Finding all stable matchings with assignment constraints

TL;DR

This paper introduces an algorithm to determine the existence of stable matchings under specific assignment constraints and to enumerate all such matchings efficiently, aiding market design.

Contribution

The paper presents a novel algorithm based on iterated deletion to check feasibility and find all stable matchings with assignment constraints.

Findings

Algorithm efficiently finds all stable matchings under constraints.

Provides a polynomial-time method for feasibility testing.

Assists market designers in implementing constrained stable matchings.

Abstract

In this paper we consider stable matchings subject to assignment constraints. These are matchings that require certain assigned pairs to be included, insist that some other assigned pairs are not, and, importantly, are stable. Our main contribution is an algorithm, based on the iterated deletion of unattractive alternatives, that determines if assignment constraints are compatible with stability. Whenever there is a stable matching that satisfies the assignment constraints, our algorithm outputs all of them (each in polynomial time per solution). This provides market designers with (i) a tool to test the feasibility of stable matchings subject to assignment constraints, and (ii) a tool to implement them when feasible.