The Secretary Recommendation Problem
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In this paper we revisit the basic variant of the classical secretary problem. We propose a new approach, in which we separate between an agent that evaluates the secretary performance and one that has to make the hiring decision. The evaluating agent (the sender) signals the quality of the candidate to the hiring agent (the receiver) who must make a decision. 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 incentive-compatibility constraints of the receiver for several variants of the problem. Our results quantify the loss in performance for the sender due to online arrival. We provide optimal or near-optimal incentive-compatible mechanisms, which recover at least a constant fraction of a natural utility benchmark for the sender. The separation of evaluation and decision making can have a substantial impact on the approximation results. While in some variants, the techniques and results closely mirror the conditions in the standard secretary problem, we also exhibit variants leading to very different characteristics.
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