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The Value of Excess Supply in Spatial Matching Markets

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  • 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.

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  • 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
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    File URL: http://arxiv.org/pdf/2104.03219
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    References listed on IDEAS

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    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.
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    Cited by:

    1. Yash Kanoria, 2021. "Dynamic Spatial Matching," Papers 2105.07329, arXiv.org, revised Oct 2023.

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