Essays on Multi-Item Auctions

Multi-Item auctions are of interest to companies that run online auctions. In this dissertation, I examine auctions involving multiple items in three contexts. The first context involves revenue improvement in the simultaneous auctions of multiple items when the number of bidders and the number of bids for each item are known. In this work, the lever for revenue improvement I examine is item-bundling. Specifically, I study the problem of bundling items together in a manner that improves the seller’s revenue prior to auctioning them off in simultaneous second-price auctions. I propose an auction format, called the Pairwise Bundle Auction (PBA), that elicits truthful bids from bidders for the items on sale. I provide a mathematical formulation that computes the revenue-maximizing bundling of items in response to the bids submitted. My work on identifying a revenue-maximizing bundling of items is of use to companies that run online auctions as a core part of revenue-generation. Examples include companies such as Google or Facebook that run auctions to sell advertisement slots.
The second context involves minimizing the cost of uncertainty in the simultaneous auctions of multiple items when the number of bidders and the number of bids for each item are uncertain. In this work, the lever for revenue improvement I examine is limiting item supply. When a set of items is put out for auction by a seller, the uncertainty in the bidders’ participation decisions can result in adverse outcomes for the seller. I refer to this as the “cost of uncertainty”. Therefore, the seller would want to restrict the set of items put up for sale to minimize the cost of uncertainty. I formulate the problem of identifying an optimal subset of items to put up for simultaneous auction out of a master set of items. This optimal subset minimizes the maximum regret arising from the uncertainty in the bidders’ participation decisions. Our results focus on the computational complexity of this problem. My work on identifying a maximum regret minimizing subset of items to put up for sale is of use to companies that auction off items on online platforms (such as eBay) where participation decisions are uncertain.
The third context involves maximizing the total welfare from item allocations to bidders when allocative externalities are involved. Under the externality model I consider, the value of an item to a bidder depends on the allocation of the other items to the other bidders. I identify a class of valuation functions called the Pairwise Additive Negative Value Externalities (PANE) with interesting properties. I show that the PANE class of valuation functions correspond to anonymous and simple pricing structures that support a social-welfare-maximizing allocation of items to bidders. Like the first context, my work on identifying this class of valuation functions is of use to companies that run online auctions as a core component of revenue generation such as Google or Facebook.