A Dynamic Pricing Game in a Model of New Product Adoption with Social Influence

We examine a pricing game between firms that produce differentiated products and in which consumer preferences evolve in response to the market shares of the available products. One of the products is new and a subset of consumers (early adopters) have a relatively strong preference for it, while the remaining consumers are influenced by the relative market shares of the two products, being drawn to the product with the higher market share. We use a system of PDEs to specify the evolution of the preferences for the alternative goods. This system is nonlinear due to the influence of existing consumption choice on the distribution of preferences. The pricing game allows firms to react to the changing distribution of consumer preference. We find that allowing for the evolution of consumer preference in this way results in interesting dynamics for prices. In particular, price paths can be non-monotonic over time.