A Feasible Direction Interior Point Method for Generalized Nash Equilibrium with Shared Constraints

We present a new feasible direction interior point algorithm to compute a numerical solution of a normalized Generalized Nash Equilibrium Problem, (GNEP). The GNEP is an extension of the Nash Equilibrium Problem, (NEP). This one is an equilibrium problem that involves two or more players, each player is associated with a feasible strategy set and a payoff function. We assume that there is not collaboration among players. However, in the GNEP the feasible set depends on the strategies of the others players. The numerical method presented in this paper to compute an equilibrium point of the normalized version of the GNEP is a feasible direction Newton method to solve the necessary conditions characterizing the solution. Given an initial point at the interior of the feasible region, the present algorithm generates a feasible sequence converging to the solution of the normalized GNEP problem.