  We deal with the generalized Nash game proposed by Rosen, which is a game
with strategy sets that are coupled across players through a shared constraint.
A reduction to a classical game is shown, and as a consequence, Rosen's result
can be deduced from the one given by Arrow and Debreu. We also establish
necessary and sufficient conditions for a point to be a generalized Nash
equilibrium employing the variational inequality approach. Finally, some
existence results are given in the non-compact case under coerciveness
conditions.
