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Competing for Customers in a Social Network (R)

Author

Listed:
  • Pradeep Dubey

    (Center for Game Theory, Stony Brook University)

  • Rahul Garg

    (Opera Solutions, India)

  • Bernard De Meyer

    (CERMSEM, Universite Paris 1)

Abstract
There are many situations in which a customer�s proclivity to buy the product of any firm depends not only on the classical attributes of the product such as its price and quality, but also on who else is buying the same product. Under quite general circumstances, it turns out that customers� influence on each other dynamically converges to a steady state. Thus we can model these situations as games in which firms compete for customers located in a "social network." A canonical example is provided by competition for advertisement on the web. Nash Equilibrium (NE) in pure strategies exist in general. In the quasi-linear version of the model, NE turn out to be unique and can be precisely characterized. If there are no a priori biases between customers and firms, then there is a cut-off level above which high cost firms are blockaded at an NE, while the rest compete uniformly throughout the network. Otherwise there is a tendency towards regionalization, with firms dominating disjoint territories. We also explore the relation between the connectivity of a customer and the money firms spend on him. This relation becomes particularly transparent when externalities are dominant: NE can be characterized in terms of the invariant measures on the recurrent classes of the Markov chain underlying the social network. Finally we consider convex (instead of linear) cost functions for the firms. Here NE need not be unique as we show via an example. But uniqueness is restored if there is enough competition between firms or if their valations of clients are anonymous.

Suggested Citation

  • Pradeep Dubey & Rahul Garg & Bernard De Meyer, 2012. "Competing for Customers in a Social Network (R)," Cowles Foundation Discussion Papers 1862, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:1862
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    File URL: https://cowles.yale.edu/sites/default/files/files/pub/d18/d1862.pdf
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    References listed on IDEAS

    as
    1. Pradeep K. Dubey & Rahul Garg & Bernard de Meyer, 2006. "Competing for Customers in a Social Network," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00272889, HAL.
    2. Banerji, A. & Dutta, Bhaskar, 2009. "Local network externalities and market segmentation," International Journal of Industrial Organization, Elsevier, vol. 27(5), pages 605-614, September.
    3. Pekka S��skilahti, 2015. "Monopoly Pricing of Social Goods," International Journal of the Economics of Business, Taylor & Francis Journals, vol. 22(3), pages 429-448, November.
    4. Bernard de Meyer & Pradeep K. Dubey & Rahul Garg, 2006. "Competing for Customers in a Social Network: The Quasi-linear Case," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00367866, HAL.
    5. Bloch, Francis & Quérou, Nicolas, 2013. "Pricing in social networks," Games and Economic Behavior, Elsevier, vol. 80(C), pages 243-261.
    6. Shy,Oz, 2001. "The Economics of Network Industries," Cambridge Books, Cambridge University Press, number 9780521805001.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Nicole Tabasso, 2014. "Diffusion of Multiple Information," School of Economics Discussion Papers 0914, School of Economics, University of Surrey.
    2. Antoine Mandel & Xavier Venel, 2017. "Dynamic competition over social networks Dynamic competition over social networks," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01524453, HAL.
    3. Kolumbus, Yoav & Solomon, Sorin, 2021. "On the influence maximization problem and the percolation phase transition," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 573(C).
    4. Pradeep Dubey & Rahul Garg & Bernard De Meyer, 2006. "Competing for Customers in a Social Network," Cowles Foundation Discussion Papers 1591, Cowles Foundation for Research in Economics, Yale University.
    5. Demange, Gabrielle, 2017. "Optimal targeting strategies in a network under complementarities," Games and Economic Behavior, Elsevier, vol. 105(C), pages 84-103.
    6. Rusinowska, Agnieszka & Taalaibekova, Akylai, 2019. "Opinion formation and targeting when persuaders have extreme and centrist opinions," Journal of Mathematical Economics, Elsevier, vol. 84(C), pages 9-27.
    7. Mandel, Antoine & Venel, Xavier, 2020. "Dynamic competition over social networks," European Journal of Operational Research, Elsevier, vol. 280(2), pages 597-608.
    8. Sengupta, Abhijit & Greetham, Danica Vukadinovic, 2010. "Dynamics of brand competition: Effects of unobserved social networks," Journal of Economic Dynamics and Control, Elsevier, vol. 34(12), pages 2391-2406, December.
    9. Goyal, Sanjeev & Heidari, Hoda & Kearns, Michael, 2019. "Competitive contagion in networks," Games and Economic Behavior, Elsevier, vol. 113(C), pages 58-79.
    10. Aner Sela & Ezra Einy & 0ri Haimanko & Diego Moreno & Avishay Aiche & Benyamin Shitovitz, 2016. "Information Advantage in Common-Value Classic Tullock Contests," Working Papers 1614, Ben-Gurion University of the Negev, Department of Economics.
    11. Antoine Mandel & Xavier Venel, 2017. "Dynamic competition over social networks Dynamic competition over social networks," Post-Print halshs-01524453, HAL.
    12. Tabasso, Nicole, 2019. "Diffusion of multiple information: On information resilience and the power of segregation," Games and Economic Behavior, Elsevier, vol. 118(C), pages 219-240.
    13. Li, WenYao & Xue, Xiaoyu & Pan, Liming & Lin, Tao & Wang, Wei, 2022. "Competing spreading dynamics in simplicial complex," Applied Mathematics and Computation, Elsevier, vol. 412(C).
    14. Jie Gu & Yunjie Xu, 2022. "Battle of positioning: exploring the role of bridges in competitive diffusion," Journal of Computational Social Science, Springer, vol. 5(1), pages 319-350, May.
    15. Michel Grabisch & Antoine Mandel & Agnieszka Rusinowska & Emily Tanimura, 2018. "Strategic Influence in Social Networks," Mathematics of Operations Research, INFORMS, vol. 43(1), pages 29-50, February.
    16. Akylai Taalaibekova, 2018. "Opinion formation in social networks," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 28(2), pages 85-108.

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    More about this item

    Keywords

    Nash equilibrium; Social network; Advertisement on the web;
    All these keywords.

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D2 - Microeconomics - - Production and Organizations
    • D4 - Microeconomics - - Market Structure, Pricing, and Design
    • L1 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance

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