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Stability concepts in matching under distributional constraints

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  • Kamada, Yuichiro
  • Kojima, Fuhito

Abstract

Many real matching markets are subject to distributional constraints. To guide market designers faced with constraints, we propose new stability concepts. A matching is strongly stable if satisfying blocking pairs inevitably violates a constraint. We show that a strongly stable matching may not exist, and that existence is guaranteed if and only if all distributional constraints are trivial. To overcome this difficulty, we propose a more permissive concept, weak stability. We demonstrate a weakly stable matching always exists, implies efficiency, and is characterized by standard normative axioms. These results are obtained in a more general environment than those in existing studies, accommodating a wide variety of applications.

Suggested Citation

  • Kamada, Yuichiro & Kojima, Fuhito, 2017. "Stability concepts in matching under distributional constraints," Journal of Economic Theory, Elsevier, vol. 168(C), pages 107-142.
    • Handle: RePEc:eee:jetheo:v:168:y:2017:i:c:p:107-142
    DOI: 10.1016/j.jet.2016.12.006
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    Cited by:

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    3. Echenique, Federico & Miralles, Antonio & Zhang, Jun, 2021. "Fairness and efficiency for allocations with participation constraints," Journal of Economic Theory, Elsevier, vol. 195(C).
    4. Prem Krishnaa & Girija Limaye & Meghana Nasre & Prajakta Nimbhorkar, 2023. "Envy-freeness and relaxed stability: hardness and approximation algorithms," Journal of Combinatorial Optimization, Springer, vol. 45(1), pages 1-30, January.
    5. Balbuzanov, Ivan, 2022. "Constrained random matching," Journal of Economic Theory, Elsevier, vol. 203(C).
    6. Avataneo, Michelle & Turhan, Bertan, 2021. "Slot-specific priorities with capacity transfers," Games and Economic Behavior, Elsevier, vol. 129(C), pages 536-548.
    7. Bloch, Francis & Cantala, David & Gibaja, Damián, 2020. "Matching through institutions," Games and Economic Behavior, Elsevier, vol. 121(C), pages 204-231.
    8. Ágoston, Kolos Csaba & Biró, Péter & Kováts, Endre & Jankó, Zsuzsanna, 2022. "College admissions with ties and common quotas: Integer programming approach," European Journal of Operational Research, Elsevier, vol. 299(2), pages 722-734.
    9. Yao Cheng & Zaifu Yang, "undated". "Stable Matching Mechanisms under Distributional Constraints," Discussion Papers 23/03, Department of Economics, University of York.
    10. Itai Ashlagi & Amin Saberi & Ali Shameli, 2020. "Assignment Mechanisms Under Distributional Constraints," Operations Research, INFORMS, vol. 68(2), pages 467-479, March.
    11. Orhan Aygun & Bertan Turhan, 2020. "Designing Direct Matching Mechanism for India with Comprehensive Affirmative Action," Papers 2004.13264, arXiv.org, revised Dec 2021.
    12. Aygün, Orhan & Turhan, Bertan, 2019. "Matching with Generalized Lexicographic Choice Rules," ISU General Staff Papers 20191101070000, Iowa State University, Department of Economics.
    13. Battal Dou{g}an & Kenzo Imamura & M. Bumin Yenmez, 2022. "Market Design with Deferred Acceptance: A Recipe for Policymaking," Papers 2209.06777, arXiv.org.
    14. 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.
    15. Tomoeda, Kentaro, 2018. "Finding a stable matching under type-specific minimum quotas," Journal of Economic Theory, Elsevier, vol. 176(C), pages 81-117.
    16. Haris Aziz & Bettina Klaus, 2017. "Random Matching under Priorities: Stability and No Envy Concepts," Cahiers de Recherches Economiques du Département d'Econométrie et d'Economie politique (DEEP) 17.09, Université de Lausanne, Faculté des HEC, DEEP.
    17. Haris Aziz & Bettina Klaus, 2019. "Random matching under priorities: stability and no envy concepts," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 53(2), pages 213-259, August.
    18. Ágoston, Kolos Csaba & Biró, Péter & Szántó, Richárd, 2018. "Stable project allocation under distributional constraints," Operations Research Perspectives, Elsevier, vol. 5(C), pages 59-68.
    19. Cho, Sung-Ho & Koshimura, Miyuki & Mandal, Pinaki & Yahiro, Kentaro & Yokoo, Makoto, 2022. "Impossibility of weakly stable and strategy-proof mechanism," Economics Letters, Elsevier, vol. 217(C).
    20. Oguzhan Celebi, 2023. "Diversity Preferences, Affirmative Action and Choice Rules," Papers 2310.14442, arXiv.org.
    21. Yoichi Kasajima & Manabu Toda, 2021. "Singles monotonicity and stability in one-to-one matching problems," Working Papers 2023-1, Waseda University, Faculty of Political Science and Economics.
    22. Devansh Jalota & Michael Ostrovsky & Marco Pavone, 2022. "Matching with Transfers under Distributional Constraints," Papers 2202.05232, arXiv.org, revised Apr 2022.

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    More about this item

    Keywords

    Matching; Distributional constraints; Efficiency; Stability; Strategy-proofness;
    All these keywords.

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • D47 - Microeconomics - - Market Structure, Pricing, and Design - - - Market Design
    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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