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Matching With Pre-Existing Binding Agreements: The Agreeable Core

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  • Peter Doe

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.

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  • Peter Doe, 2024. "Matching With Pre-Existing Binding Agreements: The Agreeable Core," Papers 2406.08700, arXiv.org, revised Oct 2024.
    • Handle: RePEc:arx:papers:2406.08700
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    References listed on IDEAS

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    5. Fragiadakis, Daniel & Troyan, Peter, 2017. "Improving matching under hard distributional constraints," Theoretical Economics, Econometric Society, vol. 12(2), May.
    6. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
    7. Ivan Balbuzanov & Maciej H. Kotowski, 2019. "Endowments, Exclusion, and Exchange," Econometrica, Econometric Society, vol. 87(5), pages 1663-1692, September.
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