Abstract
In this paper, we propose a barrier function method for the generalized Nash equilibrium problem (GNEP) which, in contrast to the standard Nash equilibrium problem (NEP), allows the constraints for each player may depend on the rivals' strategies. We solve a sequence of NEPs, which are defined by logarithmic barrier functions of the joint inequality constraints. We demonstrate, under suitable conditions, that any accumulation point of the solutions to the sequence of NEPs is a solution to the GNEP. Moreover, a semismooth Newton method is used to solve the NEPs and sufficient conditions for the local superlinear convergence rate of the semismooth Newton method are derived. Finally, numerical results are reported to illustrate that the barrier approach for solving the GNEP is practical.
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