IDEAS home Printed from https://ideas.repec.org/a/spr/snopef/v4y2023i2d10.1007_s43069-023-00195-7.html
   My bibliography  Save this article

A Simple Characterization of Assignment Mechanisms on Set Constraints

Author

Listed:
  • Ping Zhan

    (Edogawa University)

Abstract

We consider the problem of allocating divisible/indivisible goods to agents according to agents’ ordinal preferences. Hashimoto et al. [15] provided a nonalgorithmic and axiomatic characterization of well-studied probabilistic serial (PS) mechanism. Recently, Fujishige et al. [12] generalized the PS mechanism where goods are enlarged from a fixed set to a family of sets which is a polytope defined by a system of linear inequalities associated with submodular functions. The above extended PS (EPS) greatly improved the flexibility of allocations. Based on these two results, in this paper, we investigate the nonalgorithmic and axiomatic characterization of EPS. We show that the EPS rule is the only mechanism satisfying the ordinal fairness and a newly defined non-wastefulness. The submodularity plays a crucial role in our arguments.

Suggested Citation

  • Ping Zhan, 2023. "A Simple Characterization of Assignment Mechanisms on Set Constraints," SN Operations Research Forum, Springer, vol. 4(2), pages 1-15, June.
    • Handle: RePEc:spr:snopef:v:4:y:2023:i:2:d:10.1007_s43069-023-00195-7
    DOI: 10.1007/s43069-023-00195-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s43069-023-00195-7
    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/s43069-023-00195-7?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 search for a different version of it.

    References listed on IDEAS

    as
    1. Chatterji, Shurojit & Liu, Peng, 2020. "Random assignments of bundles," Journal of Mathematical Economics, Elsevier, vol. 87(C), pages 15-30.
    2. Heo, Eun Jeong, 2014. "Probabilistic assignment problem with multi-unit demands: A generalization of the serial rule and its characterization," Journal of Mathematical Economics, Elsevier, vol. 54(C), pages 40-47.
    3. Balbuzanov, Ivan, 2022. "Constrained random matching," Journal of Economic Theory, Elsevier, vol. 203(C).
    4. Eric Budish & Yeon-Koo Che & Fuhito Kojima & Paul Milgrom, 2013. "Designing Random Allocation Mechanisms: Theory and Applications," American Economic Review, American Economic Association, vol. 103(2), pages 585-623, April.
    5. Bogomolnaia, Anna, 2015. "Random assignment: Redefining the serial rule," Journal of Economic Theory, Elsevier, vol. 158(PA), pages 308-318.
    6. Bogomolnaia, Anna & Heo, Eun Jeong, 2012. "Probabilistic assignment of objects: Characterizing the serial rule," Journal of Economic Theory, Elsevier, vol. 147(5), pages 2072-2082.
    7. Bogomolnaia, Anna & Moulin, Herve, 2001. "A New Solution to the Random Assignment Problem," Journal of Economic Theory, Elsevier, vol. 100(2), pages 295-328, October.
    8. Hashimoto, Tadashi & Hirata, Daisuke & Kesten, Onur & Kurino, Morimitsu & Unver, Utku, 2014. "Two axiomatic approaches to the probabilistic serial mechanism," Theoretical Economics, Econometric Society, vol. 9(1), January.
    9. Yoshio Sano & Ping Zhan, 2021. "Extended Random Assignment Mechanisms on a Family of Good Sets," SN Operations Research Forum, Springer, vol. 2(4), pages 1-30, December.
    10. Doğan, Battal & Doğan, Serhat & Yıldız, Kemal, 2018. "A new ex-ante efficiency criterion and implications for the probabilistic serial mechanism," Journal of Economic Theory, Elsevier, vol. 175(C), pages 178-200.
    11. Heo, Eun Jeong & Yılmaz, Özgür, 2015. "A characterization of the extended serial correspondence," Journal of Mathematical Economics, Elsevier, vol. 59(C), pages 102-110.
    12. 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.
    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. Ping Zhan, 2023. "Simultaneous eating algorithm and greedy algorithm in assignment problems," Journal of Combinatorial Optimization, Springer, vol. 45(5), pages 1-24, July.

