## Optimal pricing in the presence of local network effects

##### Author(s)

Candogan, Utku Ozan; Bimpikis, Konstantinos; Ozdaglar, Asuman E.
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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 e ffect. 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 o ffering discounts to certain agents3, who have a central
position in the underlying network. Our results can be summarized as follows. First, we consider a
setting where the monopolist can o er 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 o er 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 o ffered
the discounted price. Finally, we describe an approximation algorithm for finding the optimal set of
agents. We show that if the pro t is nonnegative under any feasible price allocation, the algorithm
guarantees at least 88 % of the optimal pro fit.

##### Description

URL to paper listed on conference site

##### Date issued

2010-12##### Department

Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science; Massachusetts Institute of Technology. Laboratory for Information and Decision Systems; Massachusetts Institute of Technology. Operations Research Center##### Journal

Proceedings of the 6th Workshop on Internet & Network Economics, WINE 2010

##### Citation

Candogan, Ozan, Kostas Bimpikis and Asuman Ozdaglar. "Optimal pricing in the presence of local network effects." Proceedings of the 6th Workshop on Internet & Network Economics, WINE 2010, December 13-16, 2010, Stanford University, Stanford, California, USA.

Version: Author's final manuscript