Endogenous worst-case beliefs in first-price auctions

Vitali Gretschko and Helene Mass

No 18-056, ZEW Discussion Papers from ZEW - Leibniz Centre for European Economic Research

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.

Keywords: auctions; mechanism design; beliefs; uncertainty (search for similar items in EconPapers)
JEL-codes: D44 D81 D82 (search for similar items in EconPapers)
Date: 2018
New Economics Papers: this item is included in nep-des, nep-gth, nep-mic and nep-upt
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Persistent link: https://EconPapers.repec.org/RePEc:zbw:zewdip:18056

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