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Title: Revenue Optimal Auction for Single-Minded Buyers.

Speaker: Vineet Abhishek

Abstract:We study the problem of characterizing revenue optimal auctions for single-minded buyers. Each buyer is interested only in a specific bundle of items and has a value for the same. Both his bundle and its value are his private information. The bundles that buyers are interested in and their corresponding values are assumed to be realized from known probability distributions independent across the buyers. We identify revenue optimal auctions with a simple structure, if the conditional distribution of any buyer's valuation is nondecreasing, in the hazard rates ordering of probability distributions, as a function of the bundle the buyer is interested in. The revenue optimal auction is given by the solution of a maximum weight independent set problem, with weights being an appropriate mapping of buyers' valuations, called virtual valuations. We provide a novel graphical construction of virtual valuations and highlight important properties of the resulting auction.

Speaker Bio

Vineet Abhishek is a PhD candidate in the Department of Electrical and Computer Engineering at University of Illinois, Urbana-Champaign. He is affiliated with Coordinated Science Laboratory. Prior to this, he worked at Broadcom Corporation from 2007-08. He obtained his M.S from Stanford University in 2007, and B.Tech from Indian Institute of Technology (IIT) Kanpur in 2005, both in Electrical Engineering. He is broadly interested in Game Theory, Learning, and Optimization.