How should an agent (the sender) observing multi-dimensional data (the state vector) persuade another agent to take the desired action? We show that it is always optimal for the sender to perform a (non-linear) dimension reduction by projecting the state vector onto a lower-dimensional object...

We study the general problem of Bayesian persuasion (optimal information design) with continuous actions and continuous state space in arbitrary dimensions. First, we show that with a finite signal space, the optimal information design is always given by a partition. Second, we take the limit of...

An uninformed sender designs a mechanism that discloses information about her type to a privately informed receiver, who then decides whether to act. I impose a single-crossing assumption, so that the receiver with a higher type is more willing to act. Using a linear programming approach, I...

We analyze information design games between two designers with opposite preferences and a single agent. Before the agent makes a decision, designers repeatedly disclose public information about persistent state parameters. Disclosure continues until no designer wishes to reveal further...

We study the interaction between multiple information designers who try to influence the behavior of a set of agents. When the set of messages available to each designer is finite, such games always admit subgame perfect equilibria. When designers produce public information about independent...

We study optimal auctions in a symmetric private values setting, where bidders' care about winning the object and a receiver's inference about their type. We reestablish revenue equivalence when bidders' signaling concerns are linear, and the auction makes participation observable via an entry...