# The Best-or-Worst and the Postdoc problems

## TL;DR

This paper analyzes two variants of the secretary problem, establishing their optimal strategies and exploring how additional costs or different payoff structures affect these strategies.

## Contribution

It proves that the Best-or-Worst and Postdoc problems share the same optimal stopping rule in their standard form and examines how various costs and payoffs alter optimal strategies.

## Key findings

- Both variants share the same optimal stopping rule in standard form.
- Additional costs or payoffs significantly change the optimal strategies.
- Different payments based on candidate quality influence the strategy choices.

## Abstract

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.