IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/42086.html
   My bibliography  Save this paper

A single-item continuous double auction game

Author

Listed:
  • Ruijgrok, Matthijs

Abstract

A double auction game with an infinite number of buyers and sellers is introduced. All sellers posses one unit of a good, all buyers desire to buy one unit. Each seller and each buyer has a private valuation of the good. The distribution of the valuations define supply and demand functions. One unit of the good is auctioned. At successive, discrete time instances, a player is randomly selected to make a bid (buyer) or an ask (seller). When the maximum of the bids becomes larger than the minimum of the asks, a transaction occurs and the auction is closed. The players have to choose the value of their bid or ask before the auction starts and use this value when they are selected. Assuming that the supply and demand functions are known, expected profits as functions of the strategies are derived, as well as expected transaction prices. It is shown that for linear supply and demand functions, there exists at most one Bayesian Nash equilibrium. Competitive behaviour is not an equilibrium of the game. For linear supply and demand functions, the sum of the expected profit of the sellers and the buyers is the same for the Bayesian Nash equilibrium and the market where players behave competitively. Connections are made with the ZI-C traders model and the $k$-double auction.

Suggested Citation

  • Ruijgrok, Matthijs, 2012. "A single-item continuous double auction game," MPRA Paper 42086, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:42086
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/42086/1/MPRA_paper_42086.pdf
    File Function: original version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Mikhail Anufriev & Jasmina Arifovic & John Ledyard & Valentyn Panchenko, 2013. "Efficiency of continuous double auctions under individual evolutionary learning with full or limited information," Journal of Evolutionary Economics, Springer, vol. 23(3), pages 539-573, July.
    2. Kalyan Chatterjee & William Samuelson, 1983. "Bargaining under Incomplete Information," Operations Research, INFORMS, vol. 31(5), pages 835-851, October.
    3. Satterthwaite, Mark A. & Williams, Steven R., 1989. "Bilateral trade with the sealed bid k-double auction: Existence and efficiency," Journal of Economic Theory, Elsevier, vol. 48(1), pages 107-133, June.
    4. Gode, Dhananjay K & Sunder, Shyam, 1993. "Allocative Efficiency of Markets with Zero-Intelligence Traders: Market as a Partial Substitute for Individual Rationality," Journal of Political Economy, University of Chicago Press, vol. 101(1), pages 119-137, February.
    5. Vernon L. Smith, 1962. "An Experimental Study of Competitive Market Behavior," Journal of Political Economy, University of Chicago Press, vol. 70(2), pages 111-111.
    6. Douglas D. Davis & Charles A. Holt, 1992. "Introduction to Experimental Economics," Introductory Chapters, in: Experimental Economics, Princeton University Press.
    7. Shira Fano & Marco LiCalzi & Paolo Pellizzari, 2013. "Convergence of outcomes and evolution of strategic behavior in double auctions," Journal of Evolutionary Economics, Springer, vol. 23(3), pages 513-538, 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. Shira Fano & Marco LiCalzi & Paolo Pellizzari, 2013. "Convergence of outcomes and evolution of strategic behavior in double auctions," Journal of Evolutionary Economics, Springer, vol. 23(3), pages 513-538, July.
    2. Anufriev, Mikhail & Arifovic, Jasmina & Ledyard, John & Panchenko, Valentyn, 2022. "The role of information in a continuous double auction: An experiment and learning model," Journal of Economic Dynamics and Control, Elsevier, vol. 141(C).
    3. Giuseppe Attanasi & Samuele Centorrino & Elena Manzoni, 2020. "Zero-Intelligence vs. Human Agents: An Experimental Analysis of the Efficiency of Double Auctions and Over-the-Counter Markets of Varying Sizes," Working Papers 05/2020, University of Verona, Department of Economics.
    4. Itzhak Rasooly, 2022. "Competitive equilibrium and the double auction," Economics Series Working Papers 974, University of Oxford, Department of Economics.
    5. Sabiou M. Inoua & Vernon L. Smith, 2022. "Perishable goods versus re-tradable assets: A theoretical reappraisal of a fundamental dichotomy," Chapters, in: Sascha Füllbrunn & Ernan Haruvy (ed.), Handbook of Experimental Finance, chapter 15, pages 162-171, Edward Elgar Publishing.
    6. Jakob Grazzini, 2013. "Information dissemination in an experimentally based agent-based stock market," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 8(1), pages 179-209, April.
    7. Jinpeng Ma & Qiongling Li, 2016. "Convergence of price processes under two dynamic double auctions," The Journal of Mechanism and Institution Design, Society for the Promotion of Mechanism and Institution Design, University of York, vol. 1(1), pages 1-44, December.
    8. Itzhak Rasooly, 2022. "Competitive equilibrium and the double auction," Papers 2209.07532, arXiv.org.
    9. Mikhail Anufriev & Jasmina Arifovic & John Ledyard & Valentyn Panchenko, 2013. "Efficiency of continuous double auctions under individual evolutionary learning with full or limited information," Journal of Evolutionary Economics, Springer, vol. 23(3), pages 539-573, July.
    10. Lu, Dong & Zhan, Yaosong, 2022. "Over-the-counter versus double auction in asset markets with near-zero-intelligence traders," Journal of Economic Dynamics and Control, Elsevier, vol. 143(C).
    11. Michiel Leur & Mikhail Anufriev, 2018. "Timing under individual evolutionary learning in a continuous double auction," Journal of Evolutionary Economics, Springer, vol. 28(3), pages 609-631, August.
    12. Robin Nicole & Aleksandra Alori'c & Peter Sollich, 2020. "Fragmentation in trader preferences among multiple markets: Market coexistence versus single market dominance," Papers 2012.04103, arXiv.org, revised Aug 2021.
    13. Rustichini, Aldo & Satterthwaite, Mark A & Williams, Steven R, 1994. "Convergence to Efficiency in a Simple Market with Incomplete Information," Econometrica, Econometric Society, vol. 62(5), pages 1041-1063, September.
    14. Lange, Andreas & Ross, Johannes, 2024. "Internalizing match-dependent externalities," Journal of Economic Behavior & Organization, Elsevier, vol. 218(C), pages 356-378.
    15. Crockett, Sean & Spear, Stephen & Sunder, Shyam, 2008. "Learning competitive equilibrium," Journal of Mathematical Economics, Elsevier, vol. 44(7-8), pages 651-671, July.
    16. Kittsteiner, Thomas, 2003. "Partnerships and double auctions with interdependent valuations," Games and Economic Behavior, Elsevier, vol. 44(1), pages 54-76, July.
    17. Rodolphe Buda, 2007. "Propositions for the Building of a Quantitative Austrian Modelling: An Answer to Prof. Rizzo and to Prof. Vriend," Working Papers hal-04139234, HAL.
    18. Heemeijer, Peter & Hommes, Cars & Sonnemans, Joep & Tuinstra, Jan, 2009. "Price stability and volatility in markets with positive and negative expectations feedback: An experimental investigation," Journal of Economic Dynamics and Control, Elsevier, vol. 33(5), pages 1052-1072, May.
    19. Palan, Stefan, 2010. "Digital options and efficiency in experimental asset markets," Journal of Economic Behavior & Organization, Elsevier, vol. 75(3), pages 506-522, September.
    20. Athreya, Kartik B., 2014. "Big Ideas in Macroeconomics: A Nontechnical View," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262019736, April.

    More about this item

    Keywords

    Continuous double auction; supply and demand; Bayesian Nash equilibrium; ZI-C model; k-double auction;
    All these keywords.

    JEL classification:

    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

    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:pra:mprapa:42086. 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: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.html .

    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.