IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2104.03219.html
   My bibliography  Save this paper

The Value of Excess Supply in Spatial Matching Markets

Author

Listed:
  • Mohammad Akbarpour
  • Yeganeh Alimohammadi
  • Shengwu Li
  • Amin Saberi

Abstract

We study dynamic matching in a spatial setting. Drivers are distributed at random on some interval. Riders arrive in some (possibly adversarial) order at randomly drawn points. The platform observes the location of the drivers, and can match newly arrived riders immediately, or can wait for more riders to arrive. Unmatched riders incur a waiting cost $c$ per period. The platform can match riders and drivers, irrevocably. The cost of matching a driver to a rider is equal to the distance between them. We quantify the value of slightly increasing supply. We prove that when there are $(1+\epsilon)$ drivers per rider (for any $\epsilon > 0$), the cost of matching returned by a simple greedy algorithm which pairs each arriving rider to the closest available driver is $O(\log^3(n))$, where $n$ is the number of riders. On the other hand, with equal number of drivers and riders, even the \emph{ex post} optimal matching does not have a cost less than $\Theta(\sqrt{n})$. Our results shed light on the important role of (small) excess supply in spatial matching markets.

Suggested Citation

  • Mohammad Akbarpour & Yeganeh Alimohammadi & Shengwu Li & Amin Saberi, 2021. "The Value of Excess Supply in Spatial Matching Markets," Papers 2104.03219, arXiv.org.
    • Handle: RePEc:arx:papers:2104.03219
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2104.03219
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Mohammad Akbarpour & Julien Combe & Yinghua He & Victor Hiller & Robert Shimer & Olivier Tercieux, 2020. "Unpaired Kidney Exchange: Overcoming Double Coincidence of Wants without Money," Post-Print halshs-02973042, HAL.
    2. Baccara, Mariagiovanna & Lee, SangMok & Yariv, Leeat, 2020. "Optimal dynamic matching," Theoretical Economics, Econometric Society, vol. 15(3), July.
    3. Yash Kanoria & Seungki Min & Pengyu Qian, 2020. "The Competition for Partners in Matching Markets," Papers 2006.14653, arXiv.org, revised Jan 2023.
    4. Itai Ashlagi & Yash Kanoria & Jacob D. Leshno, 2017. "Unbalanced Random Matching Markets: The Stark Effect of Competition," Journal of Political Economy, University of Chicago Press, vol. 125(1), pages 69-98.
    5. Bulow, Jeremy & Klemperer, Paul, 1996. "Auctions versus Negotiations," American Economic Review, American Economic Association, vol. 86(1), pages 180-194, March.
    6. Nick Arnosti & Peng Shi, 2019. "How (Not) to Allocate Affordable Housing," AEA Papers and Proceedings, American Economic Association, vol. 109, pages 204-208, May.
    7. Boris Pittel, 2019. "On Likely Solutions of the Stable Matching Problem with Unequal Numbers of Men and Women," Mathematics of Operations Research, INFORMS, vol. 44(1), pages 122-146, February.
    8. Vahideh H. Manshadi & Shayan Oveis Gharan & Amin Saberi, 2012. "Online Stochastic Matching: Online Actions Based on Offline Statistics," Mathematics of Operations Research, INFORMS, vol. 37(4), pages 559-573, 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. Yash Kanoria, 2021. "Dynamic Spatial Matching," Papers 2105.07329, arXiv.org, revised Oct 2023.

    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. Itai Ashlagi & Mark Braverman & Amin Saberi & Clayton Thomas & Geng Zhao, 2020. "Tiered Random Matching Markets: Rank is Proportional to Popularity," Papers 2009.05124, arXiv.org, revised Jan 2021.
    2. Linda Cai & Clayton Thomas, 2019. "Representing All Stable Matchings by Walking a Maximal Chain," Papers 1910.04401, arXiv.org.
    3. Itai Ashlagi & Mark Braverman & Geng Zhao, 2023. "Welfare Distribution in Two-sided Random Matching Markets," Papers 2302.08599, arXiv.org.
    4. Ce Liu, 2020. "Stability in Repeated Matching Markets," Papers 2007.03794, arXiv.org, revised Mar 2021.
    5. Ashlagi, Itai & Nikzad, Afshin, 2020. "What matters in school choice tie-breaking? How competition guides design," Journal of Economic Theory, Elsevier, vol. 190(C).
    6. 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.
    7. Wei He & Jiangtao Li & Weijie Zhong, 2024. "Rank-Guaranteed Auctions," Papers 2408.12001, arXiv.org.
    8. Schmitz, Patrick W., 2003. "On second-price auctions and imperfect competition," Journal of Mathematical Economics, Elsevier, vol. 39(8), pages 901-909, November.
    9. Marco LiCalzi, 2022. "Bipartite choices," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 45(2), pages 551-568, December.
    10. Jinpeng Ma, 1997. "English Auctions and Walrasian Equilibria with Multiple Objects: a dynamic approach," Departmental Working Papers 199702, Rutgers University, Department of Economics.
    11. Eshien Chong & Carine Staropoli & Anne Yvrande-Billon, 2014. "Auction versus Negotiation in Public Procurement: Looking for Empirical Evidence," Post-Print hal-00512813, HAL.
    12. Battal Doğan & M. Bumin Yenmez, 2023. "When does an additional stage improve welfare in centralized assignment?," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 76(4), pages 1145-1173, November.
    13. Boone, J., 2003. "Optimal Competition : A Benchmark for Competition Policy," Discussion Paper 2003-3, Tilburg University, Center for Economic Research.
    14. Raskovich, Alexander, 2007. "Ordered bargaining," International Journal of Industrial Organization, Elsevier, vol. 25(5), pages 1126-1143, October.
    15. Yuen Leng Chow & Isa E. Hafalir & Abdullah Yavas, 2015. "Auction versus Negotiated Sale: Evidence from Real Estate Sales," Real Estate Economics, American Real Estate and Urban Economics Association, vol. 43(2), pages 432-470, June.
    16. Michael Bates & Michael Dinerstein & Andrew C. Johnston & Isaac Sorkin, 2022. "Teacher Labor Market Equilibrium and Student Achievement," CESifo Working Paper Series 9551, CESifo.
    17. Cremer, Jacques & Khalil, Fahad, 1992. "Gathering Information before Signing a Contract," American Economic Review, American Economic Association, vol. 82(3), pages 566-578, June.
    18. Michael Greinecker & Christopher Kah, 2018. "Pairwise stable matching in large economies," Graz Economics Papers 2018-01, University of Graz, Department of Economics.
    19. Ge Yu & Sheldon H. Jacobson, 2020. "Primal-dual analysis for online interval scheduling problems," Journal of Global Optimization, Springer, vol. 77(3), pages 575-602, July.
    20. Walter Beckert, 2004. "Dynamic Monopolies with Stochastic Demand," Birkbeck Working Papers in Economics and Finance 0404, Birkbeck, Department of Economics, Mathematics & Statistics.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:arx:papers:2104.03219. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.