No ambiguity advantage in single-follower games when the ambiguous set contains the precise Stackelberg optimum

Show that in any single-follower Stackelberg game, any ambiguous leader commitment set P_L ⊆ Δ(A_L) that contains the optimal classical Stackelberg mixed strategy p_L^* is suboptimal for the leader relative to committing precisely to p_L^*, i.e., ambiguity confers no advantage when P_L includes p_L^*.

Background

Earlier in the paper, the authors prove that for single-follower games, ambiguity is generally unnecessary for pessimistic payoffs. This conjecture strengthens that intuition by asserting that any ambiguous commitment set that includes the optimal precise strategy is strictly worse than committing to that strategy alone.

Establishing this would crystallize a boundary between single- and multi-follower settings, showing that ambiguity’s benefits are fundamentally multiplex in nature and not present when only one follower responds.