Optimality of Public Persuasion in Job Seeking

Abstract

We study an information design problem in which a school advisor strategically discloses information to promote her student in a job market with n potential employers. The advisor can send different signals to different employers (i.e., private persuasion) or broadcast the same signal to all employers (i.e., public persuasion). After receiving the signals, the employers can communicate with each other to reduce uncertainty about the candidate in their self-interest. We demonstrate that as long as the candidate can accept at most one offer and has a known preference among the employers, public persuasion is optimal, regardless of how employers communicate. The optimal public persuasion can be derived from a first-best relaxation problem that only imposes the employers' participation constraints. We then focus on a specific case in which the candidate's characteristics can be summarized as a one-dimensional variable, and all of the receivers' utility functions are linear in this variable. We derive the optimal mechanism in a closed form for the two-receiver case. In the general case, a convex optimization problem with n decision variables and constraints can be efficiently solved to obtain an optimal mechanism. We provide structural properties and a better understanding of the optimal mechanism from a dual viewpoint.

Keywords: Bayesian persuasion, public information, multiple receivers, post-signal communication, Lagrangian dual