  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.
  We analyze the social-welfare performance of the VCG mechanism, for
unrestricted combinatorial auctions, when Knightian players that either (a)
choose a regret-minimizing strategy, or (b) resort to regret minimization only
to refine further their own sets of undominated strategies, if needed. We prove
that this performance is very good.
