Title: Strategic Dynamic Pricing with Network Effects,
Abstract: We study the optimal pricing strategy of a monopolist selling homogeneous
goods to customers 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 if
and only if 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. We consider a block model of network
interactions, where there are blocks of buyers subject to the same network
effect. A natural benchmark, this model allows us to provide an explicit
characterization of the optimal price sequence asymptotically as the number of
agents goes to infinity, which notably is linearly increasing in time with a
slope that depends on the network effect through a scalar 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 and out degree of the nodes increases the revenue of the
monopolist. We further study the effects of price discrimination and show that
in earlier periods monopolist offers lower prices to blocks with higher
Bonacich centrality to encourage them to purchase, which in turn further
incentivizes other customers to buy in subsequent periods.