Pricing for a product with network effects and mixed logit demand

We consider a pricing problem for a single product that experiences network effects. Demand is described by a consumer choice model in which each individual chooses between purchasing the product and not purchasing the product. We assume that there are multiple segments in the population of potential buyers, and that individuals' intrinsic values for the product and sensitivities to the network effect (ie, the extent to which their values are affected by how many others buy the product) vary across segments. The demand model may be viewed as a version of the mixed multinomial logit model, modified to incorporate network effects. We formulate and analyze an optimization problem that aims to find the seller's revenue-maximizing price. In settings with an arbitrary number of demand segments, we present a simple, effective heuristic solution approach. In settings with two segments, we obtain a solution method that outputs provably near-optimal prices. We close with an extensive numerical study.