Stable Matching with Evolving Preferences

TL;DR

This paper addresses maintaining approximate stable matchings in dynamic settings where preferences evolve randomly, proposing an algorithm that effectively minimizes blocking pairs without direct preference change reports.

Contribution

The paper introduces a novel algorithm for stable matching with evolving preferences, achieving low blocking pairs without explicit preference change notifications.

Findings

Maintains a matching with at most O((log n)^2) blocking pairs in expectation.

Operates effectively without direct knowledge of preference changes.

Works under random adjacent swaps in preference lists.

Abstract

We consider the problem of stable matching with dynamic preference lists. At each time step, the preference list of some player may change by swapping random adjacent members. The goal of a central agency (algorithm) is to maintain an approximately stable matching (in terms of number of blocking pairs) at all times. The changes in the preference lists are not reported to the algorithm, but must instead be probed explicitly by the algorithm. We design an algorithm that in expectation and with high probability maintains a matching that has at most $O((log (n))^2)$ blocking pairs.