No benefit from adding forecast uncertainty when the robust Stackelberg strategy is a singleton

Demonstrate that in the robust commitment multi-follower setting, if the optimal robust Stackelberg commitment reduces to a single distribution (a singleton), then releasing uncertainty estimates around predictions and having followers respond via maximin using these intervals does not improve outcomes for the principal.

Background

The paper connects ambiguous commitments to decision-making under forecast uncertainty and robust responses. This conjecture asserts that when the robustly optimal commitment is already precise, augmenting forecasts with uncertainty intervals and letting followers play maximin against them cannot yield a better payoff.

Resolving this would delineate when the machinery of ambiguity (via forecast intervals) is redundant, and would guide mechanism and policy design by indicating when precise disclosure is sufficient.