Title: Welfare and Profit maximization with Procurement costs

Abstract: Combinatorial Auctions are a central problem in Algorithmic
Mechanism Design: how to price and allocate goods to buyers with complex
preferences in order to maximize an objective such as social welfare or
revenue. The problem has been well-studied in the case of limited supply
(one copy of each item), and in the case of digital goods (unlimited
supply of copies). In the case of limited supply, there are strong lower
bounds known even in the case of the purely computational problem. On the
other hand, the case of unlimited supply may be too optimistic for many
settings.

In this talk, we look at how by relaxing the "strength" of the limitation
of available copies of an item, we can beat the lower bounds for the
limited supply and get a smooth transition to the case of unlimited
supply. While if the limitation is "soft", we achieve a constant factor
approximation, in case of "hard" limitation, we achieve a logarithmic
approximation. We consider arbitary combinatorial valuation of the buyers
and consider the two objective functions of social welfare and revenue.