Optimal auctions with ambiguity

A crucial assumption in the optimal auction literature is that each bidder's valuation is known to be drawn from a unique distribution. In this paper we study the optimal auction problem allowing for ambiguity about the distribution of valuations. Agents may be ambiguity averse (modeled using the maxmin expected utility model of Gilboa and Schmeidler 1989.) When the bidders face more ambiguity than the seller we show that (i) given any auction, the seller can always (weakly) increase revenue by switching to an auction providing full insurance to all types of bidders, (ii) if the seller is ambiguity neutral and any prior that is close enough to the seller's prior is included in the bidders' set of priors then the optimal auction is a full insurance auction, and (iii) in general neither the first nor the second price auction is optimal (even with suitably chosen reserve prices). When the seller is ambiguity averse and the bidders are ambiguity neutral an auction that fully insures the seller is in the set of optimal mechanisms.