This dissertation contributes to the literature on the market design of auctions. I use computational and experimental techniques to make two types of contributions to the literature. First, I provide a program that implements a state-of-the-art algorithm for solving multi-unit auctions with asymmetric bidders. This methodological contribution can be used by other economists to solve a variety of auction problems not considered in this dissertation. Second, I undertake the study of one auction environment in particular, utilizing my program to generate hypotheses when bidders participate in a particular sealed-bid, asymmetric multi-unit auction. These hypotheses are then tested in an experimental setting.