Computational complexity of k-stable matchings

Haris Aziz – Gergely Csáji – Ágnes Cseh

ACM Transactions on Economics and Computation, Vol. 13. No. 1. Paper 5. 25 p. (2025)

Abstract

We study deviations by a group of agents in the three main types of matching markets: the house allocation, the marriage, and the roommates models. For a given instance, we call a matching k-stable if no other matching exists that is more beneficial to at least k out of the n agents. The concept generalizes the recently studied majority stability [57]. We prove that whereas the verification of k-stability for a given matching is polynomial-time solvable in all three models, the complexity of deciding whether a k-stable matching exists depends on \(\frac{k}{n}\) and is characteristic of each model.

https://doi.org/10.1145/3708507