IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2507.15735.html
   My bibliography  Save this paper

The Root of Revenue Continuity

Author

Listed:
  • Sergiu Hart
  • Noam Nisan

Abstract

In the setup of selling one or more goods, various papers have shown, in various forms and for various purposes, that a small change in the distribution of a buyer's valuations may cause only a small change in the possible revenue that can be extracted. We prove a simple, clean, convenient, and general statement to this effect: let X and Y be random valuations on k additive goods, and let W(X,Y) be the Wasserstein (or "earth mover's") distance between them; then sqrt(Rev(X))-sqrt(Rev(Y))

Suggested Citation

  • Sergiu Hart & Noam Nisan, 2025. "The Root of Revenue Continuity," Papers 2507.15735, arXiv.org.
    • Handle: RePEc:arx:papers:2507.15735
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2507.15735
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Hart, Sergiu & Nisan, Noam, 2017. "Approximate revenue maximization with multiple items," Journal of Economic Theory, Elsevier, vol. 172(C), pages 313-347.
    2. Kristóf Madarász & Andrea Prat, 2017. "Sellers with Misspecified Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 84(2), pages 790-815.
    3. Manelli, Alejandro M. & Vincent, Daniel R., 2006. "Bundling as an optimal selling mechanism for a multiple-good monopolist," Journal of Economic Theory, Elsevier, vol. 127(1), pages 1-35, March.
    4. , & , J., 2015. "Maximal revenue with multiple goods: nonmonotonicity and other observations," Theoretical Economics, Econometric Society, vol. 10(3), September.
    5. Thanassoulis, John, 2004. "Haggling over substitutes," Journal of Economic Theory, Elsevier, vol. 117(2), pages 217-245, August.
    6. Alison L. Gibbs & Francis Edward Su, 2002. "On Choosing and Bounding Probability Metrics," International Statistical Review, International Statistical Institute, vol. 70(3), pages 419-435, December.
    7. Hart, Sergiu & Nisan, Noam, 2019. "Selling multiple correlated goods: Revenue maximization and menu-size complexity," Journal of Economic Theory, Elsevier, vol. 183(C), pages 991-1029.
    8. Monteiro, Paulo Klinger, 2015. "A note on the continuity of the optimal auction," Economics Letters, Elsevier, vol. 137(C), pages 127-130.
    9. Roger B. Myerson, 1981. "Optimal Auction Design," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 58-73, February.
    10. McAfee, R. Preston & McMillan, John, 1988. "Multidimensional incentive compatibility and mechanism design," Journal of Economic Theory, Elsevier, vol. 46(2), pages 335-354, December.
    Full references (including those not matched with items on IDEAS)

    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. Bikhchandani, Sushil & Mishra, Debasis, 2022. "Selling two identical objects," Journal of Economic Theory, Elsevier, vol. 200(C).
    2. Devanur, Nikhil R. & Haghpanah, Nima & Psomas, Alexandros, 2020. "Optimal multi-unit mechanisms with private demands," Games and Economic Behavior, Elsevier, vol. 121(C), pages 482-505.
    3. Sergiu Hart & Noam Nisan, 2013. "Selling Multiple Correlated Goods: Revenue Maximization and Menu-Size Complexity (old title: "The Menu-Size Complexity of Auctions")," Papers 1304.6116, arXiv.org, revised Nov 2018.
    4. Hart, Sergiu & Nisan, Noam, 2019. "Selling multiple correlated goods: Revenue maximization and menu-size complexity," Journal of Economic Theory, Elsevier, vol. 183(C), pages 991-1029.
    5. Hart, Sergiu & Nisan, Noam, 2017. "Approximate revenue maximization with multiple items," Journal of Economic Theory, Elsevier, vol. 172(C), pages 313-347.
    6. Babaioff, Moshe & Gonczarowski, Yannai A. & Nisan, Noam, 2022. "The menu-size complexity of revenue approximation," Games and Economic Behavior, Elsevier, vol. 134(C), pages 281-307.
    7. Ran Ben-Moshe & Sergiu Hart & Noam Nisan, 2022. "Monotonic Mechanisms for Selling Multiple Goods," Papers 2210.17150, arXiv.org, revised Jun 2024.
    8. Chen, Bo & Ni, Debing, 2017. "Optimal bundle pricing under correlated valuations," International Journal of Industrial Organization, Elsevier, vol. 52(C), pages 248-281.
    9. Briest, Patrick & Chawla, Shuchi & Kleinberg, Robert & Weinberg, S. Matthew, 2015. "Pricing lotteries," Journal of Economic Theory, Elsevier, vol. 156(C), pages 144-174.
    10. Yeon-Koo Che & Weijie Zhong, 2021. "Robustly Optimal Mechanisms for Selling Multiple Goods," Papers 2105.02828, arXiv.org, revised Aug 2024.
    11. Kazumura, Tomoya & Mishra, Debasis & Serizawa, Shigehiro, 2020. "Strategy-proof multi-object mechanism design: Ex-post revenue maximization with non-quasilinear preferences," Journal of Economic Theory, Elsevier, vol. 188(C).
    12. Hedyeh Beyhaghi & Linda Cai & Yiding Feng & Yingkai Li & S. Matthew Weinberg, 2025. "Competition Complexity in Multi-Item Auctions: Beyond VCG and Regularity," Papers 2506.09291, arXiv.org.
    13. Tim Roughgarden & Inbal Talgam-Cohen & Qiqi Yan, 2019. "Robust Auctions for Revenue via Enhanced Competition," Operations Research, INFORMS, vol. 68(4), pages 1074-1094, July.
    14. Bikhchandani, Sushil & Mishra, Debasis, 2024. "Rank-preserving multidimensional mechanisms: An equivalence between identical-object and heterogeneous-object models," Journal of Economic Theory, Elsevier, vol. 222(C).
    15. Tang, Pingzhong & Wang, Zihe, 2017. "Optimal mechanisms with simple menus," Journal of Mathematical Economics, Elsevier, vol. 69(C), pages 54-70.
    16. Komal Malik & Kolagani Paramahamsa, 2024. "Selling two complementary goods," International Journal of Game Theory, Springer;Game Theory Society, vol. 53(2), pages 423-447, June.
    17. Seung Han Yoo, 2018. "Membership Mechanisms," Discussion Paper Series 1804, Institute of Economic Research, Korea University.
    18. Schäfers, Sebastian, 2022. "Product Lotteries and Loss Aversion," Working papers 2022/06, Faculty of Business and Economics - University of Basel.
    19. Komal Malik & Kolagani Paramahamsa, 2020. "Selling two complementary goods," Papers 2011.05840, arXiv.org, revised Jul 2022.
    20. Rochet, Jean-Charles, 2024. "Multidimensional screening after 37 years," Journal of Mathematical Economics, Elsevier, vol. 113(C).

    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:2507.15735. 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.