IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2205.06132.html
   My bibliography  Save this paper

Core-Stability in Assignment Markets with Financially Constrained Buyers

Author

Listed:
  • Eleni Batziou
  • Martin Bichler
  • Maximilian Fichtl

Abstract

We study markets where a set of indivisible items is sold to bidders with unit-demand valuations, subject to a hard budget limit. Without financial constraints and pure quasilinear bidders, this assignment model allows for a simple ascending auction format that maximizes welfare and is incentive-compatible and core-stable. Introducing budget constraints, the ascending auction requires strong additional conditions on the unit-demand preferences to maintain its properties. We show that, without these conditions, we cannot hope for an incentive-compatible and core-stable mechanism. We design an iterative algorithm that depends solely on a trivially verifiable ex-post condition and demand queries, and with appropriate decisions made by an auctioneer, always yields a welfare-maximizing and core-stable outcome. If these conditions do not hold, we cannot hope for incentive-compatibility and computing welfare-maximizing assignments and core-stable prices is hard: Even in the presence of value queries, where bidders reveal their valuations and budgets truthfully, we prove that the problem becomes NP-complete for the assignment market model. The analysis complements complexity results for markets with more complex valuations and shows that even with simple unit-demand bidders the problem becomes intractable. This raises doubts on the efficiency of simple auction designs as they are used in high-stakes markets, where budget constraints typically play a role.

Suggested Citation

  • Eleni Batziou & Martin Bichler & Maximilian Fichtl, 2022. "Core-Stability in Assignment Markets with Financially Constrained Buyers," Papers 2205.06132, arXiv.org.
  • Handle: RePEc:arx:papers:2205.06132
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2205.06132
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Mishra, D. & Talman, A.J.J., 2006. "Overdemand and Underdemand in Economies with Indivisible Goods and Unit Demands," Discussion Paper 2006-84, Tilburg University, Center for Economic Research.
    2. 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.
    3. H. W. Kuhn, 1955. "The Hungarian method for the assignment problem," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 2(1‐2), pages 83-97, March.
    4. Elizabeth Baldwin & Paul Klemperer, 2019. "Understanding Preferences: “Demand Types”, and the Existence of Equilibrium With Indivisibilities," Econometrica, Econometric Society, vol. 87(3), pages 867-932, May.
    5. William Vickrey, 1961. "Counterspeculation, Auctions, And Competitive Sealed Tenders," Journal of Finance, American Finance Association, vol. 16(1), pages 8-37, March.
    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. Bikhchandani, Sushil & Ostroy, Joseph M., 2002. "The Package Assignment Model," Journal of Economic Theory, Elsevier, vol. 107(2), pages 377-406, December.
    8. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
    9. Bikhchandani, Sushil & Mamer, John W., 1997. "Competitive Equilibrium in an Exchange Economy with Indivisibilities," Journal of Economic Theory, Elsevier, vol. 74(2), pages 385-413, June.
    10. Gul, Faruk & Stacchetti, Ennio, 1999. "Walrasian Equilibrium with Gross Substitutes," Journal of Economic Theory, Elsevier, vol. 87(1), pages 95-124, July.
    11. Mishra, Debasis & Parkes, David C., 2007. "Ascending price Vickrey auctions for general valuations," Journal of Economic Theory, Elsevier, vol. 132(1), pages 335-366, January.
    12. Kelso, Alexander S, Jr & Crawford, Vincent P, 1982. "Job Matching, Coalition Formation, and Gross Substitutes," Econometrica, Econometric Society, vol. 50(6), pages 1483-1504, November.
    13. Satoru Fujishige & Akihisa Tamura, 2007. "A Two-Sided Discrete-Concave Market with Possibly Bounded Side Payments: An Approach by Discrete Convex Analysis," Mathematics of Operations Research, INFORMS, vol. 32(1), pages 136-155, February.
    14. Saeed Alaei & Kamal Jain & Azarakhsh Malekian, 2016. "Competitive Equilibria in Two-Sided Matching Markets with General Utility Functions," Operations Research, INFORMS, vol. 64(3), pages 638-645, June.
    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. Andrew MACKENZIE & Yu ZHOU, 2022. "Tract Housing, The Core, And Pendulum Auctions," Discussion papers e-22-005, Graduate School of Economics , Kyoto University.

