IDEAS home Printed from https://ideas.repec.org/a/spr/sochwe/v53y2019i2d10.1007_s00355-019-01181-x.html
   My bibliography  Save this article

Random matching under priorities: stability and no envy concepts

Author

Listed:
  • Haris Aziz

    (UNSW Sydney and Data61, CSIRO)

  • Bettina Klaus

    (University of Lausanne)

Abstract

We consider stability concepts for random matchings where agents have preferences over objects and objects have priorities for the agents. When matchings are deterministic, the standard stability concept also captures the fairness property of no (justified) envy. When matchings can be random, there are a number of natural stability and fairness concepts that coincide with stability and no envy whenever matchings are deterministic. We formalize known stability concepts for random matchings for a general setting that allows weak preferences and weak priorities, unacceptability, and an unequal number of agents and objects. We then present a clear taxonomy of the stability concepts and identify logical relations between them. Finally, we present a transformation from the most general setting to the most restricted setting, and show how almost all our stability concepts are preserved by that transformation.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:sochwe:v:53:y:2019:i:2:d:10.1007_s00355-019-01181-x
    DOI: 10.1007/s00355-019-01181-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00355-019-01181-x
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00355-019-01181-x?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Kojima, Fuhito & Manea, Mihai, 2010. "Incentives in the probabilistic serial mechanism," Journal of Economic Theory, Elsevier, vol. 145(1), pages 106-123, January.
    2. Vulkan, Nir & Roth, Alvin E. & Neeman, Zvika (ed.), 2013. "The Handbook of Market Design," OUP Catalogue, Oxford University Press, number 9780199570515.
    3. 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.
    4. M. Remzi Sanver & William Zwicker & Hervé Moulin & Jean-François Laslier, 2019. "The Future of Economic Design," Post-Print hal-02517300, HAL.
    5. Parag A. Pathak, 2011. "The Mechanism Design Approach to Student Assignment," Annual Review of Economics, Annual Reviews, vol. 3(1), pages 513-536, September.
    6. Wu, Qingyun & Roth, Alvin E., 2018. "The lattice of envy-free matchings," Games and Economic Behavior, Elsevier, vol. 109(C), pages 201-211.
    7. Alvin E. Roth & Uriel G. Rothblum & John H. Vande Vate, 1993. "Stable Matchings, Optimal Assignments, and Linear Programming," Mathematics of Operations Research, INFORMS, vol. 18(4), pages 803-828, November.
    8. Afacan, Mustafa Oǧuz, 2018. "The object allocation problem with random priorities," Games and Economic Behavior, Elsevier, vol. 110(C), pages 71-89.
    9. Schlegel, Jan Christoph, 2018. "A note on ex-ante stable lotteries," Economics Letters, Elsevier, vol. 164(C), pages 90-93.
    10. Kesten, Onur & Unver, Utku, 2015. "A theory of school choice lotteries," Theoretical Economics, Econometric Society, vol. 10(2), May.
    11. Roth, Alvin E, 1986. "On the Allocation of Residents to Rural Hospitals: A General Property of Two-Sided Matching Markets," Econometrica, Econometric Society, vol. 54(2), pages 425-427, March.
    12. Chung-Piaw Teo & Jay Sethuraman, 1998. "The Geometry of Fractional Stable Matchings and Its Applications," Mathematics of Operations Research, INFORMS, vol. 23(4), pages 874-891, November.
    13. Doğan, Battal & Yıldız, Kemal, 2016. "Efficiency and stability of probabilistic assignments in marriage problems," Games and Economic Behavior, Elsevier, vol. 95(C), pages 47-58.
    14. Balinski, Michel & Sonmez, Tayfun, 1999. "A Tale of Two Mechanisms: Student Placement," Journal of Economic Theory, Elsevier, vol. 84(1), pages 73-94, January.
    15. Kamada, Yuichiro & Kojima, Fuhito, 2017. "Stability concepts in matching under distributional constraints," Journal of Economic Theory, Elsevier, vol. 168(C), pages 107-142.
    16. Blum, Yosef & Roth, Alvin E. & Rothblum, Uriel G., 1997. "Vacancy Chains and Equilibration in Senior-Level Labor Markets," Journal of Economic Theory, Elsevier, vol. 76(2), pages 362-411, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. repec:cty:dpaper:17/05 is not listed on IDEAS
