(No) Foundations of Dominant-Strategy Mechanisms: A Comment on Chung and Ely (2007)

This comment revisits Chung and Ely’s [6] paper 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 argues that Chung and Ely’s maxmin definition of robustly optimal auctions requires too little of an optimal auction. It is shown that, after a small amendment of Chung and Ely’s definition, dominant strategy auctions are not optimal, and indeed no auction is optimal. We argue that it is almost obvious that Chung and Ely’s definition should be amended in the way that we propose. Our construction of mechanisms that are superior to dominant strategy mechanisms is very simple, and is built on the possibility of side bets if beliefs are not derived from common priors, as is assumed in Chung and Ely [6]. Chung and Ely [6] (hereafter abbreviated as “CE”) address the important question when a mechanism designer who does not want to make restrictive assumptions about agents’ beliefs about each other will find it optimal to choose a dominant strategy mechanism. While this question can be asked in the context of many applications of mechanism design, CE study the question in the specific context of an expected revenue maximizing seller who wants to sell a single object to buyers who have quasi-linear preferences and private values. CE construct a notion of optimality for mechanisms that reflects that the mechanism designer wants to make no assumptions about agents’ beliefs. In particular, importantly, the mechanism designer in CE does not assume that agents’ beliefs are derived from a common prior. CE refer to mechanisms that are optimal in their sense as having “maxmin foundations.” CE’s main result provides sufficient conditions for dominant strategy auctions to have maxmin foundations. These sufficient conditions generalize Myerson’s [14] regularity conditions by allowing for correlated values. I am grateful to Alexey Kushnir, David Miller, and Stephen Morris for very helpful discussions. Department of Economics, University of Michigan, [email protected].