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Convergence to Efficiency in a Simple Market with Incomplete Information

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  • Aldo Rustichini

Abstract

An independent private values model of trade with m buyers and m sellers is considered in which a double auction sets price to equate revealed demand and supply. In a symmetric Bayesian Nash equilibrium, each trader acts not as a price-taker, but instead strategically misrepresents his true demand/supply to influence price in his favor. This causes inefficiency. We show that the amount by which a trader misreports is 0(1/m) and the corresponding inefficiency is 0(1/m^2). By comparison, inefficiency is 0(1/m) for a dual price mechanism and 0(1/m^1/2) for a fixed price mechanism. Price-taking behavior and its associated efficiency thus quickly emerge in the double auction despite the asymmetric information and the noncooperative behavior of traders.

Suggested Citation

  • Aldo Rustichini, 1992. "Convergence to Efficiency in a Simple Market with Incomplete Information," Discussion Papers 995, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  • Handle: RePEc:nwu:cmsems:995
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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 1799-1819, November.
    2. Aldo Rustichini, 1990. "Convergence to Price-Taking Behavior in a Simple Market," Discussion Papers 914, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    3. Harsanyi, John C, 1995. "Games with Incomplete Information," American Economic Review, American Economic Association, vol. 85(3), pages 291-303, June.
    4. Wilson, Robert B, 1985. "Incentive Efficiency of Double Auctions," Econometrica, Econometric Society, vol. 53(5), pages 1101-1115, September.
    5. Mark A. Satterthwaite & Steven R. Williams, 1989. "The Rate of Convergence to Efficiency in the Buyer's Bid Double Auction as the Market Becomes Large," Review of Economic Studies, Oxford University Press, vol. 56(4), pages 477-498.
    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.
    7. McAfee, R. Preston, 1992. "A dominant strategy double auction," Journal of Economic Theory, Elsevier, vol. 56(2), pages 434-450, April.
    8. McAfee, R Preston & Reny, Philip J, 1992. "Correlated Information and Mechanism Design," Econometrica, Econometric Society, vol. 60(2), pages 395-421, March.
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