    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. Kazuo Murota, 2016. "Discrete convex analysis: A tool for economics and game theory," The Journal of Mechanism and Institution Design, Society for the Promotion of Mechanism and Institution Design, University of York, vol. 1(1), pages 151-273, December.
    2. Lawrence M. Ausubel, 2006. "An Efficient Dynamic Auction for Heterogeneous Commodities," American Economic Review, American Economic Association, vol. 96(3), pages 602-629, June.
    3. Vohra, Rakesh V., 2015. "Combinatorial Auctions," Handbook of Game Theory with Economic Applications,, Elsevier.
    4. Ozan Candogan & Asuman Ozdaglar & Pablo A. Parrilo, 2015. "Iterative Auction Design for Tree Valuations," Operations Research, INFORMS, vol. 63(4), pages 751-771, August.
    5. Jawad Abrache & Teodor Crainic & Michel Gendreau & Monia Rekik, 2007. "Combinatorial auctions," Annals of Operations Research, Springer, vol. 153(1), pages 131-164, September.
    6. Ben-Zwi, Oren, 2017. "Walrasian's characterization and a universal ascending auction," Games and Economic Behavior, Elsevier, vol. 104(C), pages 456-467.
    7. Akiyoshi Shioura & Zaifu Yang, 2013. "Equilibrium, Auction, Multiple Substitutes and Complements," Discussion Papers 13/17, Department of Economics, University of York.
    8. Zaifu Yang & Jingsheng Yu, 2018. "Efficient Ascending Menu Auctions with Budget Constrained Bidders," Discussion Papers 18/09, Department of Economics, University of York.
    9. Ozan Candogan & Saša Pekeč, 2018. "Efficient Allocation and Pricing of Multifeatured Items," Management Science, INFORMS, vol. 64(12), pages 5521-5543, December.
    10. Satoru Fujishige & Zaifu Yang, 2022. "Barter markets, indivisibilities, and Markovian core," Bulletin of Economic Research, Wiley Blackwell, vol. 74(1), pages 39-48, January.
    11. Bikhchandani, Sushil & Ostroy, Joseph M., 2002. "The Package Assignment Model," Journal of Economic Theory, Elsevier, vol. 107(2), pages 377-406, December.
    12. Lehmann, Benny & Lehmann, Daniel & Nisan, Noam, 2006. "Combinatorial auctions with decreasing marginal utilities," Games and Economic Behavior, Elsevier, vol. 55(2), pages 270-296, May.
    13. 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.
    14. Ma, Jinpeng, 1998. "Competitive Equilibrium with Indivisibilities," Journal of Economic Theory, Elsevier, vol. 82(2), pages 458-468, October.
    15. Lawrence M. Ausubel & Paul Milgrom, 2004. "Ascending Proxy Auctions," Discussion Papers 03-035, Stanford Institute for Economic Policy Research.
    16. Satoru Fujishige & Zaifu Yang, 2020. "A Universal Dynamic Auction for Unimodular Demand Types: An Efficient Auction Design for Various Kinds of Indivisible Commodities," Discussion Papers 20/08, Department of Economics, University of York.
    17. Tomoya Kazumura & Shigehiro Serizawa, 2016. "Efficiency and strategy-proofness in object assignment problems with multi-demand preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(3), pages 633-663, October.
    18. Satoru Fujishige & Zaifu Yang, 2002. "Existence of an Equilibrium in a General Competitive Exchange Economy with Indivisible Goods and Money," Annals of Economics and Finance, Society for AEF, vol. 3(1), pages 135-147, May.
    19. Núñez, Marina & Rafels, Carlos & Robles, Francisco, 2020. "A mechanism for package allocation problems with gross substitutes," Journal of Mathematical Economics, Elsevier, vol. 87(C), pages 6-14.
    20. Hitoshi Matsushima, 2011. "Price-Based Combinatorial Auction: Connectedness and Representative Valuations," CARF F-Series CARF-F-261, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.

    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:2205.06132. 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.