A Distributionally Robust Random Utility Model
提出分布鲁棒随机效用模型，处理偏好冲击分布误设问题，通过鲁棒社会剩余函数分析最坏和最好情形，并扩展了经典定理，适用于需求反演和福利分析。
Abstract 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 $$\phi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ϕ</mml:mi> </mml:math> -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 $$\phi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ϕ</mml:mi> </mml:math> -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.