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Robustly Optimal Auctions with Unknown Resale Opportunities

Author

Listed:
  • Gabriel Carroll
  • Ilya Segal

Abstract

The standard revenue-maximizing auction discriminates against a priori stronger bidders so as to reduce their information rents. We show that such discrimination is no longer optimal when the auction’s winner may resell to another bidder, and the auctioneer has non-Bayesian uncertainty about such resale opportunities. We identify a “worst-case” resale scenario, in which bidders’ values become publicly known after the auction and losing bidders compete Bertrand-style to buy the object from the winner. With this form of resale, misallocation no longer reduces the information rents of the high-value bidder, as he could still secure the same rents by buying the object in resale. Under regularity assumptions, we show that revenue is maximized by a version of the Vickrey auction with bidder-specific reserve prices, first proposed by Ausubel and Cramton (2004). The proof of optimality involves constructing Lagrange multipliers on a double continuum of binding non-local incentive constraints.

Suggested Citation

  • Gabriel Carroll & Ilya Segal, 2019. "Robustly Optimal Auctions with Unknown Resale Opportunities," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 86(4), pages 1527-1555.
    • Handle: RePEc:oup:restud:v:86:y:2019:i:4:p:1527-1555.
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    File URL: http://hdl.handle.net/10.1093/restud/rdy041
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    Citations

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    Cited by:

    1. Hendricks, Ken & Wiseman, Thomas, 2022. "How to sell in a sequential auction market," Theoretical Economics, Econometric Society, vol. 17(4), November.
    2. Lopomo, Giuseppe & Rigotti, Luca & Shannon, Chris, 2022. "Detectability, duality, and surplus extraction," Journal of Economic Theory, Elsevier, vol. 204(C).
    3. Moshe Babaioff & Nicole Immorlica & Yingkai Li & Brendan Lucier, 2021. "Making Auctions Robust to Aftermarkets," Papers 2107.05853, arXiv.org, revised Nov 2022.
    4. Xiaogang Che & Tilman Klumpp, 2023. "Auctions versus sequential mechanisms when resale is allowed," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 75(4), pages 1207-1245, May.
    5. Bergemann, Dirk & Ottaviani, Marco, 2021. "Information Markets and Nonmarkets," CEPR Discussion Papers 16459, C.E.P.R. Discussion Papers.
    6. Bergemann, Dirk & Brooks, Benjamin & Morris, Stephen, 2020. "Countering the winner's curse: optimal auction design in a common value model," Theoretical Economics, Econometric Society, vol. 15(4), November.
    7. Kenneth Hendricks & Thomas Wiseman, 2021. "How To Sell (or Procure) in a Sequential Auction," Papers 2110.13121, arXiv.org.
    8. Jerry Anunrojwong & Santiago R. Balseiro & Omar Besbes, 2023. "Robust Auction Design with Support Information," Papers 2305.09065, arXiv.org, revised Aug 2023.

    More about this item

    Keywords

    Ausubel-Cramton-Vickrey (ACV) auction; Auctions with resale; Duality in auction design; Non-local incentive constraints; Robust revenue maximization; Worst case;
    All these keywords.

    JEL classification:

    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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