Pay-As-Bid vs. First-Price Auctions: Similarities and Differences in Strategic Behavior

Abstract

Pay-as-bid auctions extend the rules of the well-known first-price auction to the sale of multiple units of the same good. According to a common understanding of the recent literature, strategic incentives in pay-as-bid auctions differ from those in the first-price auctions when bidders have multi-unit demand. I show that each of N symmetrically informed bidders shades his bid for 1 of N shares of a perfectly divisible good in a pay-as-bid auction as if he competed with (N-1)N bidders for one indivisible good in a first-price auction. This analogy carries over to environments where bidders have pri- vate information if equilibrium demand schedules are additively separable in the type but breaks otherwise. Whether bidding in pay-as-bid auctions is more complex than in first-price auctions thus depends on the type of uncertainty bidders face.