  For generalized Nash equilibrium problems (GNEP) with shared constraints we
focus on the notion of normalized Nash equilibrium in the nonconvex setting.
The property of nondegeneracy for normalized Nash equilibria is introduced.
Nondegeneracy refers to GNEP-tailored versions of linear independence
constraint qualification, strict complementarity and second-order regularity.
Surprisingly enough, nondegeneracy of normalized Nash equilibrium does not
prevent from degeneracies at the individual players' level. We show that
generically all normalized Nash equilibria are nondegenerate. Moreover,
nondegeneracy turns out to be a sufficient condition for the local uniqueness
of normalized Nash equilibria. We emphasize that even in the convex setting the
proposed notion of nondegeneracy differs from the sufficient condition for
(global) uniqueness of normalized Nash equilibria, which is known from the
literature.
