  The generalized Nash equilibrium problems play a significant role in modeling
and analyzing several complex economics problems. In this work, we consider
jointly convex generalized Nash games which were introduced by Rosen. We study
two important aspects related to these games, which include the weak sharpness
property for the set of normalized Nash equilibria and the linear conditioning
technique for regularized Nikaido-Isoda function. Firstly, we define the weak
sharpness property for the set of normalized Nash equilibria and then, we
provide its characterization in terms of the regularized gap function.
Furthermore, we provide the sufficient conditions under which the linear
conditioning criteria for regularized Nikaido-Isoda function becomes equivalent
to the weak sharpness property for the set of normalized Nash equilibria. We
show that an iterative algorithm used for determining a normalized Nash
equilibrium for jointly convex generalized Nash games terminates finitely under
the weak sharpness and linear conditioning assumptions. Finally, we estimate
the number of steps needed to determine a solution for the specific type of
jointly convex generalized Nash game as an application.
