On the solution of the KKT conditions of generalized Nash equilibrium problems

We consider the solution of generalized Nash equilibrium problems by concate-nating the KKT optimality conditions of each player’s optimization problem into a singleKKT-like system. We then propose two approaches for solving this KKT system. The firstapproach is rather simple and uses a merit-function/equation-based technique for the solutionof the KKT system. The second approach, partially motivated by the shortcomings of thefirst one, is an interior-point-based method. We show that this second approach has strongtheoretical properties and, in particular, that it is possible to establish global convergenceunder sensible conditions, this probably being the first result of its kind in the literature. Wediscuss the results of an extensive numerical testing on four KKT-based solution algorithmsshowing that the new interior-point method is efficient and very robust.