The field of information design studies strategic information revelation by a certain sender to receivers. The Bayesian persuasion model, introduced by Kamenica and Gentzkow, assumes that the sender can trustworthily commit to a randomized information revelation policy, called a signaling scheme. In contrast, the cheap talk model assumes that the sender does not have such a commitment power. The research focuses on optimizing the sender’s utility.
In this bundle of works, we study versions of the Bayesian persuasion and the cheap talk model motivated by various challenges of the 21st century. For a single-receiver cheap talk setting, we show that approximating the sender-optimal equilibrium utility up to a certain additive or multiplicative constant is NP-hard. It comes in a sharp contrast to the analogous well-studied problem in Bayesian persuasion, which is computationally tractable. Since the commitment power is unrealistic in some real-life scenarios, this result might seem to limit the extent of applicability of information design. Luckily, we manage to get positive computational results in some natural special cases.
For a single-receiver Bayesian persuasion setting, we provide a simple explicit formula for the sender’s minimal regret when the receiver’s utility function is chosen adversarially. We further provide positive computational results when the sender’s choice of the signaling scheme is limited by privacy constraints. For a multi-receiver Bayesian persuasion model, we consider a setting in which the sender can communicate with the receivers via several (possibly overlapping) communication channels; such a setting can be motivated by social media interactions. We show that in general, the sender’s optimization problem in this multi-channel setting is harder than both private and public Bayesian persuasion. Still, finding a sender’s optimal signaling scheme is tractable for several special cases corresponding to communication in hierarchical organizations.
Finally, we combine information design with two further burning topics: contract design and information aggregation. In the principal-agent setting in contract design, we provide a full characterization of all the implementable utility profiles and agent’s actions when the information revealed to the principal about the agent’s action is chosen by a social planner. In information aggregation, we show that the robustly optimal way to aggregate anonymous binary recommendations from symmetric agents with adversarially-correlated private information about a hidden state is the random dictator rule: picking one recommendation uniformly at random and following it.
