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Equilibrium in the Two Player, k-Double Auction with Affiliate Private Values

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  • Ohad Kadan

    (John M. Olin School of Business, Washington University in St. Louis)

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    Abstract

    We prove the existence of an increasing equilibrium, and study the comparative statics of correlation in the k-double auction with affiliated private values. This is supposedly the simplest bilateral trading mechanism that allows for dependence in valuations between buyers and sellers. In the case k ?{0 ,1} there exists a unique equilibrium in non-dominated strategies. Using this equilibrium we show that correlation has a dual effect on strategic bidding. It might impose bidders to become more or less aggressive depending on their private valuation, and on the level of correlation. In the case k ? (0 ,1), we prove the existence of a family of strictly increasing equilibria, and demonstrate them using examples. Moreover, we show that equilibria in the case of independent private values are pointwise limits of equilibria with strictly affiliated private values.

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    Bibliographic Info

    Paper provided by Fondazione Eni Enrico Mattei in its series Working Papers with number 2004.12.

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    Date of creation: Jan 2004
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    Handle: RePEc:fem:femwpa:2004.12

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    Keywords: Double auctions; Affiliation;

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    1. Fudenberg, Drew & Mobius, Markus & Szeidl, Adam, 2010. "Existence of Equilibrium in Large Double Auctions," Staff General Research Papers 32111, Iowa State University, Department of Economics.
    2. 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.
    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. Williams, Steven R, 1991. "Existence and Convergence of Equilibria in the Buyer's Bid Double Auction," Review of Economic Studies, Wiley Blackwell, vol. 58(2), pages 351-74, April.
    5. Williams, Steven R., 1987. "Efficient performance in two agent bargaining," Journal of Economic Theory, Elsevier, vol. 41(1), pages 154-172, February.
    6. Mark A. Satterthwaite & Steven R. Williams, 2002. "The Optimality of a Simple Market Mechanism," Econometrica, Econometric Society, vol. 70(5), pages 1841-1863, September.
    7. Satterthwaite, Mark A & Williams, Steven R, 1989. "The Rate of Convergence to Efficiency in the Buyer's Bid Double Auction as the Market Becomes Large," Review of Economic Studies, Wiley Blackwell, vol. 56(4), pages 477-98, October.
    8. 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.
    9. Wilson, Robert B, 1985. "Incentive Efficiency of Double Auctions," Econometrica, Econometric Society, vol. 53(5), pages 1101-15, September.
    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.
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