Stable matching: an integer programming approach

TL;DR

This paper introduces an integer programming method for stable two-sided many-to-one matchings, demonstrating existence under certain preference conditions and providing a class of preferences that satisfy these conditions.

Contribution

It develops a novel integer programming framework for stable matchings and identifies preference profiles ensuring existence in discrete markets.

Findings

Stable matchings exist under total unimodularity conditions.

A class of preference profiles satisfying these conditions is identified.

The approach extends to markets with complementarities.

Abstract

This paper develops an integer programming approach to two-sided many-to-one matching by investigating stable integral matchings of a fictitious market where each worker is divisible. We show that stable matchings exist in a discrete matching market when firms' preference profile satisfies a total unimodularity condition that is compatible with various forms of complementarities. We provide a class of firms' preference profiles that satisfy this condition.