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The Best-or-Worst and the Postdoc problems
We consider two variants of the secretary problem, the\emph{ Best-or-Worst}
and the \emph{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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