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

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 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 cannot be strictly larger than that without network effects; and the optimal assortment to each peripheral consumer must be a revenue-ordered assortment. Then, we propose a novel idea in which the sellers are allowed to offer “randomized assortments” to each node in the network by viewing each node as a consumer group. We show that randomized assortments may further increase the revenue, and for general network setting, under certain conditions, the optimal assortment must be a combination of two adjacent revenue-ordered assortments. Finally, we study the associated optimal pricing problem and develop structural properties and efficient algorithms.