    2. Niclas Boehmer & Edith Elkind, 2020. "Stable Roommate Problem with Diversity Preferences," Papers 2004.14640, arXiv.org.
    3. Aziz, Haris & Brandl, Florian, 2022. "The vigilant eating rule: A general approach for probabilistic economic design with constraints," Games and Economic Behavior, Elsevier, vol. 135(C), pages 168-187.
    4. Schlegel, J. C., 2017. "A Note on Ex-Ante Stable Lotteries," Working Papers 17/06, Department of Economics, City University London.
    5. Haris Aziz & Florian Brandl, 2020. "The Vigilant Eating Rule: A General Approach for Probabilistic Economic Design with Constraints," Papers 2008.08991, arXiv.org, revised Jul 2021.
    6. Mehdi Feizi, 2023. "The object allocation problem with favoring upper ranks," International Journal of Economic Theory, The International Society for Economic Theory, vol. 19(2), pages 370-383, June.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Haris Aziz & Florian Brandl, 2020. "The Vigilant Eating Rule: A General Approach for Probabilistic Economic Design with Constraints," Papers 2008.08991, arXiv.org, revised Jul 2021.
    3. Aziz, Haris & Brandl, Florian, 2022. "The vigilant eating rule: A general approach for probabilistic economic design with constraints," Games and Economic Behavior, Elsevier, vol. 135(C), pages 168-187.
    4. Neme, Pablo & Oviedo, Jorge, 2021. "On the set of many-to-one strongly stable fractional matchings," Mathematical Social Sciences, Elsevier, vol. 110(C), pages 1-13.
    5. 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.
    6. Afacan, Mustafa Oǧuz, 2018. "The object allocation problem with random priorities," Games and Economic Behavior, Elsevier, vol. 110(C), pages 71-89.
    7. , Emin & , Bumin & , Ali, 2013. "Effective affirmative action in school choice," Theoretical Economics, Econometric Society, vol. 8(2), May.
    8. Bettina Klaus & David F. Manlove & Francesca Rossi, 2014. "Matching under Preferences," Cahiers de Recherches Economiques du Département d'économie 14.07, Université de Lausanne, Faculté des HEC, Département d’économie.
    9. Schlegel, Jan Christoph & Mamageishvili, Akaki, 2020. "Welfare theorems for random assignments with priorities," Games and Economic Behavior, Elsevier, vol. 124(C), pages 62-81.
    10. Wu, Qingyun & Roth, Alvin E., 2018. "The lattice of envy-free matchings," Games and Economic Behavior, Elsevier, vol. 109(C), pages 201-211.
    11. John William Hatfield & Fuhito Kojima & Yusuke Narita, 2011. "Promoting School Competition Through School Choice: A Market Design Approach," Working Papers 2011-018, Human Capital and Economic Opportunity Working Group.
    12. Ágoston, Kolos Csaba & Biró, Péter & Szántó, Richárd, 2018. "Stable project allocation under distributional constraints," Operations Research Perspectives, Elsevier, vol. 5(C), pages 59-68.
    13. 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.
    14. Balbuzanov, Ivan, 2022. "Constrained random matching," Journal of Economic Theory, Elsevier, vol. 203(C).
    15. Bettina Klaus & Flip Klijn, 2021. "Minimal-Access Rights in School Choice and the Deferred Acceptance Mechanism," Working Papers 1264, Barcelona School of Economics.
    16. Doğan, Battal & Yıldız, Kemal, 2016. "Efficiency and stability of probabilistic assignments in marriage problems," Games and Economic Behavior, Elsevier, vol. 95(C), pages 47-58.
    17. Scott Duke Kominers & Alexander Teytelboym & Vincent P Crawford, 2017. "An invitation to market design," Oxford Review of Economic Policy, Oxford University Press and Oxford Review of Economic Policy Limited, vol. 33(4), pages 541-571.
    18. 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.
    19. Avataneo, Michelle & Turhan, Bertan, 2021. "Slot-specific priorities with capacity transfers," Games and Economic Behavior, Elsevier, vol. 129(C), pages 536-548.
    20. Kesten, Onur & Unver, Utku, 2015. "A theory of school choice lotteries," Theoretical Economics, Econometric Society, vol. 10(2), May.

    More about this item

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sochwe:v:53:y:2019:i:2:d:10.1007_s00355-019-01181-x. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.