Equilibrium selection in oligopolistic markets

Quantity competition between firms producing a variety of differentiated goods is considered in an oligopolistic framework. The com- petition is modelled as a Nash equilibrium problem. To tackle the pres- ence of multiple equilibria, we consider a bilevel problem to choose a so- lution among the equilibria according to some selection criterion. Since the resulting problem violates standard constraint qualifications, we in- troduce inexactness into the lower-level in order to gain regularity. An algorithm to solve the resulting inexact bilevel problem is devised rely- ing on successive approximations and exact penalization techniques. The results of some preliminary numerical tests are reported.