The generalized Nash game proposed by Rosen

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.