  We consider auctions in which the players have very limited knowledge about
their own valuations. Specifically, the only information that a Knightian
player $i$ has about the profile of true valuations, $\theta^*$, consists of a
set of distributions, from one of which $\theta_i^*$ has been drawn.
  The VCG mechanism guarantees very high social welfare both in single- and
multi-good auctions, so long as Knightian players do not select strategies that
are dominated. With such Knightian players, however, we prove that the VCG
mechanism guarantees very poor social welfare in unrestricted combinatorial
auctions.
