Optimal Auctions with Ambiguity

TLDR

A crucial assumption in the optimal auction literature is that each bidder’s valuation is known to be drawn from a unique distribution. The study investigates optimal auctions under ambiguity about bidders’ valuation distributions. The analysis models bidders as ambiguity‑averse using the max‑min expected utility framework of Gilboa and Schmeidler, and considers the seller’s ambiguity stance. When bidders face more ambiguity than the seller, the seller can always weakly increase revenue by switching to a full‑insurance auction; if the seller is ambiguity‑neutral and the bidders’ priors are close to the seller’s, the full‑insurance auction is optimal; in general first‑ or second‑price auctions are suboptimal, and when the seller is ambiguity‑averse and bidders are neutral, a fully‑insuring auction is optimal.

Abstract

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.