Strategic Dynamic Pricing with Network Externalities

Abstract

We study the optimal pricing strategy of a monopolist selling homogeneous goods to multiple buyers over multiple periods. The customers choose their time of purchase to maximize their payoff that depends on their valuation of the product, the purchase price, and the utility they derive from past purchases of others, termed the network effect. We first show that the optimal price sequence is non-decreasing. Therefore, by postponing purchase to future rounds, customers trade-off a higher utility from the network effects with a higher price. We then show that a customer's equilibrium strategy can be characterized by a threshold rule in which at each round a customer purchases the product when her valuation exceeds a certain threshold. This implies that customers face an inference problem regarding the valuations of others, i.e., observing that a customer has not yet purchased the product, signals that her valuation is below a threshold. Building on this characterization, we fully characterize the optimal price sequence asymptotically as the number of buyers goes to infinity. Notably, the optimal price sequence is linearly increasing in time with a slope that depends on the network structure through a novel scalar term given by the sum of entries of the inverse of the network weight matrix. Our characterization shows that increasing the ``imbalance'' in the network defined as the difference between the in-degree and out-degree of the nodes increases the revenue of the monopolist.