A variational inequality method for computing a normalized equilibrium in the generalized Nash game

The generalized Nash equilibrium problem is a generalization of the standard Nash equilibrium problem, in which both the utility function and the strategy space of each player may depend on the strategies chosen by all other players. This problem has been used to model various problems in applications but convergent solution algorithms are extremely scare in the literature. In this article, we show that a generalized Nash equilibrium can be calculated by solving a variational inequality (VI). Moreover, conditions for the local superlinear convergence of a semismooth Newton method being applied to the VI are also given. Some numerical results are presented to illustrate the performance of the method.