A Nonparametric Approach with Marginals for Modeling Consumer Choice

Given data on the choices made by consumers for different offer sets, a key challenge is to develop parsimonious models that describe and predict consumer choice behavior while being amenable to prescriptive tasks, such as pricing and assortment optimization. The marginal distribution model (MDM) is one such model, which requires only the specification of marginal distributions of the random utilities. This paper aims to establish necessary and sufficient conditions for given choice data to be consistent with the MDM hypothesis inspired by the usefulness of similar characterizations for the random utility model (RUM). This endeavor leads to an exact characterization of the set of choice probabilities that the MDM can represent. Verifying the consistency of choice data with this characterization is equivalent to solving a polynomial-sized linear program. Because the analogous verification task for RUM is computationally intractable and neither of these models subsume the other, MDM is helpful in striking a balance between tractability and representational power. The characterization is then used with robust optimization for making data-driven sales and revenue predictions for new unseen assortments. When the choice data lack consistency with the MDM hypothesis, finding the best-fitting MDM choice probabilities reduces to solving a mixed-integer convex program. Numerical results using real-world data and synthetic data demonstrate that MDM exhibits competitive representational power and prediction performance compared with RUM and parametric models while being significantly faster in computation than RUM. This paper was accepted by Omar Besbes, revenue management and pricing department. Funding: This work was supported by the Singapore Ministry of Education Academic Research Fund [Grants T2EP20223-0008 and T2MOE1906]. X. Li was supported in part by the Singapore Ministry of Education Academic Research Fund Tier 1 [Grants 23-0619-P0001 and 24-0500-A0001]. The research of K. Murthy was supported by the Singapore Ministry of Education Academic Research Fund [Grants MOE2019-T2-2-163 and MOE-T2EP20223-0017]. The research of K. Natarajan was partly supported by the Singapore Ministry of Education Academic Research Fund Tier 2 [Grant MOE2019-T2-2-138]. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2023.02287 .