Robust Robustness

TL;DR

This paper refines the maxmin approach to robustness, ensuring payoff guarantees are stable near the ambiguity set, and shows how to modify ambiguity sets for robustness.

Contribution

It introduces a refinement of the maxmin robustness concept and provides a method to modify ambiguity sets to ensure robustness of payoff guarantees.

Findings

Many maxmin-optimal mechanisms are fragile and not robust.

Certain ambiguity sets guarantee robustness of payoff guarantees.

Any ambiguity set can be slightly enriched to ensure robustness.

Abstract

We propose a refinement of the maxmin approach to robustness. A mechanism's payoff guarantee over an ambiguity set is \emph{robust} if the guarantee is approximately satisfied at priors near the ambiguity set (in the weak topology). We show that many maxmin-optimal mechanisms in the literature give payoff guarantees that are not robust. Such mechanisms are often tailored to degenerate worst-case priors, making them simple but fragile. Conversely, some commonly used ambiguity sets satisfy a structural property which ensures that every associated payoff guarantee is robust. We show how any ambiguity set can be slightly enriched to satisfy this property.