IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v60y2012i4p883-905.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.1120.1066
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.1120.1066?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Coralio Ballester & Antoni Calvó-Armengol & Yves Zenou, 2006. "Who's Who in Networks. Wanted: The Key Player," Econometrica, Econometric Society, vol. 74(5), pages 1403-1417, September.
    2. Andrea Galeotti & Sanjeev Goyal, 2009. "Influencing the influencers: a theory of strategic diffusion," RAND Journal of Economics, RAND Corporation, vol. 40(3), pages 509-532, September.
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Jadbabaie, Ali & Kakhbod, Ali, 2019. "Optimal contracting in networks," Journal of Economic Theory, Elsevier, vol. 183(C), pages 1094-1153.
    2. Elias Carroni & Paolo Pin & Simone Righi, 2020. "Bring a Friend! Privately or Publicly?," Management Science, INFORMS, vol. 66(5), pages 2269-2290, May.
    3. Zhang, Yang & Du, Xiaomin, 2017. "Network effects on strategic interactions: A laboratory approach," Journal of Economic Behavior & Organization, Elsevier, vol. 143(C), pages 133-146.
    4. Gary Charness & Francesco Feri & Miguel A. Meléndez‐Jiménez & Matthias Sutter, 2014. "Experimental Games on Networks: Underpinnings of Behavior and Equilibrium Selection," Econometrica, Econometric Society, vol. 82, pages 1615-1670, September.
    5. Sanjeev Goyal, 2015. "Networks in Economics: A Perspective on the Literature," Cambridge Working Papers in Economics 1548, Faculty of Economics, University of Cambridge.
    6. Zenou, Yves, 2014. "Key Players," CEPR Discussion Papers 10277, C.E.P.R. Discussion Papers.
    7. Jackson, Matthew O. & Zenou, Yves, 2015. "Games on Networks," Handbook of Game Theory with Economic Applications,, Elsevier.
    8. Goyal, S., 2016. "Networks and Markets," Cambridge Working Papers in Economics 1652, Faculty of Economics, University of Cambridge.
    9. Sanjeev Goyal & Andrea Galeotti, 2007. "A Theory of Strategic Diffusion," Working Papers 2007.70, Fondazione Eni Enrico Mattei.
    10. Arun Sundararajan & Foster Provost & Gal Oestreicher-Singer & Sinan Aral, 2013. "Research Commentary ---Information in Digital, Economic, and Social Networks," Information Systems Research, INFORMS, vol. 24(4), pages 883-905, December.
    11. Evan Sadler & Benjamin Golub, 2021. "Games on Endogenous Networks," Papers 2102.01587, arXiv.org, revised Feb 2024.
    12. Amir Ajorlou & Ali Jadbabaie & Ali Kakhbod, 2018. "Dynamic Pricing in Social Networks: The Word-of-Mouth Effect," Management Science, INFORMS, vol. 64(2), pages 971-979, February.
    13. Galeotti, Andrea & Goyal, Sanjeev, 2007. "A Theory of Strategic Diffusion," Economics Discussion Papers 2983, University of Essex, Department of Economics.
    14. Dunia López-Pintado, 2017. "Influence networks and public goods," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 8(1), pages 97-112, March.
    15. Allouch, Nizar, 2017. "The cost of segregation in (social) networks," Games and Economic Behavior, Elsevier, vol. 106(C), pages 329-342.
    16. Kovarik, J. & Mengel, F. & Romero, J.G., 2009. "(Anti-) coordination in networks," Research Memorandum 041, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    17. Cabrales, Antonio & Calvó-Armengol, Antoni & Zenou, Yves, 2011. "Social interactions and spillovers," Games and Economic Behavior, Elsevier, vol. 72(2), pages 339-360, June.
    18. Goyal, Sanjeev & Heidari, Hoda & Kearns, Michael, 2019. "Competitive contagion in networks," Games and Economic Behavior, Elsevier, vol. 113(C), pages 58-79.
    19. Joshi, Sumit & Mahmud, Ahmed Saber, 2018. "Unilateral and multilateral sanctions: A network approach," Journal of Economic Behavior & Organization, Elsevier, vol. 145(C), pages 52-65.
    20. Chen, Ying-Ju & Zenou, Yves & Zhou, Junjie, 2022. "The impact of network topology and market structure on pricing," Journal of Economic Theory, Elsevier, vol. 204(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:oropre:v:60:y:2012:i:4:p:883-905. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.