Geodesic
The postdoc variant of the secretary problem
Mathematica Applicanda, Tome 49 (2021) no. 1, pp. 3-13.

Voir la notice de l'article provenant de la source Annales Societatis Mathematicae Polonae Series

The classical secretary problem involves sequentially interviewing a pool of n applicants with the aim of hiring exactly the best one in the pool—nothing less is good enough. The optimal decision strategy is easy to describe and the probability of success is 1/e. In this paper, we consider a minor variant of this classical problem. We wish to pick not the best but the second-best (the best is going to Harvard). In this case, an explicit solution can be given both for the optimal strategy and the associated optimal success probability. As n goes to infinity, the probability of success tends to 1/4. Apparently, it is easier to pick the best than the second best.
DOI : 10.14708/ma.v49i1.7076
Classification : 60G40, 62L15
Mots-clés : Secretary problem, online learning, online auctions, optimal stopping 
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Robert J. Vanderbei. The postdoc variant of the secretary problem. Mathematica Applicanda, Tome 49 (2021) no. 1, pp.  3-13. doi : 10.14708/ma.v49i1.7076. http://geodesic.mathdoc.fr/articles/10.14708/ma.v49i1.7076/

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