(No) Foundations of dominant-strategy mechanisms: a comment on Chung and Ely (2007)

This comment revisits Chung and Ely (Rev Econ Stud 74:447–476, 2007) in which robustly optimal auctions where investigated. Chung and Ely used a maxmin approach to define robust optimality. Chung and Ely provided conditions under which dominant strategy auctions are robustly optimal in their sense. This comment proposes a refinement of Chung and Ely’s criterion and shows that, with this refined criterion, dominant strategy auctions are not optimal if there are at least three bidders. According to the refinement the auctioneer should not choose dominated auctions, that is, auctions for which there exist other mechanisms that never generate lower expected revenue, and sometimes higher expected revenue. We construct such a dominating mechanism for dominant strategy auctions. The construction exploits the possibility of side bets when beliefs are not derived from common priors. Chung and Ely (Rev Econ Stud 74:447–476, 2007) admitted such beliefs.