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The generalized Nash equilibrium problems play a significant role in modelingand analyzing several complex economics problems. In this work, we considerjointly convex generalized Nash games which were introduced by Rosen. We studytwo important aspects related to these games, which include the weak sharpnessproperty for the set of normalized Nash equilibria and the linear conditioningtechnique for regularized Nikaido-Isoda function. Firstly, we define the weaksharpness property for the set of normalized Nash equilibria and then, weprovide its characterization in terms of the regularized gap function.Furthermore, we provide the sufficient conditions under which the linearconditioning criteria for regularized Nikaido-Isoda function becomes equivalentto the weak sharpness property for the set of normalized Nash equilibria. Weshow that an iterative algorithm used for determining a normalized Nashequilibrium for jointly convex generalized Nash games terminates finitely underthe weak sharpness and linear conditioning assumptions. Finally, we estimatethe number of steps needed to determine a solution for the specific type ofjointly convex generalized Nash game as an application.

Finite Convergence Criteria for Normalized Nash Equilibrium through Weak Sharpness and Linear Conditioning