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Endogenous worst-case beliefs in first-price auctions

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  • Gretschko, Vitali
  • Mass, Helene

Abstract

Bidding in first-price auctions crucially depends on the beliefs of the bidders about their competitors' willingness to pay. We analyze bidding behavior in a first-price auction in which the knowledge of the bidders about the distribution of their competitors' valuations is restricted to the support and the mean. To model this situation, we assume that under such uncertainty a bidder will expect to face the distribution of valuations that minimizes her expected utility, given her bid is an optimal reaction to the bids of her competitors induced by this distribution. This introduces a novel way to endogenize beliefs in games of incomplete information. We find that for a bidder with a given valuation her worst-case belief just puts sufficient probability weight on lower valuations of her competitors to induce a high bid. At the same time the worst-case belief puts as much as possible probability weight on the same valuation in order to minimize the bidder's winning probability. This implies that even though the worst-case beliefs are type dependent in a non-monotonic way, an efficient equilibrium of the first-price auction exists.

Suggested Citation

  • Gretschko, Vitali & Mass, Helene, 2018. "Endogenous worst-case beliefs in first-price auctions," ZEW Discussion Papers 18-056, ZEW - Leibniz Centre for European Economic Research.
    • Handle: RePEc:zbw:zewdip:18056
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    References listed on IDEAS

    as
    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. Hanming Fang & Stephen Morris, 2012. "Multidimensional Private Value Auctions," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 9, pages 319-356, World Scientific Publishing Co. Pte. Ltd..
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    4. Dirk Bergemann & Karl H. Schlag, 2012. "Pricing Without Priors," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 12, pages 405-415, World Scientific Publishing Co. Pte. Ltd..
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    6. Carrasco, Vinicius & Farinha Luz, Vitor & Kos, Nenad & Messner, Matthias & Monteiro, Paulo & Moreira, Humberto, 2018. "Optimal selling mechanisms under moment conditions," Journal of Economic Theory, Elsevier, vol. 177(C), pages 245-279.
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    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    auctions; mechanism design; beliefs; uncertainty;
    All these keywords.

    JEL classification:

    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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