Knightian Analysis of the VCG Mechanism in Unrestricted Combinatorial Auctions

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.