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Optimal Pricing in Networks with Externalities

Author

Listed:
  • Ozan Candogan

    (Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139)

  • Kostas Bimpikis

    (Graduate School of Business, Stanford University, Stanford, California 94305)

  • Asuman Ozdaglar

    (Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139)

Abstract

We study the optimal pricing strategies of a monopolist selling a divisible good (service) to consumers who 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. Our results can be summarized as follows. First, we consider a setting where the monopolist can offer individualized prices and derive a 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 consists of three components: (i) a nominal term that is independent of the network structure, (ii) a discount term proportional to the influence that this agent exerts over the rest of the social network (quantified by the agent's Bonacich centrality ), and (iii) a markup term proportional to the influence that the network exerts on the agent. In the second part of the paper, we discuss the optimal strategy of a monopolist who 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. Third, we assume that the monopolist can offer the good in two prices, full and discounted, and we 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 who 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 who does not take into account the network effects when choosing her pricing policy to those of a monopolist who uses this information optimally.

Suggested Citation

  • Ozan Candogan & Kostas Bimpikis & Asuman Ozdaglar, 2012. "Optimal Pricing in Networks with Externalities," Operations Research, INFORMS, vol. 60(4), pages 883-905, August.
    • Handle: RePEc:inm:oropre:v:60:y:2012:i:4:p:883-905
    DOI: 10.1287/opre.1120.1066
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    References listed on IDEAS

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    3. Katz, Michael L & Shapiro, Carl, 1986. "Technology Adoption in the Presence of Network Externalities," Journal of Political Economy, University of Chicago Press, vol. 94(4), pages 822-841, August.
    4. Arun Sundararajan, 2004. "Local Network Effects and Network Structure," Industrial Organization 0412011, University Library of Munich, Germany.
    5. Bramoulle, Yann & Kranton, Rachel, 2007. "Public goods in networks," Journal of Economic Theory, Elsevier, vol. 135(1), pages 478-494, July.
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