Welfare and Profit maximization with Procurement costs
Carnegie Mellon University.
What is the problem? A limited resource needs to be allocated amongst a set of self-interested agents. Combinatorial Auctions, that capture this situation, 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.
Hmm.. I see. So, what is your contribution? The problem has been well-studied in the case of limited supply (few copies of each item), and unlimited supply. While in the case of limited supply, there are strong lower bounds known, 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.
Highlight of the results. In a work with Avrim Blum, Anupam Gupta and Yishay Mansour, we initiate the study of resource allocation in a more realistic modeling of limitation where each resource has an increasing procurement cost. In this talk, we describe a simple pricing scheme that achieves a constant factor approximation to the optimal social welfare for polynomial and logarithmic procurement cost curves. Furthermore, for arbitrary procurement cost curves, we describe a pricing scheme that achieves a logarithmic approximation to optimal welfare.
We consider arbitrary combinatorial valuation of the buyers and consider the two objective functions of social welfare and revenue.
The results are part of a work that appeared at Foundations of Computer Science (FOCS), 2011. Joint work with Avrim Blum, Anupam Gupta and Yishay Mansour.
Bio: Ankit Sharma is a graduate student at Carnegie Mellon University. He is advised by Avrim Blum and Anupam Gupta. His current research focuses on algorithms and algorithmic game theory.