Saturating stable matchings
Computer Science and Game Theory
2021-07-09 v2 Theoretical Economics
Combinatorics
Abstract
I relate bipartite graph matchings to stable matchings. I prove a necessary and sufficient condition for the existence of a saturating stable matching, where every agent on one side is matched, for all possible preferences. I extend my analysis to perfect stable matchings, where every agent on both sides is matched.
Keywords
Cite
@article{arxiv.2011.06046,
title = {Saturating stable matchings},
author = {Muhammad Maaz},
journal= {arXiv preprint arXiv:2011.06046},
year = {2021}
}
Comments
10 pages, 2 figures. Version 2: removed simulation and discussion, added section 2.1 "equivalent statements", shortened proofs