On Sisterhood in the Gale-Shapley Matching Algorithm

Lying in order to manipulate the Gale-Shapley matching algorithm has been studied in [2] and [3] and was shown to be generally more appealing to the proposed-to side (denoted as the women in [1]) 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.