Matching with Couples Revisited

TL;DR

This paper introduces a new matching algorithm for markets with couples, demonstrating high-probability stability in large random markets and analyzing the conditions under which stable matchings exist or not.

Contribution

A novel matching algorithm for markets with couples that achieves high-probability stability in large random markets with many couples.

Findings

The algorithm finds stable matchings with high probability in large markets.

Truth-telling is an approximate equilibrium under the new algorithm.

Stable matchings may not exist with constant probability when the number of couples grows linearly.

Abstract

It is well known that a stable matching in a many-to-one matching market with couples need not exist. We introduce a new matching algorithm for such markets and show that for a general class of large random markets the algorithm will find a stable matching with high probability. In particular we allow the number of couples to grow at a near-linear rate. Furthermore, truth-telling is an approximated equilibrium in the game induced by the new matching algorithm. Our results are tight: for markets in which the number of couples grows at a linear rate, we show that with constant probability no stable matching exists.