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Secretary Problem with Possible Errors in Observation

Author

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  • Marek Skarupski

    (Faculty of Pure and Applied Mathematics, Wrocław University of Science and Technology, Wyb. Wyspianskiego 27, 50-370 Wrocław, Poland)

Abstract

The classical secretary problem models a situation in which the decision maker can select or reject in the sequential observation objects numbered by the relative ranks. In theoretical studies, it is known that the strategy is to reject the first 37% of objects and select the next relative best one. However, an empirical result for the problem is that people do not apply the optimal rule. In this article, we propose modeling doubts of decision maker by considering a modification of the secretary problem. We assume that the decision maker can not observe the relative ranks in a proper way. We calculate the optimal strategy in such a problem and the value of the problem. In special cases, we also combine this problem with the no-information best choice problem and a no-information second-best choice problem.

Suggested Citation

  • Marek Skarupski, 2020. "Secretary Problem with Possible Errors in Observation," Mathematics, MDPI, vol. 8(10), pages 1-10, September.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:10:p:1639-:d:417778
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    References listed on IDEAS

    as
    1. Seale, Darryl A. & Rapoport, Amnon, 1997. "Sequential Decision Making with Relative Ranks: An Experimental Investigation of the "Secretary Problem">," Organizational Behavior and Human Decision Processes, Elsevier, vol. 69(3), pages 221-236, March.
    2. repec:spr:thdchp:978-3-540-48935-1_11 is not listed on IDEAS
    3. repec:cup:judgdm:v:15:y:2020:i:1:p:82-92 is not listed on IDEAS
    4. Abba M. Krieger & Ester Samuel-Cahn, 2012. "The Noisy Secretary Problem and Some Results on Extreme Concomitant Variables," Discussion Paper Series dp599, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
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