Signaling through Bayesian persuasion

• Published in: Mathematical social sciences 2024-12, Vol.132, p.15-27
• Main Author: Hedlund, Jonas
• Format: Article
• Language: English
• Subjects: Bayesian persuasion; Information transmission; Signaling
• ISSN: 0165-4896
• DOI: 10.1016/j.mathsocsci.2024.08.002

This paper examines the conditions under which separating outcomes occur in informed persuasion, that is, in Bayesian persuasion settings in which the sender is privately informed about the payoff-relevant state prior to committing to an experiment. We consider a setting with finite payoff-relevant states and sender payoffs that are continuous and monotonic in the receiver’s posterior beliefs. The paper finds that if full disclosure of the payoff-relevant state reduces the sender’s expected payoff under any common prior (i.e., if the sender’s payoff function is outer concave), then single-crossing properties arise such that the high sender type can separate from the low type by choosing more informative experiments. This single-crossing condition leads to the selection of “least costly” separating equilibria by the D1 criterion, i.e., the sender’s choice of experiment signals his type. Further, separating equilibria are characterized by simple constrained maximization problems. •Bayesian persuasion with private sender information and many states.•Outer concave payoff function leads to selection of separating outcomes by D1 criterion.•Signaling of private information through the choice of experiment.