The secretary recommendation problem

Abstract

We revisit the basic variant of the classical secretary problem. We propose a new approach in which we separate between an agent (the sender) that evaluates the secretary performance and one (the receiver) that makes the hiring decision. The sender signals the quality of the candidate to the hiring agent. Whenever the two agents' interests are not fully aligned, this induces an information transmission (signaling) challenge for the sender. We study the sender's optimization problem subject to persuasiveness constraints for the receiver in several variants of the problem. Our results quantify the loss in performance for the sender due to online arrival. We provide optimal and near-optimal persuasive mechanisms. In most cases the sender can recover at least a constant fraction of the utility that he would have obtained had he been able to access all information at the outset.