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 alternati