On the calculation of Nash equilibrium points with the aid of the smoothing approach

Let us consider a game with n players where the set of possible strategies depend on the decision of the other player. In this case, if the players behave rationally the solution is a point of generalized Nash equilibrium (GNE). These points can be obtained as solutions of a special class of bilevel programs. In this work, the bilevel problem is substituted by a simpler model which can be solved by the so called smoothing approach for mathematical programs with complementarity constraints. We discuss if the hypothesis for the convergence of this method are generically fulfilled or not.