Non-uniformly Stable Matchings
Computer Science and Game Theory
2024-08-30 v1
Abstract
Super-stability and strong stability are properties of a matching in the stable matching problem with ties. In this paper, we introduce a common generalization of super-stability and strong stability, which we call non-uniform stability. First, we prove that we can determine the existence of a non-uniformly stable matching in polynomial time. Next, we give a polyhedral characterization of the set of non-uniformly stable matchings. Finally, we prove that the set of non-uniformly stable matchings forms a distributive lattice.
Cite
@article{arxiv.2408.16271,
title = {Non-uniformly Stable Matchings},
author = {Naoyuki Kamiyama},
journal= {arXiv preprint arXiv:2408.16271},
year = {2024}
}