Ulric B. and Evelyn L. Bray Social Sciences Seminar
Abstract: Pay-as-bid is a prominent auction format for selling homogenous goods such as treasury securities and commodities. For the pay-as-bid auction we prove the unique-ness of pure-strategy Bayesian-Nash equilibria, establish a sufficient condition for the existence of this equilibrium, and obtain an unexpectedly tractable representation of equilibrium bids. Building on these results we analyze the optimal design of pay-as-bid auctions, as well as uniform-price auctions (the main alternative auction format). We show that seller's transparency about supply is optimal in pay-as-bid but not necessarily in uniform-price; pay-as-bid is weakly revenue dominant while the welfare comparison depends on the equilibrium selected in uniform-price; and, under strategy selection commonly applied in empirical work, the two formats are revenue and welfare equivalent.
Written with Kyle Woodward.