IDEAS home Printed from https://ideas.repec.org/a/eee/gamebe/v127y2021icp155-178.html
   My bibliography  Save this article

Optimal and efficient mechanisms with asymmetrically budget constrained buyers

Author

Listed:
  • Boulatov, Alexei
  • Severinov, Sergei

Abstract

The paper characterizes the optimal (revenue-maximizing) mechanism for allocating a good to buyers who face asymmetric budget constraints. The optimal mechanism belongs to one of two classes. When the budget differences between the buyers are small, the mechanism discriminates only between high-valuation types for whom the budget constraint is binding. All low valuations buyers are treated symmetrically despite budget differences. When budget differences are sufficiently large, the mechanism discriminates in favor of buyers with small budgets when the valuations are low, and in favor of buyers with larger budgets when the valuations are high. We also provide a characterization of the constrained-efficient (surplus maximizing) mechanism and demonstrate that it shares the above properties of the optimal mechanism.

Suggested Citation

  • Boulatov, Alexei & Severinov, Sergei, 2021. "Optimal and efficient mechanisms with asymmetrically budget constrained buyers," Games and Economic Behavior, Elsevier, vol. 127(C), pages 155-178.
    • Handle: RePEc:eee:gamebe:v:127:y:2021:i:c:p:155-178
    DOI: 10.1016/j.geb.2021.02.001
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0899825621000166
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.geb.2021.02.001?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. Jeremy Bulow & Jonathan Levin & Paul Milgrom, 2009. "Winning Play in Spectrum Auctions," NBER Working Papers 14765, National Bureau of Economic Research, Inc.
    2. Pitchik, Carolyn, 2009. "Budget-constrained sequential auctions with incomplete information," Games and Economic Behavior, Elsevier, vol. 66(2), pages 928-949, July.
    3. Bobkova, Nina, 2020. "Asymmetric budget constraints in a first-price auction," Journal of Economic Theory, Elsevier, vol. 186(C).
    4. Alexey Malakhov & Rakesh Vohra, 2008. "Optimal auctions for asymmetrically budget constrained bidders," Review of Economic Design, Springer;Society for Economic Design, vol. 12(4), pages 245-257, December.
    5. Myerson, Roger B, 1979. "Incentive Compatibility and the Bargaining Problem," Econometrica, Econometric Society, vol. 47(1), pages 61-73, January.
    6. Che, Yeon-Koo & Gale, Ian, 2000. "The Optimal Mechanism for Selling to a Budget-Constrained Buyer," Journal of Economic Theory, Elsevier, vol. 92(2), pages 198-233, June.
    7. Zheng, Charles Z., 2001. "High Bids and Broke Winners," Journal of Economic Theory, Elsevier, vol. 100(1), pages 129-171, September.
    8. Yeon-Koo Che & Ian Gale, 1998. "Standard Auctions with Financially Constrained Bidders," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 65(1), pages 1-21.
    9. Che, Yeon-Koo & Gale, Ian & Kim, Jinwoo, 2013. "Efficient assignment mechanisms for liquidity-constrained agents," International Journal of Industrial Organization, Elsevier, vol. 31(5), pages 659-665.
    10. Philippe Jehiel & Laurent Lamy, 2015. "On Discrimination in Auctions with Endogenous Entry," American Economic Review, American Economic Association, vol. 105(8), pages 2595-2643, August.
    11. Maskin, Eric S., 2000. "Auctions, development, and privatization: Efficient auctions with liquidity-constrained buyers," European Economic Review, Elsevier, vol. 44(4-6), pages 667-681, May.
    12. Yeon-Koo Che & Ian Gale & Jinwoo Kim, 2013. "Assigning Resources to Budget-Constrained Agents," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 80(1), pages 73-107.
    13. Richter, Michael, 2019. "Mechanism design with budget constraints and a population of agents," Games and Economic Behavior, Elsevier, vol. 115(C), pages 30-47.
    14. Michael H. Rothkopf, 2007. "Thirteen Reasons Why the Vickrey-Clarke-Groves Process Is Not Practical," Operations Research, INFORMS, vol. 55(2), pages 191-197, April.
    15. Che, Yeon-Koo & Gale, Ian, 1996. "Expected revenue of all-pay auctions and first-price sealed-bid auctions with budget constraints," Economics Letters, Elsevier, vol. 50(3), pages 373-379, March.
    16. Roger B. Myerson, 1981. "Optimal Auction Design," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 58-73, February.
    17. Pai, Mallesh M. & Vohra, Rakesh, 2014. "Optimal auctions with financially constrained buyers," Journal of Economic Theory, Elsevier, vol. 150(C), pages 383-425.
    18. Hafalir, Isa E. & Ravi, R. & Sayedi, Amin, 2012. "A near Pareto optimal auction with budget constraints," Games and Economic Behavior, Elsevier, vol. 74(2), pages 699-708.
    19. Laffont, Jean-Jacques & Robert, Jacques, 1996. "Optimal auction with financially constrained buyers," Economics Letters, Elsevier, vol. 52(2), pages 181-186, August.
    20. Dobzinski, Shahar & Lavi, Ron & Nisan, Noam, 2012. "Multi-unit auctions with budget limits," Games and Economic Behavior, Elsevier, vol. 74(2), pages 486-503.
    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. Holzer, Jorge & McConnell, Kenneth, 2023. "Extraction rights allocation with liquidity constraints," Resource and Energy Economics, Elsevier, vol. 71(C).
    2. Savas Dayanik & Semih O. Sezer, 2023. "Optimal dynamic multi-keyword bidding policy of an advertiser in search-based advertising," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 97(1), pages 25-56, February.

