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

Author

Listed:
  • Ohad Kadan

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

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.

Suggested Citation

  • Ohad Kadan, 2004. "Equilibrium in the Two Player, k-Double Auction with Affiliate Private Values," Working Papers 2004.12, Fondazione Eni Enrico Mattei.
  • Handle: RePEc:fem:femwpa:2004.12
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    References listed on IDEAS

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    1. Fudenberg, Drew & Mobius, Markus & Szeidl, Adam, 2007. "Existence of equilibrium in large double auctions," Journal of Economic Theory, Elsevier, vol. 133(1), pages 550-567, March.
    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. 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.
    4. Wilson, Robert B, 1985. "Incentive Efficiency of Double Auctions," Econometrica, Econometric Society, vol. 53(5), pages 1101-1115, September.
    5. 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.
    6. 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.
    7. 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.
    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. Williams, Steven R., 1987. "Efficient performance in two agent bargaining," Journal of Economic Theory, Elsevier, vol. 41(1), pages 154-172, February.
    10. Mark A. Satterthwaite & Steven R. Williams, 2002. "The Optimality of a Simple Market Mechanism," Econometrica, Econometric Society, vol. 70(5), pages 1841-1863, September.
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    More about this item

    Keywords

    Double auctions; Affiliation;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions

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