Justin Burkett

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.

When bidders’ valuations are derived from a downstream market in which they may compete, the allocation to the firms with the lowest costs can differ from the allocation that maximizes the ex post valuations of the bidders. I consider the problem of auctioning two goods to bidders whose valuations for a good flexibly depend on their and their rival’s costs as well as the identity of the rival. I show that revealing the identities of winners through a sequential auction procedure leads to allocations in which bidders tend to have higher ex post valuations but also higher costs when compared to a simultaneous auction.

We compare equilibrium bidding in uniform-price and discriminatory auctions when a single large bidder (i.e., with multi-unit demand) competes against many small bidders, each with single-unit demands. We show that the large bidder prefers the discriminatory auction over the uniform-price auction, and we provide general conditions under which small bidders have the reverse preference. We use examples to show that the efficiency and revenue rankings of the two auctions are ambiguous.

We study mechanisms for allocating objects to pairs of agents when agents may have nontrivial preferences over objects and pairings. In this environment, the mechanism may distort agents’ preferences over pairings. Compared to certain distortive mechanisms, a non-distortive one always has a stable allocation in our model, and selects stable outcomes that are ex ante preferred by all students under a regularity condition on the distribution of pair values.

We model multi-unit auctions in which bidders' valuations are multidimensional private information. Under a natural constraint on aggregate demand we show that the last accepted bid uniform-pricing rule admits a unique equilibrium with a simple characterization: bids are identical to those submitted in a single-unit first price auction. The form of equilibrium bids suggests that last accepted bid uniform-pricing is a generalization of single-unit first-pricing: in both auctions winners pay the highest market clearing price. Contrasting the separating equilibrium of the last accepted bid auction, we show that equilibrium bids in pay as bid and first rejected bid uniform price auctions must pool information. Thus other common multi-unit auction formats cannot generalize single-unit first-pricing, in which equilibria do not pool information. The existence of a unique equilibrium implies that price selection may be an additional tool for avoiding the zero-revenue equilibria which exist in the first rejected bid uniform price auction. Finally, we show that equilibrium bids in our private information model are significantly flatter than in an analogous random supply model, suggesting that uniform price auction bids may not be as steep as commonly believed.

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.

When bidders’ valuations are derived from a downstream market in which they may compete, the allocation to the firms with the lowest costs can differ from the allocation that maximizes the ex post valuations of the bidders. I consider the problem of auctioning two goods to bidders whose valuations for a good flexibly depend on their and their rival’s costs as well as the identity of the rival. I show that revealing the identities of winners through a sequential auction procedure leads to allocations in which bidders tend to have higher ex post valuations but also higher costs when compared to a simultaneous auction.

We compare equilibrium bidding in uniform-price and discriminatory auctions when a single large bidder (i.e., with multi-unit demand) competes against many small bidders, each with single-unit demands. We show that the large bidder prefers the discriminatory auction over the uniform-price auction, and we provide general conditions under which small bidders have the reverse preference. We use examples to show that the efficiency and revenue rankings of the two auctions are ambiguous.

We study mechanisms for allocating objects to pairs of agents when agents may have nontrivial preferences over objects and pairings. In this environment, the mechanism may distort agents’ preferences over pairings. Compared to certain distortive mechanisms, a non-distortive one always has a stable allocation in our model, and selects stable outcomes that are ex ante preferred by all students under a regularity condition on the distribution of pair values.