Optimal auctions with ambiguity

A crucial assumption in the optimal auction literature has been that each bidder's valuation is known to be drawn from a single unique distribution. In this paper we relax this assumption and study the optimal auction problem when there is ambiguity about the distribution from which these valuations are drawn and where the seller or the bidder may display ambiguity aversion. We model ambiguity aversion using the maxmin expected utility model where an agent evaluates an action on the basis of the minimum expected utility over the set of priors, and then chooses the best action amongst them. We first consider the case where the bidders are ambiguity averse (and the seller is ambiguity neutral). Our first result shows that the optimal incentive compatible and individually rational mechanism must be such that for each type of bidder the minimum expected utility is attained by using the seller's prior. Using this result we show that an auction that provides full insurance to all types of bidders is always in the set of optimal auctions. In particular, when the bidders' set of priors is the ε- contamination of the seller's prior the unique optimal auction provides full insurance to bidders of all types. We also show that in general, many classical auctions, including first and second price are not the optimal mechanism (even with suitably chosen reserve prices). We next consider the case when the seller is ambiguity averse (and the bidders are ambiguity neutral). Now, the optimal auction involves the seller being perfectly insured. Hence, as long as bidders are risk and ambiguity neutral, ambiguity aversion on the part of the seller seems to play a similar role to that of risk aversion.