Personalized Pricing and Assortment Optimization Under Consumer Choice Models with Local Network Effects

In this paper, we introduce a consumer choice model where each consumer’s utility is affected by their neighbors’ purchase probabilities in a network. We first characterize the choice probabilities in this model and then consider the associated personalized assortment optimization problem. Although this problem is NP-hard, we show that for star networks, the optimal assortment to the central consumer and peripheral consumers cannot be strictly larger than that without network effects, and the optimal assortment to each peripheral consumer must be a revenue-ordered assortment. Then, because each node in a network can represent a group of consumers, we propose a novel idea where the sellers are allowed to offer “randomized assortments” to each node in the network. We show that allowing for randomized assortments may further increase the revenue, and for general network setting, under certain conditions, the optimal assortment for each consumer must be a combination of two adjacent revenue-ordered assortments. Such a result gives important insights and allows us to convert the problem into a (nonconvex) continuous optimization problem. Finally, we consider the optimal pricing problem under this model. We develop some structural properties as well as efficient algorithms for the optimal pricing problem.