Stable Nash Equilibria in the Gale-Shapley Matching Game
Abstract
In this article we study the stable marriage game induced by the men-proposing Gale-Shapley algorithm. Our setting is standard: all the lists are complete and the matching mechanism is the men-proposing Gale-Shapley algorithm. It is well known that in this setting, men cannot cheat, but women can. In fact, Teo, Sethuraman and Tan \cite{TST01}, show that there is a polynomial time algorithm to obtain, for a given strategy (the set of all lists) and a woman , the best partner attainable by changing her list. However, what if the resulting matching is not stable with respect to ? Obviously, such a matching would be vulnerable to further manipulation, but is not mentioned in \cite{TST01}. In this paper, we consider (safe) manipulation that implies a stable matching in a most general setting. Specifically, our goal is to decide for a given , if w can manipulate her list to obtain a strictly better partner with respect to the true strategy (which may be different from ), and also the outcome is a stable matching for .
Keywords
Cite
@article{arxiv.1509.04344,
title = {Stable Nash Equilibria in the Gale-Shapley Matching Game},
author = {Sushmita Gupta and Kazuo Iwama and Shuichi Miyazaki},
journal= {arXiv preprint arXiv:1509.04344},
year = {2015}
}