The recent auctions literature has devoted much attention to mechanisms that allow package bidding: all-or-nothing bids for sets of items. Introducing package bids can improve efficiency by reducing the bidders "exposure" risk of winning undesirable combinations of items. However, package bids can also create a free-rider problem for relatively small bidders since they need to compete jointly against their larger opponents, potentially reducing efficiency. The inherent asymmetry among different package bids significantly complicates an equilibrium analysis of the costs and benefits of allowing package bids in auctions.

The first chapter makes progress in solving for Bayesian-Nash equilibria of the first-price package auction. We develop a new computational method which is based on a complementarity formulation of the system of equilibrium inequalities. Additionally, we establish existence of equilibrium for special cases. Our analysis shows that introducing package bidding can significantly improve efficiency when the exposure risk faced by bidders is large, but it can reduce efficiency otherwise. We also compare the first-price package auction with other leading package alternatives. Surprisingly, in the environment considered, the first-price package auction performs reasonably well, with respect to both revenue and efficiency, despite the presence of a strong free-rider problem.

The second chapter studies the core-selecting auctions that were proposed recently as alternatives to the famous Vickrey-Clarke Groves (VCG) mechanism for environments with complementarities. The existing literature on core-selecting auctions is limited to only a complete-information analysis. We consider a simple incomplete-information model which allows us to do a full equilibrium analysis, including closed-form solutions for some distributions, for four different core-selecting auction formats suggested in the literature. Our model also admits correlations among bidders values. We second that the revenues and efficiency from core-selecting auctions improve as correlations among bidders values increase, while the revenues from the Vickrey auction worsen. Thus, there may be good reasons for policymakers to utilize a core-selecting auction rather than a VCG mechanism in realistic environments.