Cycles to compute the full set of many-to-many stable matchings

TL;DR

This paper introduces a novel algorithm that computes all stable matchings in many-to-many models by leveraging cycles in preferences, extending previous one-to-one matching algorithms.

Contribution

It generalizes the Roth and Sotomayor (1990) algorithm to many-to-many settings using cycles in preferences, enabling comprehensive stable matching computation.

Findings

Algorithm successfully computes the full set of stable matchings.

Extends one-to-one matching algorithms to many-to-many models.

Provides a new perspective using cycles in preferences.

Abstract

In a many-to-many matching model in which agents' preferences satisfy substitutability and the law of aggregate demand, we present an algorithm to compute the full set of stable matchings. This algorithm relies on the idea of "cycles in preferences" and generalizes the algorithm presented in Roth and Sotomayor (1990) for the one-to-one model.