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A Distributionally Robust Random Utility Model
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DOI：10.1007/s00199-025-01680-2.png)
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Abstract
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This paper introduces a Distributionally Robust Random Utility Model (DRO-RUM) that accounts for misspecification or uncertainty in the distribution of preference shocks (unobserved heterogeneity). By leveraging distributionally robust optimization techniques, we contribute to theory and applications in discrete choice modeling through the robust social surplus function, which evaluates best- and worst-case scenarios under distributions that are phi\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\phi $$\end{document}-divergent from a reference distribution. Our contributions are threefold. First, we establish key convex-analytic properties of the robust social surplus function, including extending the celebrated Williams-Daly-Zachary theorem to misspecified environments and a robust version of the Fenchel duality result. Second, we demonstrate how mean utilities can be nonparametrically identified using convex duality, providing insights into robust demand inversion problems. Third, we extend our approach beyond the phi\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\phi $$\end{document}-divergence case, illustrating how the DRO-RUM framework can be analyzed using the Sinkhorn distance. These results deepen the understanding of how uncertainty in distributional assumptions influences choice modeling, welfare analysis, and broader economic insights.
Keywords:
Discrete choice
Random utility
Convex analysis
Distributionally robust optimization
C35
C61
D90
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