Secretary Problem with quality-based payoff

TL;DR

This paper studies a variant of the Secretary Problem focused on maximizing the expected quality of the selected candidate, providing bounds and examples to understand optimal hiring strategies.

Contribution

It introduces a new quality-based payoff model for the Secretary Problem, deriving bounds and demonstrating sharpness of the results.

Findings

Established an upper bound for the optimal hiring rule.

Provided examples showing the bounds are sharp.

Recovered classical Secretary Problem results as a special case.

Abstract

We consider a variant of the classical Secretary Problem. In this setting, the candidates are ranked according to some exchangeable random variable and the quest is to maximize the expected quality of the chosen aspirant. We find an upper bound for the optimal hiring rule, present examples showing it is sharp, and recover the classical case, among other results.