Strategic Dynamic Pricing with Network Externalities

We study the optimal pricing policy of a strategic monopolist selling durable goods in a dynamic pricing game with multiple rounds. Customers are forward-looking and experience a (positive) network externality, i.e., each customer’s utility depends not only on her valuation of the item and the offered price, but also the weighted sum of the number of other customers who have purchased the item. The monopolist announces and commits to a price sequence and strategic buyers decide on when (if ever) to buy the good in a perfect Bayesian equilibrium. We fully characterize the optimal pricing policy and show that it is linearly increasing in time, where the slope of the price path is described by a single network measure: sum of the entries of the inverse of network externality matrix, termed network effect. Our result shows that increasing the number of rounds and network effect increases both revenue and social welfare. We also study the effect of price discrimination and establish that in the earlier rounds the price offered to more central buyers is lower. This is to encourage them to buy earlier which in turn increases the externality of other buyers and incentivize them to buy in subsequent rounds.