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Matching with a Status Quo: The Agreeable Core

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  • Peter Doe

Abstract

We provide a framework to unify classic models of two-sided matching with recent models of recontracting. In the classic model, agents from two sides must be matched; in models of recontracting, agents improve a status quo match. We generalize the core (matches not blocked by any coalition) from cooperative game theory to our setting by restricting the set of permissible coalitions to coalitions containing neither or both agents in a status quo match, dubbed "agreeable" coalitions. The agreeable core is the set of all weak improvements of the status quo that are not blocked by any agreeable coalition. Our main result is that the agreeable core is nonempty and can be found through a computationally efficient and economically meaningful algorithm: our Propose-Exchange algorithm. The applications of the agreeable core include early decision, out-of-match agreements in the NRMP, matching with minimum constraints, and efficiency in school choice.

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  • Peter Doe, 2024. "Matching with a Status Quo: The Agreeable Core," Papers 2406.08700, arXiv.org.
    • Handle: RePEc:arx:papers:2406.08700
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    References listed on IDEAS

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    1. Atila Abdulkadiroglu & Tayfun Sönmez, 2003. "School Choice: A Mechanism Design Approach," American Economic Review, American Economic Association, vol. 93(3), pages 729-747, June.
    2. Julien Combe, 2023. "Reallocation with priorities and minimal envy mechanisms," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 76(2), pages 551-584, August.
    3. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
    4. Ivan Balbuzanov & Maciej H. Kotowski, 2019. "Endowments, Exclusion, and Exchange," Econometrica, Econometric Society, vol. 87(5), pages 1663-1692, September.
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