Reputation-based persuasion platforms

In this paper, we introduce a two-stage Bayesian persuasion model in which a third-party platform controls the information available to the sender about users' preferences. We aim to characterize the optimal information disclosure policy of the platform, which maximizes average user utility, under the assumption that the sender also follows its own optimal policy. We show that this problem can be reduced to a model of market segmentation, in which probabilities are mapped into valuations. We then introduce a repeated variation of the persuasion platform problem in which myopic users arrive sequentially. In this setting, the platform controls the sender's information about users and maintains a reputation for the sender, punishing it if it fails to act truthfully on a certain subset of signals. We provide a characterization of the optimal platform policy in the reputation-based setting, which is then used to simplify the optimization problem of the platform.