Worst- and Average-Case Robustness of Stable Matchings: (Counting) Complexity and Experiments

TL;DR

This paper investigates the robustness of stable matchings in the bipartite Stable Marriage problem, analyzing computational complexity and experimental behavior under adversarial and random preference swaps.

Contribution

It introduces new robustness measures for stable matchings, analyzes their computational complexity, and provides extensive experimental insights into their behavior.

Findings

Stable matchings are highly unrobust to adversarial swaps.

Average-case robustness is more nuanced and informative.

Computational complexity results for robustness measures.

Abstract

Focusing on the bipartite Stable Marriage problem, we investigate different robustness measures related to stable matchings. We analyze the computational complexity of computing them and analyze their behavior in extensive experiments on synthetic instances. For instance, we examine whether a stable matching is guaranteed to remain stable if a given number of adversarial swaps in the agent's preferences are performed and the probability of stability when applying swaps uniformly at random. Our results reveal that stable matchings in our synthetic data are highly unrobust to adversarial swaps, whereas the average-case view presents a more nuanced and informative picture.