    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. Burkett, Justin, 2016. "Optimally constraining a bidder using a simple budget," Theoretical Economics, Econometric Society, vol. 11(1), January.
    2. Hummel, Patrick, 2017. "Endogenous budget constraints," Mathematical Social Sciences, Elsevier, vol. 88(C), pages 11-15.
    3. Carbajal, Juan Carlos & Mu'alem, Ahuva, 2020. "Selling mechanisms for a financially constrained buyer," Games and Economic Behavior, Elsevier, vol. 124(C), pages 386-405.
    4. Burkett, Justin, 2015. "Endogenous budget constraints in auctions," Journal of Economic Theory, Elsevier, vol. 158(PA), pages 1-20.
    5. Kotowski, Maciej H., 2020. "First-price auctions with budget constraints," Theoretical Economics, Econometric Society, vol. 15(1), January.
    6. Jianxin Rong & Ning Sun & Dazhong Wang, 2019. "A New Evaluation Criterion for Allocation Mechanisms with Application to Vehicle License Allocations in China," The Journal of Mechanism and Institution Design, Society for the Promotion of Mechanism and Institution Design, University of York, vol. 4(1), pages 39-86, November.
    7. Ghosh, Gagan, 2021. "Simultaneous auctions with budgets: Equilibrium existence and characterization," Games and Economic Behavior, Elsevier, vol. 126(C), pages 75-93.
    8. Pai, Mallesh M. & Vohra, Rakesh, 2014. "Optimal auctions with financially constrained buyers," Journal of Economic Theory, Elsevier, vol. 150(C), pages 383-425.
    9. Richter, Michael, 2019. "Mechanism design with budget constraints and a population of agents," Games and Economic Behavior, Elsevier, vol. 115(C), pages 30-47.
    10. Le, Phuong, 2018. "Pareto optimal budgeted combinatorial auctions," Theoretical Economics, Econometric Society, vol. 13(2), May.
    11. Gerard van der Laan & Zaifu Yang, 2016. "An ascending multi-item auction with financially constrained bidders," The Journal of Mechanism and Institution Design, Society for the Promotion of Mechanism and Institution Design, University of York, vol. 1(1), pages 109-149, December.
    12. Baisa, Brian, 2017. "Auction design without quasilinear preferences," Theoretical Economics, Econometric Society, vol. 12(1), January.
    13. Che, Yeon-Koo & Gale, Ian & Kim, Jinwoo, 2013. "Efficient assignment mechanisms for liquidity-constrained agents," International Journal of Industrial Organization, Elsevier, vol. 31(5), pages 659-665.
    14. Baisa, Brian & Rabinovich, Stanislav, 2016. "Optimal auctions with endogenous budgets," Economics Letters, Elsevier, vol. 141(C), pages 162-165.
    15. Santiago R. Balseiro & Omar Besbes & Gabriel Y. Weintraub, 2019. "Dynamic Mechanism Design with Budget-Constrained Buyers Under Limited Commitment," Operations Research, INFORMS, vol. 67(3), pages 711-730, May.
    16. Zaifu Yang & Jingsheng Yu, 2018. "Efficient Ascending Menu Auctions with Budget Constrained Bidders," Discussion Papers 18/09, Department of Economics, University of York.
    17. Phuong Le, 2017. "Mechanisms for combinatorial auctions with budget constraints," Review of Economic Design, Springer;Society for Economic Design, vol. 21(1), pages 1-31, March.
    18. Zhonghao Shui, 2023. "Rejection prices and an auctioneer with non-monotonic utility," International Journal of Game Theory, Springer;Game Theory Society, vol. 52(3), pages 925-951, September.
    19. Ghosh, Gagan & Liu, Heng, 2019. "Sequential second-price auctions with private budgets," Games and Economic Behavior, Elsevier, vol. 113(C), pages 611-632.
    20. Santiago R. Balseiro & Ozan Candogan, 2017. "Optimal Contracts for Intermediaries in Online Advertising," Operations Research, INFORMS, vol. 65(4), pages 878-896, August.

    More about this item

    Keywords

    Mechanism Design; Optimal and efficient mechanisms; Auctions; Asymmetric budget constraints;
    All these keywords.

    JEL classification:

    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

    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:eee:gamebe:v:127:y:2021:i:c:p:155-178. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/622836 .

    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.