We study whether single-leader-multi-follower (SLMF) problems can be reformulated as bilevel optimization problems. We consider both optimistic and pessimistic formulations in which the followers solve a generalized Nash equilibrium problem. For the optimistic case the answer is positive: we derive an equivalent bilevel problem by representing the followers’ equilibria as fixed points of the solution mapping of a single optimization problem. For pessimistic problems, the situation is different: we show that every optimistic trilevel problem admits an equivalent pessimistic SLMF formulation with two followers. Conversely, for every pessimistic SLMF problem verifying a mild attainability assumption we establish an equivalent optimistic trilevel reformulation. For rational linear data, these reformulations preserve linearity, have polynomial encoding length, and can be constructed in polynomial time. Consequently, the decision problem for optimistic single-leader multi-follower problems with rational linear data is NP-complete, whereas its pessimistic counterpart is Σ2p-complete. Thus, unless NP=Σ2p, the decision problem for general pessimistic SLMF problems with rational linear data does not admit a polynomial-time, polynomial-size reduction to rational linear bilevel optimization, which reveals a potentially unexpected difference between optimistic and pessimistic SLMF problems.