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Stable Matching in Large Economies

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  • Yeon‐Koo Che
  • Jinwoo Kim
  • Fuhito Kojima

Abstract

We study stability of two‐sided many‐to‐one matching in which firms' preferences for workers may exhibit complementarities. Although such preferences are known to jeopardize stability in a finite market, we show that a stable matching exists in a large market with a continuum of workers, provided that each firm's choice is convex and changes continuously as the set of available workers changes. We also study the existence and structure of stable matchings under preferences exhibiting substitutability and indifferences in a large market. Building on these results, we show that an approximately stable matching exists in large finite economies. We extend our framework to ensure a stable matching with desirable incentive and fairness properties in the presence of indifferences in firms' preferences.

Suggested Citation

  • Yeon‐Koo Che & Jinwoo Kim & Fuhito Kojima, 2019. "Stable Matching in Large Economies," Econometrica, Econometric Society, vol. 87(1), pages 65-110, January.
    • Handle: RePEc:wly:emetrp:v:87:y:2019:i:1:p:65-110
    DOI: 10.3982/ECTA13547
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    Citations

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    Cited by:

    1. Chao Huang, 2021. "Stable matching: an integer programming approach," Papers 2103.03418, arXiv.org, revised Apr 2022.
    2. Schwartz, Jacob & Song, Kyungchul, 2024. "The law of large numbers for large stable matchings," Journal of Econometrics, Elsevier, vol. 241(1).
    3. Umut Dur & Thayer Morrill & William Phan, 2024. "Partitionable choice functions and stability," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 63(2), pages 359-375, September.
    4. Minoru Kitahara & Yasunori Okumura, 2023. "School Choice with Multiple Priorities," Papers 2308.04780, arXiv.org, revised Oct 2024.
    5. Hai Nguyen & Thành Nguyen & Alexander Teytelboym, 2021. "Stability in Matching Markets with Complex Constraints," Management Science, INFORMS, vol. 67(12), pages 7438-7454, December.
    6. Huang, Chao, 2023. "Stable matching: an integer programming approach," Theoretical Economics, Econometric Society, vol. 18(1), January.
    7. Afodjo, Nabil & Pongou, Roland, 2024. "Efficiency and maximality in anonymous two-sided economies," Games and Economic Behavior, Elsevier, vol. 146(C), pages 184-195.
    8. Chao Huang, 2022. "Firm-worker hypergraphs," Papers 2211.06887, arXiv.org, revised Nov 2023.
    9. Chao Huang, 2023. "Concave many-to-one matching," Papers 2309.04181, arXiv.org.
    10. Aaron L. Bodoh-Creed, 2020. "Optimizing for Distributional Goals in School Choice Problems," Management Science, INFORMS, vol. 66(8), pages 3657-3676, August.
    11. Chao Huang, 2022. "Two-sided matching with firms' complementary preferences," Papers 2205.05599, arXiv.org, revised May 2022.
    12. Di Feng, 2023. "Efficiency in Multiple-Type Housing Markets," Papers 2308.14989, arXiv.org, revised Dec 2023.
    13. Yannai A. Gonczarowski & Scott Duke Kominers & Ran I. Shorrer, 2019. "To Infinity and Beyond: A General Framework for Scaling Economic Theories," Papers 1906.10333, arXiv.org, revised Apr 2023.
    14. Chen, Bo, 2021. "Labor market matching with ensuing competitive externalities in large economies," Mathematical Social Sciences, Elsevier, vol. 109(C), pages 12-17.
    15. Fisher, James C.D., 2020. "Existence of stable allocations in matching markets with infinite contracts: A topological approach," Journal of Mathematical Economics, Elsevier, vol. 91(C), pages 136-140.
    16. Xinyang Wang, 2020. "Cooperation in Small Groups -- an Optimal Transport Approach," Papers 2005.11244, arXiv.org.
    17. Dur, Umut & Pathak, Parag A. & Sönmez, Tayfun, 2020. "Explicit vs. statistical targeting in affirmative action: Theory and evidence from Chicago's exam schools," Journal of Economic Theory, Elsevier, vol. 187(C).
    18. Chao Huang, 2021. "Unidirectional substitutes and complements," Papers 2108.12572, arXiv.org.

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