IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1412.0542.html
   My bibliography  Save this paper

Budget Imbalance Criteria for Auctions: A Formalized Theorem

Author

Listed:
  • Marco B. Caminati
  • Manfred Kerber
  • Colin Rowat

Abstract

We present an original theorem in auction theory: it specifies general conditions under which the sum of the payments of all bidders is necessarily not identically zero, and more generally not constant. Moreover, it explicitly supplies a construction for a finite minimal set of possible bids on which such a sum is not constant. In particular, this theorem applies to the important case of a second-price Vickrey auction, where it reduces to a basic result of which a novel proof is given. To enhance the confidence in this new theorem, it has been formalized in Isabelle/HOL: the main results and definitions of the formal proof are re- produced here in common mathematical language, and are accompanied by an informal discussion about the underlying ideas.

Suggested Citation

  • Marco B. Caminati & Manfred Kerber & Colin Rowat, 2014. "Budget Imbalance Criteria for Auctions: A Formalized Theorem," Papers 1412.0542, arXiv.org.
    • Handle: RePEc:arx:papers:1412.0542
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1412.0542
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Milgrom,Paul, 2004. "Putting Auction Theory to Work," Cambridge Books, Cambridge University Press, number 9780521536721.
    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. Laurent Lamy, 2013. "“Upping the ante”: how to design efficient auctions with entry?," RAND Journal of Economics, RAND Corporation, vol. 44(2), pages 194-214, June.
    2. Scott Duke Kominers & Alexander Teytelboym & Vincent P Crawford, 2017. "An invitation to market design," Oxford Review of Economic Policy, Oxford University Press and Oxford Review of Economic Policy Limited, vol. 33(4), pages 541-571.
    3. Amadou Boly & Robert Gillanders & Topi Miettinen, 2016. "Deterrence, peer effect, and legitimacy in anti-corruption policy-making: An experimental analysis," WIDER Working Paper Series 137, World Institute for Development Economic Research (UNU-WIDER).
    4. Jeremy Bulow & Jonathan Levin & Paul Milgrom, 2009. "Winning Play in Spectrum Auctions," NBER Working Papers 14765, National Bureau of Economic Research, Inc.
    5. Brunner, Christoph & Hu, Audrey & Oechssler, Jörg, 2014. "Premium auctions and risk preferences: An experimental study," Games and Economic Behavior, Elsevier, vol. 87(C), pages 467-484.
    6. Frank Kelly & Peter Key & Neil Walton, 2016. "Efficient Advert Assignment," Operations Research, INFORMS, vol. 64(4), pages 822-837, August.
    7. Sylvain Mignot & Stéphanie Saba & Annick Vignes, 2016. "To trust or to bid: an empirical analysis of social relationships on a fish market," Working Papers halshs-01298872, HAL.
    8. Lamprirni Zarpala & Dimitris Voliotis, 2022. "A core-selecting auction for portfolio's packages," Papers 2206.11516, arXiv.org, revised Feb 2024.
    9. Michael Padilla & Benjamin Van Roy, 2012. "Intermediated Blind Portfolio Auctions," Management Science, INFORMS, vol. 58(9), pages 1747-1760, September.
    10. Yokote, Koji, 2021. "Consistency of the doctor-optimal equilibrium price vector in job-matching markets," Journal of Economic Theory, Elsevier, vol. 197(C).
    11. Loertscher, Simon & Mezzetti, Claudio, 2021. "A dominant strategy, double clock auction with estimation-based tatonnement," Theoretical Economics, Econometric Society, vol. 16(3), July.
    12. Malueg, David A. & Orzach, Ram, 2009. "Revenue comparison in common-value auctions: Two examples," Economics Letters, Elsevier, vol. 105(2), pages 177-180, November.
    13. Alessandra Casella & Adam B. Cox, 2018. "A Property Rights Approach to Temporary Work Visas," The Journal of Legal Studies, University of Chicago Press, vol. 47(S1), pages 195-227.
    14. 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.
    15. Robert Kleinberg & Bo Waggoner & E. Glen Weyl, 2016. "Descending Price Optimally Coordinates Search," Papers 1603.07682, arXiv.org, revised Dec 2016.
    16. Steven Schilizzi & Uwe Latacz-Lohmann, 2012. "Evaluating Conservation Auctions with Unknown Bidder Costs: The Scottish Fishing Vessel Decommissioning Program," Land Economics, University of Wisconsin Press, vol. 88(4), pages 658-673.
    17. Hu, Audrey & Offerman, Theo & Zou, Liang, 2011. "Premium auctions and risk preferences," Journal of Economic Theory, Elsevier, vol. 146(6), pages 2420-2439.
    18. Sosung Baik & Sung-Ha Hwang, 2021. "Auction design with ambiguity: Optimality of the first-price and all-pay auctions," Papers 2110.08563, arXiv.org.
    19. A. Talman & Zaifu Yang, 2015. "An efficient multi-item dynamic auction with budget constrained bidders," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(3), pages 769-784, August.
    20. Robert W. Day & Peter Cramton, 2012. "Quadratic Core-Selecting Payment Rules for Combinatorial Auctions," Operations Research, INFORMS, vol. 60(3), pages 588-603, June.

    More about this item

    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:1412.0542. 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.