Regulating externalities is a major challenge when economic agents face uncertainty and disagreement. Traditional Pigouvian and Coasean approaches often struggle because they require either precise knowledge of externality costs or frictionless bargaining. We propose an "uncertainty-based regulation" (UBR) mechanism that leverages both uncertainty and firms' heterogeneous information to achieve socially efficient outcomes without requiring disclosure of private information. UBR adjusts firms' payoffs by adding a...