Approximations by Computationally-Efficient VCG-Based Mechanisms

We consider computationally-efficient incentive-compatible mechanisms that use the VCG payment scheme, and study how well they can approximate the social welfare in auction settings. We obtain a 2-approximation for multi-unit auctions, and show that this is best possible, even though from a purely computational perspective an FPTAS exists. For combinatorial auctions among submodular (or subadditive) bidders, we prove an Ω(m 1 6 ) lower bound, which is close to the known upper bound of O(m 1 2 ), and qualitatively higher than the constant factor approximation possible from a purely computational point of view.

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