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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)

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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    6. 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.
    7. 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.
    8. 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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    Cited by:

    1. Kadan, Ohad, 2006. "So who gains from a small tick size?," Journal of Financial Intermediation, Elsevier, vol. 15(1), pages 32-66, January.

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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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