Stable Secretaries
Abstract
We define and study a new variant of the secretary problem. Whereas in the classic setting multiple secretaries compete for a single position, we study the case where the secretaries arrive one at a time and are assigned, in an on-line fashion, to one of multiple positions. Secretaries are ranked according to talent, as in the original formulation, and in addition positions are ranked according to attractiveness. To evaluate an online matching mechanism, we use the notion of blocking pairs from stable matching theory: our goal is to maximize the number of positions (or secretaries) that do not take part in a blocking pair. This is compared with a stable matching in which no blocking pair exists. We consider the case where secretaries arrive randomly, as well as that of an adversarial arrival order, and provide corresponding upper and lower bounds.
Keywords
Cite
@article{arxiv.1705.01589,
title = {Stable Secretaries},
author = {Yakov Babichenko and Yuval Emek and Michal Feldman and Boaz Patt-Shamir and Ron Peretz and Rann Smorodinsky},
journal= {arXiv preprint arXiv:1705.01589},
year = {2017}
}
Comments
Accepted for presentation at the 18th ACM conference on Economics and Computation (EC 2017)