Lexicographic Robustness and the Efficiency of Optimal Mechanisms

A central challenge in mechanism design is to identify mechanisms whose performance is robust under uncertainty about the environment. The maxmin optimality criterion is commonly used for this purpose, but it often yields a large and economically uninformative set of mechanisms. This paper proposes a lexicographic approach to refining the maxmin criterion and characterizes the efficiency of optimal mechanisms. In canonical screening and auction environments, the strongest refinement $\text{unicode}x2013$ proper robustness $\text{unicode}x2013$ selects ex post efficient mechanisms. By contrast, in a public good provision environment, it identifies the precise form of optimal inefficiencies, which become severe in large economies.