Lexicographic Robustness and the Efficiency of Optimal Mechanisms

TL;DR

This paper introduces a lexicographic refinement of the maxmin robustness criterion in mechanism design, showing it leads to ex post efficient mechanisms in some settings and characterizes inefficiencies in others.

Contribution

It proposes a new lexicographic approach to robustness, refining maxmin optimality, and characterizes the efficiency of mechanisms across different environments.

Findings

Proper robustness selects ex post efficient mechanisms in screening and auctions.

In public good environments, it identifies specific inefficiencies that grow large in big economies.

The approach refines the set of robust mechanisms, making them more economically meaningful.

Abstract

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 $\unicode{x2013}$ proper robustness $\unicode{x2013}$ 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.