Discriminatory price auctions with resale and optimal quantity caps

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.