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

Knightian Analysis of the VCG Mechanism in Unrestricted Combinatorial Auctions