IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1907.11915.html
   My bibliography  Save this paper

Electronic markets with multiple submodular buyers

Author

Listed:
  • Allan Borodin
  • Akash Rakheja

Abstract

We discuss the problem of setting prices in an electronic market that has more than one buyer. We assume that there are self-interested sellers each selling a distinct item that has an associated cost. Each buyer has a submodular valuation for purchasing any subset of items. The goal of the sellers is to set a price for their item such that their profit from possibly selling their item to the buyers is maximized. Our most comprehensive results concern a multi copy setting where each seller has m copies of their item and there are m buyers. In this setting, we give a necessary and sufficient condition for the existence of market clearing pure Nash equilibrium. We also show that not all equilibria are market clearing even when this condition is satisfied contrary to what was shown in the case of a single buyer in [2]. Finally, we investigate the pricing problem for multiple buyers in the limited supply setting when each seller only has a single copy of their item.

Suggested Citation

  • Allan Borodin & Akash Rakheja, 2019. "Electronic markets with multiple submodular buyers," Papers 1907.11915, arXiv.org, revised Sep 2019.
    • Handle: RePEc:arx:papers:1907.11915
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1907.11915
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. William C. Brainard & Herbert E. Scarf, 2005. "How to Compute Equilibrium Prices in 1891," American Journal of Economics and Sociology, Wiley Blackwell, vol. 64(1), pages 57-83, January.
    2. Gul, Faruk & Stacchetti, Ennio, 1999. "Walrasian Equilibrium with Gross Substitutes," Journal of Economic Theory, Elsevier, vol. 87(1), pages 95-124, July.
    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. Erlanson, Albin & Szwagrzak, Karol, 2013. "Strategy-Proof Package Assignment," Working Papers 2013:43, Lund University, Department of Economics.
    2. G. A. Koshevoy, 2016. "Stability of rejections and Stable Many-to-Many Matchings," Documents de recherche 16-02, Centre d'Études des Politiques Économiques (EPEE), Université d'Evry Val d'Essonne.
    3. Yokote, Koji, 2021. "Consistency of the doctor-optimal equilibrium price vector in job-matching markets," Journal of Economic Theory, Elsevier, vol. 197(C).
    4. Chao Huang, 2021. "Stable matching: an integer programming approach," Papers 2103.03418, arXiv.org, revised Apr 2022.
    5. Kazuo Murota & Akiyoshi Shioura & Zaifu Yang, 2014. "Time Bounds for Iterative Auctions: A Unified Approach by Discrete Convex Analysis," Discussion Papers 14/27, Department of Economics, University of York.
    6. Nicolas C. Bedard & Jacob K. Goeree & Philippos Louis & Jingjing Zhang, 2020. "The Favored but Flawed Simultaneous Multiple-Round Auction," Working Paper Series 2020/03, Economics Discipline Group, UTS Business School, University of Technology, Sydney.
    7. Kirill Rudov, 2024. "Fragile Stable Matchings," Papers 2403.12183, arXiv.org.
    8. Marilda Sotomayor, 2010. "Stability property of matchings is a natural solution concept in coalitional market games," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(1), pages 237-248, March.
    9. Bikhchandani, Sushil & Ostroy, Joseph M., 2002. "The Package Assignment Model," Journal of Economic Theory, Elsevier, vol. 107(2), pages 377-406, December.
    10. Fu, Hu & Kleinberg, Robert & Lavi, Ron & Smorodinsky, Rann, 2017. "Job security, stability and production efficiency," Theoretical Economics, Econometric Society, vol. 12(1), January.
    11. Nikhil Garg & Ashish Goel & Benjamin Plaut, 2021. "Markets for public decision-making," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 56(4), pages 755-801, May.
    12. Hector Chade & Lones Smith, 2006. "Simultaneous Search," Econometrica, Econometric Society, vol. 74(5), pages 1293-1307, September.
    13. Saurabh Amin & Patrick Jaillet & Haripriya Pulyassary & Manxi Wu, 2023. "Market Design for Capacity Sharing in Networks," Papers 2307.03994, arXiv.org, revised Nov 2024.
    14. Martin Bichler & Pasha Shabalin & Jürgen Wolf, 2013. "Do core-selecting Combinatorial Clock Auctions always lead to high efficiency? An experimental analysis of spectrum auction designs," Experimental Economics, Springer;Economic Science Association, vol. 16(4), pages 511-545, December.
    15. Danilov, V. & Koshevoy, G. & Lang, C., 2013. "Equilibria in Markets with Indivisible Goods," Journal of the New Economic Association, New Economic Association, vol. 18(2), pages 10-34.
    16. 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.
    17. Sherstyuk, Katerina, 2003. "On competitive equilibria with common complementarities," Mathematical Social Sciences, Elsevier, vol. 46(1), pages 55-62, August.
    18. Daniele Condorelli, 2007. "Efficient and Equitable Airport Slot Allocation," Rivista di Politica Economica, SIPI Spa, vol. 97(1), pages 81-104, January-F.
    19. Ortega, Josué, 2020. "Multi-unit assignment under dichotomous preferences," Mathematical Social Sciences, Elsevier, vol. 103(C), pages 15-24.
    20. Ozan Candogan & Markos Epitropou & Rakesh V. Vohra, 2021. "Competitive Equilibrium and Trading Networks: A Network Flow Approach," Operations Research, INFORMS, vol. 69(1), pages 114-147, January.

    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:1907.11915. 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.