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Optimal Trading Mechanisms with Ex Ante Unidentified Traders

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  • Hu Lu

    (University of Ottawa)

  • Jacques Robert

    (University of Montreal)

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    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.

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    Bibliographic Info

    Paper provided by Econometric Society in its series Econometric Society World Congress 2000 Contributed Papers with number 1612.

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    Date of creation: 01 Aug 2000
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    Handle: RePEc:ecm:wc2000:1612

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    1. Holmstrom, Bengt & Myerson, Roger B, 1983. "Efficient and Durable Decision Rules with Incomplete Information," Econometrica, Econometric Society, vol. 51(6), pages 1799-819, November.
    2. 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.
    3. 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 1041-63, September.
    4. Myerson, Roger B, 1979. "Incentive Compatibility and the Bargaining Problem," Econometrica, Econometric Society, vol. 47(1), pages 61-73, January.
    5. Makowski, L. & Mezzetti, C., 1989. "The Possibility Of Efficient Mechanisms For Trading In Indivisible Object," Papers 344, California Davis - Institute of Governmental Affairs.
    6. Williams, Steven R., 1987. "Efficient performance in two agent bargaining," Journal of Economic Theory, Elsevier, vol. 41(1), pages 154-172, February.
    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 708, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    8. Roger B. Myerson & Mark A. Satterthwaite, 1981. "Efficient Mechanisms for Bilateral Trading," Discussion Papers 469S, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    9. Jean-Charles Rochet & Philippe Chone, 1998. "Ironing, Sweeping, and Multidimensional Screening," Econometrica, Econometric Society, vol. 66(4), pages 783-826, July.
    10. 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.
    11. Mussa, Michael & Rosen, Sherwin, 1978. "Monopoly and product quality," Journal of Economic Theory, Elsevier, vol. 18(2), pages 301-317, August.
    12. 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.
    13. Roger B. Myerson, 1978. "Optimal Auction Design," Discussion Papers 362, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    14. McAfee, R. Preston, 1991. "Efficient allocation with continuous quantities," Journal of Economic Theory, Elsevier, vol. 53(1), pages 51-74, February.
    15. Wilson, Robert B, 1985. "Incentive Efficiency of Double Auctions," Econometrica, Econometric Society, vol. 53(5), pages 1101-15, September.
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