IDEAS home Printed from https://ideas.repec.org/p/ecm/wc2000/1612.html
   My bibliography  Save this paper

Optimal Trading Mechanisms with Ex Ante Unidentified Traders

Author

Listed:
  • Hu Lu

    (University of Ottawa)

  • Jacques Robert

    (University of Montreal)

Abstract

We analyze optimal trading mechanisms in an exchange economy where each trader owns some units of a good to be traded and may be either a seller or a buyer, depending on the realization of the privately observed valuations. The concept of virtual valuation is extended to ex ante unidentified traders; contrary to the case where each trader is assigned a role as either a buyer or a seller, the traders' virtual valuations now depend on the choice of the trading mechanism and are generally non-monotonic even if the distribution of valuations is regular. We show that the trading mechanisms that maximize a broker's expected profit or expected total gains from trade are generalized double auctions which maximize the gains from trade measured in some modified monotonic virtual valuations for the traders. The bunching phenomena, which are here specific to ex ante unidentified traders, will be a general feature in these mechanisms. Furthermore, the randomization rule by which ties are broken is now part of the design of the optimal mechanisms. Finally, we show that the optimal mechanism converges toward a simple bid-ask mechanism as the number of participants in the market increases.

Suggested Citation

  • Hu Lu & Jacques Robert, 2000. "Optimal Trading Mechanisms with Ex Ante Unidentified Traders," Econometric Society World Congress 2000 Contributed Papers 1612, Econometric Society.
    • Handle: RePEc:ecm:wc2000:1612
    as

