Matching With Pre-Existing Binding Agreements: The Agreeable Core

TL;DR

This paper introduces the agreeable core, a new solution concept for matching markets with pre-existing binding agreements, and provides an algorithm to find such matches applicable to various real-world markets.

Contribution

It develops a novel solution concept and an algorithm combining Deferred Acceptance and Top Trading Cycles for markets with binding agreements.

Findings

The algorithm constructs stable matches respecting binding agreements.

The agreeable core is robust to manipulations.

Applications include hospital, college, school, and labor markets.

Abstract

Matching market models ignore prior commitments. Yet many job seekers, for example, are already employed, and the same holds for many other matching markets. I analyze two-sided matching markets with pre-existing binding agreements between market participants. In this model, a pair of participants bound to each other by a pre-existing agreement must agree to any action they take. To analyze their behavior, I propose a new solution concept, the agreeable core, consisting of the matches which cannot be renegotiated without violating the binding agreements. My main contribution is an algorithm that constructs such a match by a novel combination of the Deferred Acceptance and Top Trading Cycles algorithms. The algorithm is robust to various manipulations and has applications to numerous markets including the resident-to-hospital match, college admissions, school choice, and labor markets.