Contracts can be more than salaries: Hassidim, Romm, and Shorrer in EL

Not all matching with contracts is simple: here's a recent paper that helps put that in perspective.

Assaf Romm writes: "despite the insightful embedding results of Echenique (2012), Schlegel (2015) and Jagadeesan (2019), some real-life matching with contracts markets cannot be represented as markets with salaries. Specifically,  college admissions markets often contain schools that have preferences that do not satisfy unilateral substitutability, but do satisfy bilateral substitutability (Hatfield and Kojima, 2010) and/or hidden substitutes (Hatfield and Kominers, 2015). In this kind of markets the student-proposing deferred acceptance algorithm always concludes with a stable matching, but the existence of a student-optimal stable matching is not guaranteed, and this rules out any embedding into a Kelso-Crawford type of market (in which a student-optimal stable matching does exist)."

Economics Letters

Volume 181, August 2019, Pages 40-42

Contracts are not salaries in the hidden-substitutes domain☆

Author links open overlay panelAvinatan HassidimaAssaf RommbcRan I.Shorrerd

https://doi.org/10.1016/j.econlet.2019.04.025

Highlights

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Real-life two-sided matching with contracts markets may not be embeddable into labor markets.

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Hidden substitutes and bi-lateral substitutes preferences do not assure embeddability.

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We provide examples of centralized college admissions markets that fall under this category.

Abstract

We show that many-to-one matching markets with contracts where colleges’ preferences satisfy the hidden substitutes condition of Hatfield and Kominers (2015) may not be embedded, in the sense of Echenique (2012) into a Kelso and Crawford(1982) matching-with-salaries market. Our proof relies on a configurations of preferences that is observed in many college admissions markets.