MinSup with Nash equilibrium constraints

We consider a two-stage model where a leader, according to its risk-averse proneness, solves a MinSup problem with constraints, corresponding to the reaction sets of a follower, defined by Nash equilibria of a non-cooperative game. We show that, in general, the security value of such MinSup problem is not stable under perturbations, in the sense that the sequence of the security values for the perturbed problems may not converge to the security value of the original problem even in presence of nice data. Then, we introduce different types of approximate values, close to the exact value under suitable assumptions, and we investigate their asymptotic behavior under perturbations.