  We analyze the Vickrey mechanism for auctions of multiple identical goods
when the players have both Knightian uncertainty over their own valuations and
incomplete preferences. In this model, the Vickrey mechanism is no longer
dominant-strategy, and we prove that all dominant-strategy mechanisms are
inadequate. However, we also prove that, in undominated strategies, the social
welfare produced by the Vickrey mechanism in the worst case is not only very
good, but also essentially optimal.
