Bayesian Persuasion with Data Brokers

We study Bayesian persuasion for a binary decision problem in the presence of a data broker intermediary, who can garble the information she receives to maximize her revenue. We derive several structural properties of the broker's optimal menu under her information constraint, including that optimal and responsive menus must lie on the information frontier. For binary signals and binary types, we characterize the sender's solution and compare the receiver's equilibrium information to that of the benchmarks of ex-ante and ex-post persuasion. When the proportion of high types is small enough, we find that the presence of the broker strictly increases the equilibrium informativeness of the receiver's information, even though the broker can only garble