Sequential Recommendation and Pricing Under the Mixed Cascade Model

Motivated by a research gap in modeling consumers' purchase behavior over multiple pages of a recommender system, we propose a mixed cascade model to describe consumers' decisions and study the corresponding assortment optimization and pricing problems. We first test the fitness of our proposed model through a real-world dataset, and observe that our model outperforms other multi-page choice models in terms of predictability. Due to the computational difficulty of estimating the distribution of preference lists in our model, we study the corresponding robust assortment optimization problem when the distribution is unknown. We show that the optimal robust solution has a sequential revenue-ordered property. We also investigate the performance of the robust solution by comparing it with a clairvoyant who knows the exact distribution and establish a constant performance guarantee of the robust solution. We then extend the above results to the constrained assortment optimization problems and derive efficient algorithms. We also study the joint assortment and pricing problem under our model. We establish the NP-hardness of the problem and propose several constant-factor approximation algorithms. The development of the approximation algorithms utilizes some existing results in submodular maximization problems. Our results show the superior performance of the sequential revenue-ordered assortments, which provides online platforms with an efficient and easy-to-implement recommendation strategy. Our results also indicate the limitation of personalization: the extra revenue improvement by knowing the exact information of consumers is bounded