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The properness of weak stability notions

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  • Zhang, Luosai

Abstract

Multiple weak stability notions have been proposed for two-sided matching problems, each based on a different perspective to justify the existence of certain blocking pairs. We introduce a criterion, called properness, to evaluate these weak stability notions. We say a notion of weak stability is proper if, whenever a matching is weakly stable, every matching that is more stable than it (admitting a subset of blocking pairs) is also weakly stable. We show that among existing notions of weak stability: the von Neumann and Morgenstern stable set, reasonable stability, α-equitability, partial stability, and the Tang-Zhang weak stability are proper, whereas the Klijn-Massó weak stability, essential stability, and priority-neutrality are not proper.

Suggested Citation

  • Zhang, Luosai, 2025. "The properness of weak stability notions," Economics Letters, Elsevier, vol. 247(C).
    • Handle: RePEc:eee:ecolet:v:247:y:2025:i:c:s0165176524006475
    DOI: 10.1016/j.econlet.2024.112163
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    References listed on IDEAS

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    1. Battal Doğan & Lars Ehlers, 2022. "Robust Minimal Instability of the Top Trading Cycles Mechanism," American Economic Journal: Microeconomics, American Economic Association, vol. 14(4), pages 556-582, November.
    2. José Alcalde & Antonio Romero-Medina, 2017. "Fair student placement," Theory and Decision, Springer, vol. 83(2), pages 293-307, August.
    3. Klijn, Flip & Masso, Jordi, 2003. "Weak stability and a bargaining set for the marriage model," Games and Economic Behavior, Elsevier, vol. 42(1), pages 91-100, January.
    4. Atila Abdulkadiroğlu & Yeon-Koo Che & Parag A. Pathak & Alvin E. Roth & Olivier Tercieux, 2020. "Efficiency, Justified Envy, and Incentives in Priority-Based Matching," American Economic Review: Insights, American Economic Association, vol. 2(4), pages 425-442, December.
    5. Atila Abdulkadiroglu & Parag A. Pathak & Alvin E. Roth, 2009. "Strategy-proofness versus Efficiency in Matching with Indifferences: Redesigning the New York City High School Match," NBER Working Papers 14864, National Bureau of Economic Research, Inc.
    6. Ehlers, Lars, 2007. "Von Neumann-Morgenstern stable sets in matching problems," Journal of Economic Theory, Elsevier, vol. 134(1), pages 537-547, May.
    7. Dur, Umut & Gitmez, A. Arda & Yılmaz, Özgür, 2019. "School choice under partial fairness," Theoretical Economics, Econometric Society, vol. 14(4), November.
    8. Tang, Qianfeng & Yu, Jingsheng, 2014. "A new perspective on Kesten's school choice with consent idea," Journal of Economic Theory, Elsevier, vol. 154(C), pages 543-561.
    9. Philip J. Reny, 2022. "Efficient Matching in the School Choice Problem," American Economic Review, American Economic Association, vol. 112(6), pages 2025-2043, June.
    10. Qianfeng Tang & Yongchao Zhang, 2021. "Weak stability and Pareto efficiency in school choice," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(2), pages 533-552, March.
    11. Lars Ehlers & Thayer Morrill, 2020. "(Il)legal Assignments in School Choice," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 87(4), pages 1837-1875.
    12. Atila Abdulkadiroglu & Tayfun Sönmez, 2003. "School Choice: A Mechanism Design Approach," American Economic Review, American Economic Association, vol. 93(3), pages 729-747, June.
    13. Haluk I. Ergin, 2002. "Efficient Resource Allocation on the Basis of Priorities," Econometrica, Econometric Society, vol. 70(6), pages 2489-2497, November.
    14. Atila Abdulkadiroglu & Parag A. Pathak & Alvin E. Roth, 2009. "Strategy-Proofness versus Efficiency in Matching with Indifferences: Redesigning the NYC High School Match," American Economic Review, American Economic Association, vol. 99(5), pages 1954-1978, December.
    15. Troyan, Peter & Delacrétaz, David & Kloosterman, Andrew, 2020. "Essentially stable matchings," Games and Economic Behavior, Elsevier, vol. 120(C), pages 370-390.
    16. Onur Kesten, 2010. "School Choice with Consent," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 125(3), pages 1297-1348.
    17. Zhou Lin, 1994. "A New Bargaining Set of an N-Person Game and Endogenous Coalition Formation," Games and Economic Behavior, Elsevier, vol. 6(3), pages 512-526, May.
    18. Alvin E. Roth, 1982. "The Economics of Matching: Stability and Incentives," Mathematics of Operations Research, INFORMS, vol. 7(4), pages 617-628, November.
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