ON THE CALCULATION OF NASH EQUILIBRIUM POINTS WITH THE AID OF THE SMOOTHING APPROACH

Abstract

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.