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The lattice of envy-free matchings

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  • Wu, Qingyun
  • Roth, Alvin E.

Abstract

In a many-to-one matching model, we show that the set of envy-free matchings is a lattice. A Tarski operator on this lattice, which can be interpreted as modeling vacancy chains, has the set of stable matchings as its fixed points.

Suggested Citation

  • Wu, Qingyun & Roth, Alvin E., 2018. "The lattice of envy-free matchings," Games and Economic Behavior, Elsevier, vol. 109(C), pages 201-211.
    • Handle: RePEc:eee:gamebe:v:109:y:2018:i:c:p:201-211
    DOI: 10.1016/j.geb.2017.12.016
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    References listed on IDEAS

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    1. Ehlers, Lars & Hafalir, Isa E. & Yenmez, M. Bumin & Yildirim, Muhammed A., 2014. "School choice with controlled choice constraints: Hard bounds versus soft bounds," Journal of Economic Theory, Elsevier, vol. 153(C), pages 648-683.
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    Citations

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    Cited by:

    1. David Pérez-Castrillo & Marilda Sotomayor, 2023. "Constrained-optimal tradewise-stable outcomes in the one-sided assignment game: a solution concept weaker than the core," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 76(3), pages 963-994, October.
    2. 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.
    3. Bonifacio, Agustín G. & Guiñazú, Nadia & Juarez, Noelia & Neme, Pablo & Oviedo, Jorge, 2022. "The lattice of worker-quasi-stable matchings," Games and Economic Behavior, Elsevier, vol. 135(C), pages 188-200.
    4. Juárez, Noelia & Neme, Pablo & Oviedo, Jorge, 2022. "Lattice structure of the random stable set in many-to-many matching markets," Games and Economic Behavior, Elsevier, vol. 132(C), pages 255-273.
    5. Agustin G. Bonifacio & Nadia Guiñazú & Noelia Juarez & Pablo Neme & Jorge Oviedo, 2024. "The lattice of envy-free many-to-many matchings with contracts," Theory and Decision, Springer, vol. 96(1), pages 113-134, February.
    6. 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.
    7. Jacob Schwartz & Kyungchul Song, 2021. "The Law of Large Numbers for Large Stable Matchings," Papers 2101.00399, arXiv.org, revised Mar 2024.
    8. Yi-You Yang, 2023. "Firm-quasi-stability and re-equilibration in matching markets with contracts," Papers 2305.17948, arXiv.org, revised Jul 2023.
    9. Eirinakis, Pavlos & Mourtos, Ioannis & Zampou, Eleni, 2022. "Random Serial Dictatorship for horizontal collaboration in logistics," Omega, Elsevier, vol. 111(C).
    10. Takehiro Ito & Yuni Iwamasa & Naonori Kakimura & Naoyuki Kamiyama & Yusuke Kobayashi & Yuta Nozaki & Yoshio Okamoto & Kenta Ozeki, 2022. "Reforming an Envy-Free Matching," Papers 2207.02641, arXiv.org.
    11. 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.
    12. Ayumi Igarashi & Yasushi Kawase & Warut Suksompong & Hanna Sumita, 2022. "Fair Division with Two-Sided Preferences," Papers 2206.05879, arXiv.org, revised Aug 2024.
    13. Mill'an Guerra Beatriz Alejandra, 2022. "The outcome of the restabilization process in matching markets," Papers 2202.12452, arXiv.org.
    14. Wu, Qingyun, 2020. "Entering classes in the college admissions model," Games and Economic Behavior, Elsevier, vol. 124(C), pages 579-587.
    15. Doğan, Battal & Yenmez, M. Bumin, 2019. "Unified versus divided enrollment in school choice: Improving student welfare in Chicago," Games and Economic Behavior, Elsevier, vol. 118(C), pages 366-373.

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    More about this item

    Keywords

    Matching; Envy-free; Lattice; Vacancy chain;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D47 - Microeconomics - - Market Structure, Pricing, and Design - - - Market Design

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