A continuity result for the Nash equilibrium of a class of network games

We investigate a class of Nash equilibrium problems on networks where both the utility function and the strategy space of each player are parametrized by means of continuous functions of a vector parameter. We provide a variational inequality reformulation of the Nash equilibrium problem which turns out to be much simpler than the original problem. Moreover, under additional assumptions, the continuity of the solution with respect to the parameter is proved.