Relatively robust decisions

It is natural for humans to judge the outcome of a decision under uncertainty as a percentage of an ex-post optimal performance. We propose a robust decision-making framework based on a relative performance index. It is shown that if the decision maker's preferences satisfy quasisupermodularity, single-crossing, and a nondecreasing log-differences property, the worst-case relative performance index can be represented as the lower envelope of two extremal performance ratios. The latter is used to characterize the agent's optimal robust decision, which has implications both computationally and for obtaining closed-form solutions. We illustrate our results in an application which compares the performance of relative robustness to solutions that optimize worst-case payoffs, maximum absolute regret, and expected payoffs under a Laplacian prior.

Automated summary

This paper proposes a robust decision-making framework based on a relative performance index. The worst-case relative performance index is represented as the lower envelope of two extremal performance ratios under certain preference conditions. The results are applied to compare the performance of relative robustness to other solutions in a specific application.