A Case for Pay-as-Bid Auctions

Pay-as-bid (or discriminatory or multiple-price) auctions are used to sell homogenous goods such as treasury securities and commodities.We prove the uniqueness of their pure-strategy Bayesian Nash equilibrium and establish a tractable representation of equilibrium bids for symmetrically-informed bidders.Analyzing design, we show that supply transparency and full disclosure are revenue-maximizing in pay as bid, though not necessarily in uniform-price (or single-price) auctions, the main alternative auction format.Pay as bid raises weakly more revenue than uniform price and may lead to higher welfare.Our results provide an explanation for the revenue equivalence observed in empirical studies of treasury auctions.