Preference Cycles in Stable Matchings

TL;DR

This paper introduces the concept of preference cycles in stable matchings, providing a simple and natural way to understand and prove classical results in the theory of stable matchings.

Contribution

It presents the novel idea of preference cycles and demonstrates their role in simplifying proofs of fundamental stable matching theorems.

Findings

Preference cycles are naturally present in stable matchings.

Preference cycles can be used to prove classical results more simply.

The approach offers an elementary perspective on stable matching theory.

Abstract

Consider the stable matching problem on two sets. We introduce the concept of a preference cycle and show how its natural presence in stable matchings proves a series of classical results in an elementary way.