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Optimal Auction Design in a Common Value Model

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  • Bergemann, Dirk
  • Brooks, Benjamin A
  • Morris, Stephen

Abstract

We study auction design when bidders have a pure common value equal to the maximum of their independent signals. In the revenue maximizing mechanism, each bidder makes a payment that is independent of his signal and the allocation discriminates in favor of bidders with lower signals. We provide a necessary and sufficient condition under which the optimal mechanism reduces to a posted price under which all bidders are equally likely to get the good. This model of pure common values can equivalently be interpreted as model of resale: the bidders have independent private values at the auction stage, and the winner of the auction can make a take-it-or-leave-it-offer in the secondary market under complete information.

Suggested Citation

  • Bergemann, Dirk & Brooks, Benjamin A & Morris, Stephen, 2017. "Optimal Auction Design in a Common Value Model," CEPR Discussion Papers 11783, C.E.P.R. Discussion Papers.
  • Handle: RePEc:cpr:ceprdp:11783
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    References listed on IDEAS

    as
    1. Dirk Bergemann & Benjamin Brooks & Stephen Morris, 2017. "Firstā€Price Auctions With General Information Structures: Implications for Bidding and Revenue," Econometrica, Econometric Society, vol. 85, pages 107-143, January.
    2. Haile, Philip A., 2003. "Auctions with private uncertainty and resale opportunities," Journal of Economic Theory, Elsevier, vol. 108(1), pages 72-110, January.
    3. Colin Campbell & Dan Levin, 2006. "When and why not to auction," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 27(3), pages 583-596, April.
    4. Roger B. Myerson, 1981. "Optimal Auction Design," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 58-73, February.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    common values; descending auction; global incentive constraints; local incentive constraints; maximum value game; Optimal auction; posted price; resale; revenue maximization; wallet game;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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