We consider two variants of the secretary problem, the Best-or-Worst and the Postdoc problems, which are closely related. First, we prove that both variants, in their standard form with binary… Click to show full abstract
We consider two variants of the secretary problem, the Best-or-Worst and the Postdoc problems, which are closely related. First, we prove that both variants, in their standard form with binary payoff 1 or 0, share the same optimal stopping rule. We also consider additional cost/perquisites depending on the number of interviewed candidates. In these situations the optimal strategies are very different. Finally, we also focus on the Best-or-Worst variant with different payments depending on whether the selected candidate is the best or the worst.
               
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