English

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.

Keywords

Cite

@article{arxiv.2408.16271,
  title  = {Non-uniformly Stable Matchings},
  author = {Naoyuki Kamiyama},
  journal= {arXiv preprint arXiv:2408.16271},
  year   = {2024}
}
R2 v1 2026-06-28T18:27:17.485Z