General helpfulness of ambiguous commitment

Determine whether allowing the leader to commit to an ambiguous (set-valued) mixed strategy is generally helpful for maximizing the leader’s worst-case payoff in multi-follower Stackelberg games under the pessimistic payoff definition, and characterize conditions under which ambiguity helps or hurts.

Background

Throughout the paper, the authors provide examples where ambiguity strictly helps, strictly hurts, or is neutral for the leader’s payoff, indicating that benefits are highly context-dependent. They explicitly note uncertainty about the general usefulness of ambiguity.

A resolution would require characterizing game structures and response rules under which ambiguity is advantageous or detrimental, enabling principled mechanism design with ambiguous commitments.