Optimality of Public Persuasion for Single-Good Allocation

We study an information design problem in which a sender seeks to allocate an indivisible good to n receivers by strategically disclosing information. The good can be allocated to at most one receiver, and each receiver decides whether to accept it based on self-interest. Relevant applications include school advisors promoting students for job placements, incubators introducing start-ups to potential investors, and biotech firms seeking partnerships with larger pharmaceutical companies. In this setting, the sender can either send different signals to different receivers (i.e., private persuasion) or broadcast the same signal to all receivers (i.e., public persuasion). After receiving signals, receivers may communicate with one another in their self-interest to further reduce uncertainty about the good. We demonstrate that, when the sender has a known preference among the receivers, public persuasion is optimal regardless of how the receivers communicate. The optimal public persuasion can be derived from a first-best relaxation problem that imposes only the receivers’ participation constraints. We then focus on a special case in which the good’s characteristics are captured by a one-dimensional variable and all receivers’ utility functions are linear in this variable. Using a dual approach, we derive optimality conditions for persuasion mechanisms. These conditions reveal that the persuasion problem decouples over linear segments of a piecewise-linear upper envelope function, which is derived from the Lagrangian relaxation of the first-best relaxation problem. We explicitly characterize this upper envelope function. This dual approach yields closed-form optimal mechanisms for the two-receiver case and an explicit characterization of the set of optimal mechanisms in the general case, thereby enhancing our understanding of their structural properties.

Supplemental Material: All supplemental materials, including the code, data, and files required to reproduce the results, are available at https://doi.org/10.1287/opre.2024.1279.