Bayesian Persuasion with a Risk-Conscious Receiver
For mechanism designers and economists, this paper extends Bayesian persuasion to risk-conscious receivers, showing that while standard results break, the problem remains tractable under explicit finite-state models.
The paper studies Bayesian persuasion when the receiver uses Conditional Value-at-Risk (CVaR) instead of expected utility, showing that standard direct-recommendation reduction fails but an active-facet revelation principle enables an exact polynomial-size linear program. It also identifies a tractability boundary and provides an approximation scheme for certain risk preferences.
We study Bayesian persuasion when the receiver evaluates actions by reward-side Conditional Value-at-Risk (CVaR) rather than expected utility. CVaR preferences break the standard action-based direct-recommendation reduction: merging signals that recommend the same action can change the receiver's tail-risk ranking and destroy incentive compatibility. We show that this failure does not imply intractability in the explicit finite-state model. Each CVaR action value is max-affine in the posterior, and refining recommendations by the active affine piece yields an active-facet revelation principle and an exact polynomial-size linear program. We further identify a representation boundary: listed polyhedral risks remain tractable by the same LP, whereas succinctly represented facet families make exact persuasion NP-hard. Finally, we give a finite-precision approximation scheme for risk preferences determined by finitely many stable posterior statistics.