Genericity Analysis of Multi-Leader-Disjoint-Followers Game

Multi-leader-follower games are models which combine bilevel programming with generalized Nash games. Due to their many applications, they have attracted more and more attention in the last few years. We introduce here a particular case of the so-called multi-leader-disjoint-followers (MLDF) game where there are several leaders acting according to a generalized Nash game and each leader has a number of exclusive followers who interact through a standard Nash game between them. The aim of this paper is to characterize the generic properties of the solutions for an MLDF problem. We show that, generically, good properties such as constraint qualifications and nondegeneracy of the solutions are satisfied at each bilevel problem, except for a zero-Lebesgue measure set and with at most quadratic perturbations of the involved functions. We also prove that these properties will remain stable under small perturbations of the involved functions.