  We study the optimal pricing strategies of a monopolist selling a divisible
good (service) to consumers that are embedded in a social network. A key
feature of our model is that consumers experience a (positive) local network
effect. In particular, each consumer's usage level depends directly on the
usage of her neighbors in the social network structure. Thus, the monopolist's
optimal pricing strategy may involve offering discounts to certain agents, who
have a central position in the underlying network.
  First, we consider a setting where the monopolist can offer individualized
prices and derive an explicit characterization of the optimal price for each
consumer as a function of her network position. In particular, we show that it
is optimal for the monopolist to charge each agent a price that is proportional
to her Bonacich centrality in the social network. In the second part of the
paper, we discuss the optimal strategy of a monopolist that can only choose a
single uniform price for the good and derive an algorithm polynomial in the
number of agents to compute such a price. Thirdly, we assume that the
monopolist can offer the good in two prices, full and discounted, and study the
problem of determining which set of consumers should be given the discount. We
show that the problem is NP-hard, however we provide an explicit
characterization of the set of agents that should be offered the discounted
price. Next, we describe an approximation algorithm for finding the optimal set
of agents. We show that if the profit is nonnegative under any feasible price
allocation, the algorithm guarantees at least 88% of the optimal profit.
Finally, we highlight the value of network information by comparing the profits
of a monopolist that does not take into account the network effects when
choosing her pricing policy to those of a monopolist that uses this information
optimally.
