On Sisterhood in the Gale-Shapley Matching Algorithm

TL;DR

This paper explores strategic lying in the Gale-Shapley matching algorithm, revealing a strong dichotomy and sisterhood effects among women, with implications for understanding manipulation and fairness in matching markets.

Contribution

It establishes a new dichotomy between the goals of men and women in lying scenarios and uncovers sisterhood effects among women in the Gale-Shapley algorithm.

Findings

No woman worse-off implies no man better-off.

A sisterhood effect among women holds under certain conditions.

Strategic lying impacts the stability and fairness of matchings.

Abstract

Lying in order to manipulate the Gale-Shapley matching algorithm has been studied by Dubins and Friedman and by Gale and Sotomayor and was shown to be generally more appealing to the proposed-to side (denoted as the women in Gale and Shapley's original paper) than to the proposing side (denoted as men there). It can also be shown that in the case of lying women, for every woman who is better-off due to lying, there exists a man who is worse-off. In this paper, we show that an even stronger dichotomy between the goals of the sexes holds, namely, if no woman is worse-off then no man is better-off, while a form of sisterhood between the lying and the "innocent" women also holds, namely, if none of the former are worse-off, then neither is any of the latter. This paper is based upon an undergraduate ("Amirim") thesis of the first author.