  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.

Computer Science and Game Theory