and characterize classes of
networks that satisfy each of these conditions.
