The Best of Many Robustness Criteria in Decision Making: Formulation and Application to Robust Pricing

37 Pages Posted: 15 Apr 2024

See all articles by Jerry Anunrojwong

Jerry Anunrojwong

Columbia University

Santiago Balseiro

Columbia University - Columbia Business School, Decision Risk and Operations; Google Research

Omar Besbes

Columbia University - Columbia Business School, Decision Risk and Operations

Date Written: March 18, 2024

Abstract

In robust decision-making under non-Bayesian uncertainty, different robust optimization criteria, such as maximin performance, minimax regret, and maximin ratio, have been proposed. In many problems, all three criteria are well-motivated and well-grounded from a decision-theoretic perspective, yet different criteria give different prescriptions. This paper initiates a systematic study of overfitting to robustness criteria. How good is a prescription derived from one criterion when evaluated against another criterion? Does there exist a prescription that performs well against all criteria of interest? We formalize and study these questions through the prototypical problem of robust pricing under various information structures, including support, moments, and percentiles of the distribution of values. We provide a unified analysis of three focal robust criteria across various information structures and evaluate the relative performance of mechanisms optimized for each criterion against the others. We find that mechanisms optimized for one criterion often perform poorly against other criteria, highlighting the risk of overfitting to a particular robustness criterion. Remarkably, we show it is possible to design mechanisms that achieve good performance across all three criteria simultaneously, suggesting that decision-makers need not compromise among criteria.

Suggested Citation

Anunrojwong, Jerry and Balseiro, Santiago and Besbes, Omar, The Best of Many Robustness Criteria in Decision Making: Formulation and Application to Robust Pricing (March 18, 2024). Available at SSRN: https://ssrn.com/abstract=4759889 or http://dx.doi.org/10.2139/ssrn.4759889

Santiago Balseiro

Columbia University - Columbia Business School, Decision Risk and Operations ( email )

3022 Broadway
New York, NY 10027
United States

Google Research ( email )

Omar Besbes

Columbia University - Columbia Business School, Decision Risk and Operations ( email )

New York, NY
United States

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