Constrained Persuasion with Private Information

Abstract I study a model of strategic communication between a privately informed sender who can persuade a receiver using Blackwell experiments. Hedlund (2017). “Bayesian Persuasion by a Privately Informed Sender.” Journal of Economic Theory 167 (January): 229–68, shows that private information in such a setting results in extremely informative equilibria. I make three points: first, the informativeness of equilibria relies crucially on two features – the mere availability of a fully revealing experiment, and a compact action space for the receiver. I show by examples that absent these features, equilibria may be uninformative. Secondly, I characterize equilibria in a simple model with constraints for the sender (only two experiments available, none are fully revealing) and the receiver (discrete action space). I argue that noisy experiments and discrete actions are the norm rather than the exception (and therefore, private information need not result in information revelation). Thirdly, I define a novel refinement that selects the most informative equilibria in most cases.