Pay-as-bid Auctions with Private Information

Daniel Linnenbrink

VfS Annual Conference 2025 (Cologne): Revival of Industrial Policy from Verein für Socialpolitik / German Economic Association

Abstract: The pay-as-bid auction is one of the most prominent mechanisms allocating divisible goods like energy. This paper analyzes equilibrium behavior in pay-as-bid auctions within a general environment where bidders are privately informed about their valuations. The key methodological innovation is to represent the auction as a continuum of asymmetric first-price auctions. I define an everywhere-optimal Bayes-Nash equilibrium, in which bid functions satisfy pointwise optimality, and characterize equilibrium strategies. With two bidders, I establish equilibrium uniqueness. The characterization enables accurate predictions of equilibrium bids even when estimated valuations contain small errors. For a class of linear marginal valuations, I derive closed-form solutions and show that pay-as-bid generates higher revenue than the VCG mechanism.

Keywords: auctions; discriminatory auction; equilibrium uniqueness (search for similar items in EconPapers)
JEL-codes: C72 D44 D47 D82 (search for similar items in EconPapers)
Date: 2025, Revised 2025
New Economics Papers: this item is included in nep-com, nep-des and nep-gth
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Persistent link: https://EconPapers.repec.org/RePEc:zbw:vfsc25:325443

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