Netvendor: Newsvendor Selling to a Social Network

Abstract

We study the inventory problem faced by a newsvendor, referred to as a ``netvendor," when selling a product of network effects to customers located on a social network. The customers decide on product adoption subject to product availability, from which they derive values not only from the product itself but also from the adoptions by their network neighbors. Both the customers and netvendor only have distributional information regarding the underlying network structure. Each individual customer also has local information on the exact number of their connected neighbors. The random demand for the product is driven by the random intrinsic product value to the customers. The netvendor needs to commit to an inventory level before observing the realization of the intrinsic product value. We provide complete and closed-form characterizations of equilibria of the customer adoption game, as well as the optimal inventory level for the netvendor. In the context of a scale-free network characterized by its asymmetry and density, we show that the netvendor benefits (both in terms of the optimal profit and sales volume) from selling to a more unequal network with stronger asymmetry in connectivity. We find that for a netvendor, increasing network density will lead to not only higher optimal expected profit and order quantity but also rising expected waste (i.e., leftover inventory). The pattern of increase (i.e., concavity or convexity) in optimal profit and waste hinges on the exponent of a scale-free network that measures the network asymmetry. Moreover, if a netvendor such as Shein is equipped with quick response capability to operate in the make-to-order mode as opposed to the make-to-stock mode, we show that the value of quick response capability increases with the network density. Meanwhile, the pattern of increase (i.e., concavity or convexity) depends on the degree of network asymmetry. The value of quick response can either rise or fall with increasing network asymmetry, conditional on the level of network density, even though the netvendor without quick response always benefits from network asymmetry.