    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. Balbuzanov, Ivan, 2022. "Constrained random matching," Journal of Economic Theory, Elsevier, vol. 203(C).
    2. Mustafa Oğuz Afacan, 2023. "Axiomatic characterizations of the constrained probabilistic serial mechanism," Theory and Decision, Springer, vol. 95(3), pages 465-484, October.
    3. Yoshio Sano & Ping Zhan, 2021. "Extended Random Assignment Mechanisms on a Family of Good Sets," SN Operations Research Forum, Springer, vol. 2(4), pages 1-30, December.
    4. Haris Aziz & Yoichi Kasajima, 2017. "Impossibilities for probabilistic assignment," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 49(2), pages 255-275, August.
    5. Andrew McLennan & Shino Takayama & Yuki Tamura, 2024. "An Efficient, Computationally Tractable School Choice Mechanism," Discussion Papers Series 668, School of Economics, University of Queensland, Australia.
    6. Youngsub Chun & Kiyong Yun, 2020. "Upper-contour strategy-proofness in the probabilistic assignment problem," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 54(4), pages 667-687, April.
    7. Yajing Chen & Patrick Harless & Zhenhua Jiao, 2021. "The probabilistic rank random assignment rule and its axiomatic characterization," Papers 2104.09165, arXiv.org.
    8. 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.
    9. Ping Zhan, 2023. "Simultaneous eating algorithm and greedy algorithm in assignment problems," Journal of Combinatorial Optimization, Springer, vol. 45(5), pages 1-24, July.
    10. Wonki Jo Cho, 2018. "Probabilistic assignment: an extension approach," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 51(1), pages 137-162, June.
    11. Huang, Chao & Tian, Guoqiang, 2017. "Guaranteed size ratio of ordinally efficient and envy-free mechanisms in the assignment problem," Games and Economic Behavior, Elsevier, vol. 105(C), pages 1-8.
    12. Chang, Hee-In & Chun, Youngsub, 2017. "Probabilistic assignment of indivisible objects when agents have the same preferences except the ordinal ranking of one object," Mathematical Social Sciences, Elsevier, vol. 90(C), pages 80-92.
    13. Basteck, Christian & Ehlers, Lars, 2021. "Strategy-Proof and Envy-Free Random Assignment," Rationality and Competition Discussion Paper Series 307, CRC TRR 190 Rationality and Competition.
    14. Harless, Patrick, 2019. "Efficient rules for probabilistic assignment," Journal of Mathematical Economics, Elsevier, vol. 84(C), pages 107-116.
    15. Cho, Wonki Jo, 2016. "When is the probabilistic serial assignment uniquely efficient and envy-free?," Journal of Mathematical Economics, Elsevier, vol. 66(C), pages 14-25.
    16. Heo, Eun Jeong & Yılmaz, Özgür, 2015. "A characterization of the extended serial correspondence," Journal of Mathematical Economics, Elsevier, vol. 59(C), pages 102-110.
    17. Bogomolnaia, Anna & Moulin, Herve, 2015. "Size versus fairness in the assignment problem," Games and Economic Behavior, Elsevier, vol. 90(C), pages 119-127.
    18. 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.
    19. Balbuzanov, Ivan, 2020. "Short trading cycles: Paired kidney exchange with strict ordinal preferences," Mathematical Social Sciences, Elsevier, vol. 104(C), pages 78-87.
    20. Basteck, Christian & Ehlers, Lars, 2023. "Strategy-proof and envy-free random assignment," Journal of Economic Theory, Elsevier, vol. 209(C).

    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:snopef:v:4:y:2023:i:2:d:10.1007_s43069-023-00195-7. 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.