Dynamic Nonlinear Pricing in Networks with Interdependent Demand

Abstract

We consider the pricing decision for a new product whose consumption value increases as the network of adopters expands. This demand interdependence is a characteristic feature of telecommunications networks. The paper analyzes the case of a single supplier offering the product to a heterogeneous population. Consumers decide on network access and consumption quantity. The pricing decision consists of choosing a pricing schedule (over the dimensions of quantity and time) that maximizes the present value of a weighted sum of total surplus and producer profits, subject to the dynamics of market growth. We find that the decision can be decoupled into two nested optimization problems: (a) given some market size, what should the optimal nonlinear price schedule be? and (b) how should the price schedule be changed optimally over time? This separation enables us to solve the pricing problem. Explicit consideration of the dynamics, the discounting of future surpluses, and the extent of market growth anticipation affect not only the price and network size trajectories, but also their steady-state equilibrium values.

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