Facilitating adoption of network services with externalities via cost subsidization

This paper investigates the adoption level of a network service where the net utility perceived by each user incorporates three key features, namely, user service affinity heterogeneity, a network externality, and a subscription cost. Services with network externality face a “chicken and egg” adoption problem in that the service requires customers in order to attract customers. In this paper we study cost subsidization as a means to “reach the knee” and thereby change the equilibrium adoption level from zero to one. By focusing on a simple subsidy structure and a simple model for user heterogeneity, we can derive explicit expressions for quantities of natural interest, such as the minimum subsidy required, the minimum subsidy duration, and the aggregate cost of the subsidy to the service provider. We show that small or large subsidies are inefficient, but that there is a Pareto efficient frontier for “intermediate” subsidies wherein subsidy duration and aggregate cost are in tension with one another.