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The secretary recommendation problem

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  • Hahn, Niklas
  • Hoefer, Martin
  • Smorodinsky, Rann

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.

Suggested Citation

  • Hahn, Niklas & Hoefer, Martin & Smorodinsky, Rann, 2022. "The secretary recommendation problem," Games and Economic Behavior, Elsevier, vol. 134(C), pages 199-228.
    • Handle: RePEc:eee:gamebe:v:134:y:2022:i:c:p:199-228
    DOI: 10.1016/j.geb.2022.05.002
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    References listed on IDEAS

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    1. Emir Kamenica & Matthew Gentzkow, 2011. "Bayesian Persuasion," American Economic Review, American Economic Association, vol. 101(6), pages 2590-2615, October.
    2. Jeffrey Ely & Alexander Frankel & Emir Kamenica, 2015. "Suspense and Surprise," Journal of Political Economy, University of Chicago Press, vol. 123(1), pages 215-260.
    3. Moran Feldman & Ola Svensson & Rico Zenklusen, 2018. "A Simple O (log log(rank))-Competitive Algorithm for the Matroid Secretary Problem," Mathematics of Operations Research, INFORMS, vol. 43(2), pages 638-650, May.
    4. Renault, Jérôme & Solan, Eilon & Vieille, Nicolas, 2017. "Optimal dynamic information provision," Games and Economic Behavior, Elsevier, vol. 104(C), pages 329-349.
    5. Arieli, Itai & Babichenko, Yakov, 2019. "Private Bayesian persuasion," Journal of Economic Theory, Elsevier, vol. 182(C), pages 185-217.
    6. Pak Hung Au, 2015. "Dynamic information disclosure," RAND Journal of Economics, RAND Corporation, vol. 46(4), pages 791-823, October.
    Full references (including those not matched with items on IDEAS)

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