IDEAS home Printed from https://ideas.repec.org/p/snu/ioerwp/no92.html
   My bibliography  Save this paper

A Graph Theoretic Approach to the Slot Allocation Problem

Author

Listed:
  • Youngsub Chun
  • Boram Park

Abstract

We consider a problem of assigning slots to a group of agents. Each slot can serve only one agent at a time and it is located along a line. Each agent has a most preferred slot and incurs disutility when she is assigned away from the most preferred slot. Furthermore, we assume that each agent¡¯s utility is equal to the amount of monetary transfer minus the distance from the peak to her assigned slot. In this paper, we investigate how to assign slots to agents in an efficient and fair way. First, by using a bipartite graph of the slot allocation problem, we present a simple way of identifying all efficient assignments. Next, we introduce two allocation rules for the problem, the leximin and the leximax rules, and discuss their properties.

Suggested Citation

  • Youngsub Chun & Boram Park, 2014. "A Graph Theoretic Approach to the Slot Allocation Problem," Working Paper Series no92, Institute of Economic Research, Seoul National University.
    • Handle: RePEc:snu:ioerwp:no92
    as

    Download full text from publisher

    File URL: https://ier.snu.ac.kr/activity/working-papers?md=download&seqidx=33
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. James Schummer & Rakesh V. Vohra, 2013. "Assignment of Arrival Slots," American Economic Journal: Microeconomics, American Economic Association, vol. 5(2), pages 164-185, May.
    2. Hougaard, Jens Leth & Moreno-Ternero, Juan D. & Østerdal, Lars Peter, 2014. "Assigning agents to a line," Games and Economic Behavior, Elsevier, vol. 87(C), pages 539-553.
    3. 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.
    4. Sprumont, Yves, 1991. "The Division Problem with Single-Peaked Preferences: A Characterization of the Uniform Allocation Rule," Econometrica, Econometric Society, vol. 59(2), pages 509-519, March.
    5. Schummer, James & Abizada, Azar, 2017. "Incentives in landing slot problems," Journal of Economic Theory, Elsevier, vol. 170(C), pages 29-55.
    6. Svensson, Lars-Gunnar, 1983. "Large Indivisibles: An Analysis with Respect to Price Equilibrium and Fairness," Econometrica, Econometric Society, vol. 51(4), pages 939-954, July.
    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. K. J. Arrow & A. K. Sen & K. Suzumura (ed.), 2011. "Handbook of Social Choice and Welfare," Handbook of Social Choice and Welfare, Elsevier, edition 1, volume 2, number 2.
    9. Anna Bogomolnaia & Herve Moulin, 2004. "Random Matching Under Dichotomous Preferences," Econometrica, Econometric Society, vol. 72(1), pages 257-279, January.
    10. YIlmaz, Özgür, 2009. "Random assignment under weak preferences," Games and Economic Behavior, Elsevier, vol. 66(1), pages 546-558, May.
    11. Katta, Akshay-Kumar & Sethuraman, Jay, 2006. "A solution to the random assignment problem on the full preference domain," Journal of Economic Theory, Elsevier, vol. 131(1), pages 231-250, November.
    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. Aziz, Haris & Hougaard, Jens Leth & Moreno-Ternero, Juan D. & Østerdal, Lars Peter, 2017. "Computational aspects of assigning agents to a line," Mathematical Social Sciences, Elsevier, vol. 90(C), pages 93-99.
    2. Youngsub Chun & Manipushpak Mitra & Suresh Mutuswami, 2019. "Recent developments in the queueing problem," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(1), pages 1-23, April.
    3. Yu Zhou & Youngsub Chun & Shigehiro Serizawa, 2022. "A characterization of the Vickrey rule in slot allocation problems," International Journal of Economic Theory, The International Society for Economic Theory, vol. 18(1), pages 38-49, March.

    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. Hougaard, Jens Leth & Moreno-Ternero, Juan D. & Østerdal, Lars Peter, 2014. "Assigning agents to a line," Games and Economic Behavior, Elsevier, vol. 87(C), pages 539-553.
    2. 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.
    3. 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.
    4. 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.
    5. Bogomolnaia, Anna, 2015. "Random assignment: Redefining the serial rule," Journal of Economic Theory, Elsevier, vol. 158(PA), pages 308-318.
    6. Anna Bogomolnaia, 2015. "The Most Ordinally-Efficient of Random Voting Rules," HSE Working papers WP BRP 106/EC/2015, National Research University Higher School of Economics.
    7. Eun Heo, 2014. "The extended serial correspondence on a rich preference domain," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(2), pages 439-454, May.
    8. Balbuzanov, Ivan, 2020. "Short trading cycles: Paired kidney exchange with strict ordinal preferences," Mathematical Social Sciences, Elsevier, vol. 104(C), pages 78-87.
    9. Youngsub Chun & Manipushpak Mitra & Suresh Mutuswami, 2019. "Recent developments in the queueing problem," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(1), pages 1-23, April.
    10. Thomson, William, 2011. "Chapter Twenty-One - Fair Allocation Rules," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 2, chapter 21, pages 393-506, Elsevier.
    11. Balbuzanov, Ivan, 2022. "Constrained random matching," Journal of Economic Theory, Elsevier, vol. 203(C).
    12. 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.
    13. Afacan, Mustafa Oǧuz, 2018. "The object allocation problem with random priorities," Games and Economic Behavior, Elsevier, vol. 110(C), pages 71-89.
    14. 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.
    15. 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.
    16. 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.
    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. Youngsub Chun & Manipushpak Mitra & Suresh Mutuswami, 2014. "Egalitarian equivalence and strategyproofness in the queueing problem," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 56(2), pages 425-442, June.
    19. Ortega, Josué, 2020. "Multi-unit assignment under dichotomous preferences," Mathematical Social Sciences, Elsevier, vol. 103(C), pages 15-24.
    20. Kesten, Onur & Unver, Utku, 2015. "A theory of school choice lotteries," Theoretical Economics, Econometric Society, vol. 10(2), May.

    More about this item

    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:snu:ioerwp:no92. 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: Hojung Lee (email available below). General contact details of provider: https://edirc.repec.org/data/iesnukr.html .

    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.