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 ... more >>>

Many commonly-used auction mechanisms are ``maximal-in-range''. We show that any maximal-in-range mechanism for $n$ bidders and $m$ items cannot both approximate the social welfare with a ratio better than $\min(n, m^\eta)$ for any constant $\eta < 1/2$ and run in polynomial time, unless $NP \subseteq P/poly$. This significantly improves upon ... more >>>