    Download full text from publisher

    File URL: http://fmwww.bc.edu/RePEc/es2000/1612.pdf
    File Function: main text
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Makowski Louis & Mezzetti Claudio, 1993. "The Possibility of Efficient Mechanisms for Trading an Indivisible Object," Journal of Economic Theory, Elsevier, vol. 59(2), pages 451-465, April.
    2. 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.
    3. Jean-Jacques Laffont & Jean Tirole, 1993. "A Theory of Incentives in Procurement and Regulation," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262121743, December.
    4. Roger B. Myerson, 1978. "Optimal Auction Design," Discussion Papers 362, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    5. Jean-Charles Rochet & Philippe Chone, 1998. "Ironing, Sweeping, and Multidimensional Screening," Econometrica, Econometric Society, vol. 66(4), pages 783-826, July.
    6. Holmstrom, Bengt & Myerson, Roger B, 1983. "Efficient and Durable Decision Rules with Incomplete Information," Econometrica, Econometric Society, vol. 51(6), pages 1799-1819, November.
    7. Thomas A. Gresik & Mark A. Satterthwaite, 1985. "The Rate at Which a Simple Market Becomes Efficient as the Number of Traders Increases: An Asymptotic Result for Optimal Trading Mechanisms," Discussion Papers 641, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    8. McAfee, R. Preston, 1991. "Efficient allocation with continuous quantities," Journal of Economic Theory, Elsevier, vol. 53(1), pages 51-74, February.
    9. Tirole, Jean, 1986. "Procurement and Renegotiation," Journal of Political Economy, University of Chicago Press, vol. 94(2), pages 235-259, April.
    10. Myerson, Roger B, 1979. "Incentive Compatibility and the Bargaining Problem," Econometrica, Econometric Society, vol. 47(1), pages 61-73, January.
    11. Spulber, Daniel F., 1988. "Bargaining and regulation with asymmetric information about demand and supply," Journal of Economic Theory, Elsevier, vol. 44(2), pages 251-268, April.
    12. Myerson, Roger B. & Satterthwaite, Mark A., 1983. "Efficient mechanisms for bilateral trading," Journal of Economic Theory, Elsevier, vol. 29(2), pages 265-281, April.
    13. Gresik, Thomas A. & Satterthwaite, Mark A., 1989. "The rate at which a simple market converges to efficiency as the number of traders increases: An asymptotic result for optimal trading mechanisms," Journal of Economic Theory, Elsevier, vol. 48(1), pages 304-332, June.
    14. Wilson, Robert B, 1985. "Incentive Efficiency of Double Auctions," Econometrica, Econometric Society, vol. 53(5), pages 1101-1115, September.
    15. 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.
    16. Mussa, Michael & Rosen, Sherwin, 1978. "Monopoly and product quality," Journal of Economic Theory, Elsevier, vol. 18(2), pages 301-317, August.
    17. Leininger, W. & Linhart, P. B. & Radner, R., 1989. "Equilibria of the sealed-bid mechanism for bargaining with incomplete information," Journal of Economic Theory, Elsevier, vol. 48(1), pages 63-106, June.
    18. Roger B. Myerson, 1981. "Optimal Auction Design," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 58-73, February.
    19. Williams, Steven R., 1987. "Efficient performance in two agent bargaining," Journal of Economic Theory, Elsevier, vol. 41(1), pages 154-172, February.
    20. Kalyan Chatterjee & William Samuelson, 1983. "Bargaining under Incomplete Information," Operations Research, INFORMS, vol. 31(5), pages 835-851, October.
    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. Lu, Hu & Robert, Jacques, 2001. "Optimal Trading Mechanisms with Ex Ante Unidentified Traders," Journal of Economic Theory, Elsevier, vol. 97(1), pages 50-80, March.
    2. Hu Lu & Jacques Robert, 1997. "Optimal Trading Mechanisms with Ex Ante Unidentified Traders," CIRANO Working Papers 97s-29, CIRANO.
    3. Zacharias, Eleftherios & Williams, Steven R., 2001. "Ex Post Efficiency in the Buyer's Bid Double Auction When Demand Can Be Arbitrarily Larger Than Supply," Journal of Economic Theory, Elsevier, vol. 97(1), pages 175-190, March.
    4. Simon Loertscher & Leslie M. Marx, 2022. "Incomplete Information Bargaining with Applications to Mergers, Investment, and Vertical Integration," American Economic Review, American Economic Association, vol. 112(2), pages 616-649, February.
    5. Kjell Hausken, 1997. "Game-theoretic and Behavioral Negotiation Theory," Group Decision and Negotiation, Springer, vol. 6(6), pages 511-528, December.
    6. Schottmüller, Christoph, 2023. "Optimal information structures in bilateral trade," Theoretical Economics, Econometric Society, vol. 18(1), January.
    7. Kadan, Ohad, 2007. "Equilibrium in the two-player, k-double auction with affiliated private values," Journal of Economic Theory, Elsevier, vol. 135(1), pages 495-513, July.
    8. Yoon, Kiho, 2001. "The Modified Vickrey Double Auction," Journal of Economic Theory, Elsevier, vol. 101(2), pages 572-584, December.
    9. Bichler, Martin & Kohring, Nils & Oberlechner, Matthias & Pieroth, Fabian R., 2023. "Learning equilibrium in bilateral bargaining games," European Journal of Operational Research, Elsevier, vol. 311(2), pages 660-678.
    10. Ohad Kadan, 2004. "Equilibrium in the Two Player, k-Double Auction with Affiliate Private Values," Working Papers 2004.12, Fondazione Eni Enrico Mattei.
    11. Shneyerov, Artyom & Wong, Adam Chi Leung, 2010. "The rate of convergence to perfect competition of matching and bargaining mechanisms," Journal of Economic Theory, Elsevier, vol. 145(3), pages 1164-1187, May.
    12. Saran, Rene, 2011. "Bilateral trading with naive traders," Games and Economic Behavior, Elsevier, vol. 72(2), pages 544-557, June.
    13. Tobias Widmer & Paul Karaenke & Vijayan Sugumaran, 2021. "Two‐sided service markets: Effects of quality differentiation on market efficiency," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 42(3), pages 588-604, April.
    14. Blumrosen, Liad & Dobzinski, Shahar, 2021. "(Almost) efficient mechanisms for bilateral trading," Games and Economic Behavior, Elsevier, vol. 130(C), pages 369-383.
    15. Steven R. Williams, 1994. "A Characterization of Efficient," Discussion Papers 1100, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    16. Kadan, Ohad, 2006. "So who gains from a small tick size?," Journal of Financial Intermediation, Elsevier, vol. 15(1), pages 32-66, January.
    17. Ledyard, John O. & Palfrey, Thomas R., 2007. "A general characterization of interim efficient mechanisms for independent linear environments," Journal of Economic Theory, Elsevier, vol. 133(1), pages 441-466, March.
    18. Bradley J Larsen, 2021. "The Efficiency of Real-World Bargaining: Evidence from Wholesale Used-Auto Auctions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 88(2), pages 851-882.
    19. Mark A. Satterthwaite & Steven R. Williams, 1987. "Bilateral Trade With The Sealed Bid K-Double Action: Existence And Efficiency," Discussion Papers 723R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    20. Cramton, Peter & Gibbons, Robert & Klemperer, Paul, 1987. "Dissolving a Partnership Efficiently," Econometrica, Econometric Society, vol. 55(3), pages 615-632, May.

    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:ecm:wc2000:1612. 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: Christopher F. Baum (email available below). General contact details of provider: https://edirc.repec.org/data/essssea.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.