Knightian Robustness from Regret Minimization

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, θ∗, consists of a set of distributions, from one of which θ∗ 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.