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Selling to Intermediaries: Optimal Auction Design in a Common Value Model

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Abstract

We characterize revenue maximizing auctions when the bidders are intermediaries who wish to resell the good. The bidders have differential information about their common resale opportunities: each bidder privately observes an independent draw of a resale opportunity, and the highest signal is a sufficient statistic for the value of winning the good. If the good must be sold, then the optimal mechanism is simply a posted price at which all bidders are willing to purchase the good, and all bidders are equally likely to be allocated the good, irrespective of their signals. If the seller can keep the good, then under the optimal mechanism, all bidders make the same expected payment and have the same expected probability of receiving the good, independent of the signal. Conditional on the good being sold, the allocation discriminates in favor of bidders with lower signals. In some cases, the optimal mechanism again reduces to a posted price. The model provides a foundation for posted prices in multi-agent screening problems.

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  • Dirk Bergemann & Benjamin Brooks & Stephen Morris, 2016. "Selling to Intermediaries: Optimal Auction Design in a Common Value Model," Cowles Foundation Discussion Papers 2064R, Cowles Foundation for Research in Economics, Yale University, revised Jul 2017.
    • Handle: RePEc:cwl:cwldpp:2064r
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    File URL: https://cowles.yale.edu/sites/default/files/files/pub/d20/d2064-r.pdf
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    References listed on IDEAS

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    1. Dirk Bergemann & Benjamin Brooks & Stephen Morris, 2017. "First‐Price Auctions With General Information Structures: Implications for Bidding and Revenue," Econometrica, Econometric Society, vol. 85, pages 107-143, January.
    2. Hannu Vartiainen, 2003. "Auction Design without Commitment," Working Papers 2003.24, Fondazione Eni Enrico Mattei.
    3. Riley, John G & Samuelson, William F, 1981. "Optimal Auctions," American Economic Review, American Economic Association, vol. 71(3), pages 381-392, June.
    4. Hannu Vartiainen, 2013. "Auction Design Without Commitment," Journal of the European Economic Association, European Economic Association, vol. 11(2), pages 316-342, April.
    5. 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.
    6. Roger B. Myerson, 1981. "Optimal Auction Design," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 58-73, February.
    7. Gupta, Madhurima & Lebrun, Bernard, 1999. "First price auctions with resale," Economics Letters, Elsevier, vol. 64(2), pages 181-185, August.
    8. Haile,P.A., 1999. "Auctions with resale," Working papers 33, Wisconsin Madison - Social Systems.
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    Cited by:

    1. Lopomo, Giuseppe & Rigotti, Luca & Shannon, Chris, 2022. "Detectability, duality, and surplus extraction," Journal of Economic Theory, Elsevier, vol. 204(C).
    2. Gagan Aggarwal & Kshipra Bhawalkar & Guru Guruganesh & Andres Perlroth, 2021. "Maximizing revenue in the presence of intermediaries," Papers 2111.10472, arXiv.org.
    3. Dirk Bergemann & Juuso Välimäki, 2019. "Dynamic Mechanism Design: An Introduction," Journal of Economic Literature, American Economic Association, vol. 57(2), pages 235-274, June.

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    More about this item

    Keywords

    Optimal auction; Intermediaries; Posted price; Guaranteed demand auction; Common values; Revenue maximization; Revenue equivalence; First-price auction; Second-price auction; Resale; Maximum value game; Descending auction; Local incentive constraints; Global incentive constraints;
    All these keywords.

    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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