Existence of sender gain from ambiguous communication under prior ambiguity (non-singleton priors)

Determine whether, in the ambiguous persuasion game with Maxmin Expected Utility preferences and a non-singleton ambiguous prior set P over a finite state space, there exists an ambiguous experiment Σ (a closed, convex set of statistical experiments) such that the receiver’s obedient strategy that follows action recommendations is a best response to Σ but not a best response to any individual statistical experiment σ in Σ, thereby enabling the sender to strictly benefit from ambiguous communication beyond standard (non-ambiguous) experiments.

Background

The paper studies ambiguous persuasion with prior ambiguity under Maxmin Expected Utility (MEU). For singleton prior sets, earlier work shows that ambiguous communication does not benefit the sender because obedience of an ambiguous experiment implies obedience of some contained statistical experiment, eliminating any gain from ambiguity.

When the prior set P is non-singleton, the set of worst-case joint distributions K*(Σ) for an ambiguous experiment may include convex combinations of extreme points induced by different priors. Consequently, obedience of Σ need not decompose into obedience for any particular σ ∈ Σ, creating a potential pathway for sender gains from ambiguity. The note proves that no such gain arises in the binary state and binary action case, but does not resolve whether such gains can occur in more general environments.