Anton Likhodedov and Tuomas Sandholm
We study the recognized open problem of designing revenue-maximizing combinatorial auctions. It is unsolved even for two bidders and two items for sale. Rather than pursuing the pure economic approach of attempting to characterize the optimal auction, we explore techniques for automatically modifying existing mechanisms in a way that increase expected revenue. We introduce a general family of auctions, based on bidder weighting and allocation boosting, which we call virtual valuations combinatorial auctions (VVCA). All auctions in the family are based on the Vickrey-Clarke-Groves (VCG) mechanism, executed on virtual valuations that are linear transformations of the bidders’ real valuations. The restriction to linear transformations is motivated by incentive compatibility. The auction family is parameterized by the coefficients in the linear transformations. The problem of designing a high revenue mechanism is therefore reduced to search in the parameter space of VVCA. We analyze the complexity of the search for the optimal such mechanism and conclude that the search problem is computationally hard. Despite that, optimal parameters for VVCA can be found at least in settings with few items and bidders (the experiments show that VVCA yield a substantial increase in revenue over the traditionally used VCG). In larger auctions locally optimal parameters, which still yield an improvement over VCG, can be found.