<p>This work explores bilevel problems in the context of cardinality constraints. More specifically, Single-Leader-Multi-Follower (SLMF) games involving cardinality constraints are considered in two different configurations: one with the cardinality constraint at the leader’s level and a mixed structure in which the cardinality constraint is split between the leader and the followers. We prove existence results in both cases and provide equivalent reformulations allowing the numerical treatment of these complex problems. The results are illustrated thanks to an application to a facility location problem.</p>