Discriminatory price auctions with resale and optimal quantity caps

Abstract

We present a model of a discriminatory price auction in which a large bidder competes against many small bidders, followed by a post-auction resale stage in which the large bidder is endogenously determined to be a buyer or a seller. We extend results on first-price auctions with resale to this setting and use these results to give a tractable characterization of equilibrium behavior. We use this characterization to study the policy of capping the amount that may be won by large bidders in the auction, a policy that has received little attention in the auction literature. Our analysis shows that the trade-offs involved when adjusting these quantity caps can be understood in terms familiar to students of asymmetric first-price single-unit auctions. Furthermore, whether one seeks to maximize welfare or revenue can have contradictory implications for the choice of cap.We thank the anonymous referees for their helpful comments and suggestions.1 This policy currently restricts bidders to winning at most 35% of the market supply, but it has evolved over the course of the 20th century, with its size varying between 25% and 35% (Garbade and Ingber, 2005). Bartolini and Cottarelli (1997) find in their survey of "treasury" auctions around the world that 23% of the countries in their sample impose a ceiling on auction awards.

Strategy and design of multi‐unit auction in grouped asymmetric setting

“…However, scholars still explore some different ideas in the field of asymmetric multi-unit auction. Baisa and Burkett (2018) studied the asymmetric divisible good auction with large bidders, but the authors focused on the efficiency and revenue of the auction rather than the optimal strategy of the bidder, which was continued in Baisa and Burkett (2020). Burkett and Woodward (2020) Holmberg and Wolak (2018) analysed how market design influenced bidding in multi-unit procurement auctions and found that uniform pricing was preferable to discriminatory pricing for buyer whilst considering asymmetry of suppliers' cost.…”

A review of multiunit auctions with homogeneous goods

“…They further show that a symmetric and monotone equilibrium may not exist when the seller has more than two units. Finally, Baisa and Burkett (2020) study resale effects on a discriminatory price auction where a large bidder is competing with many small bidders. They characterize equilibrium behavior, which extends the results on first-price auctions with resale.…”