  We consider an extension of a noncooperative game problem where players have
joint binding constraints. In this case, justification of a generalized
equilibrium point needs a reasonable mechanism for attaining this state. We
suggest to combine a penalty method together with shares allocation of
right-hand sides, which replaces the initial problem with a sequence of the
usual Nash equilibrium problems together with an upper level variational
inequality as a master problem. We show convergence of solutions of these
auxiliary penalized problems to a solution of the initial game problem under
weak coercivity conditions.
