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A single-item continuous double auction game

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  • Ruijgrok, Matthijs
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    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.

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    File URL: http://mpra.ub.uni-muenchen.de/42086/
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    Bibliographic Info

    Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 42086.

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    Date of creation: 19 Oct 2012
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    Handle: RePEc:pra:mprapa:42086

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    Keywords: Continuous double auction; supply and demand; Bayesian Nash equilibrium; ZI-C model; k-double auction;

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    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. Vernon L. Smith, 1962. "An Experimental Study of Competitive Market Behavior," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 70, pages 111.
    3. Douglas D. Davis & Charles A. Holt, 1992. "Introduction to Experimental Economics
      [Experimental Economics]
      ," Introductory Chapters, Princeton University Press.
    4. 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.
    5. 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, University of Chicago Press, vol. 101(1), pages 119-37, February.
    6. 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.
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