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Optimal Trading Mechanisms with Ex Ante Unidentified Traders

Author

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  • Hu Lu
  • Jacques Robert

Abstract

We analyze optimal trading mechanisms in environments 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 privately observed valuations. First, the concept of virtual valuation is extended to ex ante unidentified traders; contrary to the case with identified traders, the traders' virtual valuations now depend on the trading mechanisms and are generally not 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 completely characterized by some modified monotonic virtual valuations. Here, the bunching phenomenon, which is specific to ex ante unidentified traders, will be a general feature in these mechanisms. We also show that the randomization rule by which ties are broken is now an important instrument in the design of the optimal mechanisms. Nous analysons les mécanismes optimaux d'échange dans un contexte où chaque participant possède quelques unités d'un bien à être échangé et pourrait être soit un acheteur, soit un vendeur, dépendant de la réalisation des valorisations qui sont de l'information privée des participants. D'abord, le concept de valeur virtuelle est généralisé aux agents qui ne sont pas ex ante identifiés comme acheteurs ou vendeurs; contrairement au cas où les agents sont bien identifiés, les valeurs virtuelles des agents dépendent0501ntenant du mécanisme d'échange et ne sont généralement pas monotones même si la distribution des valorisations est régulière. Nous montrons que les mécanismes optimaux d'échange, qui maximisent l'espérance de profit ou de gains d'échange d'un intermédiaire, sont complètement caratérisés par ces valeurs virtuelles. Le phénomène de discrimination incomplète (bunching), qui est ici spécifique aux agents non identifiés ex ante, va être une caractéristique générale dans les mécanismes optimaux. Nous montrons aussi que la règle de répartition aléatoire par laquelle les égalités sont brisées est0501ntenant un instrument important dans le design de ces mécanismes.

Suggested Citation

  • Hu Lu & Jacques Robert, 1997. "Optimal Trading Mechanisms with Ex Ante Unidentified Traders," CIRANO Working Papers 97s-29, CIRANO.
  • Handle: RePEc:cir:cirwor:97s-29
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    File URL: http://www.cirano.qc.ca/files/publications/97s-29.pdf
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    References listed on IDEAS

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    1. Roger B. Myerson, 1978. "Optimal Auction Design," Discussion Papers 362, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    2. Holmstrom, Bengt & Myerson, Roger B, 1983. "Efficient and Durable Decision Rules with Incomplete Information," Econometrica, Econometric Society, vol. 51(6), pages 1799-1819, November.
    3. Myerson, Roger B, 1984. "Two-Person Bargaining Problems with Incomplete Information," Econometrica, Econometric Society, vol. 52(2), pages 461-487, March.
    4. Hagerty, Kathleen M. & Rogerson, William P., 1987. "Robust trading mechanisms," Journal of Economic Theory, Elsevier, vol. 42(1), pages 94-107, June.
    5. Steven R. Williams, 1991. "Existence and Convergence of Equilibria in the Buyer's Bid Double Auction," Review of Economic Studies, Oxford University Press, vol. 58(2), pages 351-374.
    6. McAfee, R. Preston, 1991. "Efficient allocation with continuous quantities," Journal of Economic Theory, Elsevier, vol. 53(1), pages 51-74, February.
    7. Rochet, J. C., 1985. "The taxation principle and multi-time Hamilton-Jacobi equations," Journal of Mathematical Economics, Elsevier, vol. 14(2), pages 113-128, April.
    8. Wilson, Robert B, 1985. "Incentive Efficiency of Double Auctions," Econometrica, Econometric Society, vol. 53(5), pages 1101-1115, September.
    9. Mussa, Michael & Rosen, Sherwin, 1978. "Monopoly and product quality," Journal of Economic Theory, Elsevier, vol. 18(2), pages 301-317, August.
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    More about this item

    Keywords

    Mechanism design; efficient trading; intermediation; bunching; asymmetric information; Design de mécanisme; échange efficace; intermédiation; discrimination incomplète; information asymétrique;

    JEL classification:

    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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