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Competing for Customers in a Social Network: The Quasi-linear Case

Author

Listed:
  • Bernard de Meyer

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • Pradeep K. Dubey

    (SBU - Stony Brook University [SUNY] - SUNY - State University of New York)

  • Rahul Garg

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. We model these situations as games in which firms compete for customers located in a "social network". Nash Equilibrium (NE) in pure strategies exist and are unique. Indeed there are closed-form formulae for the NE in terms of the exogenous parameters of the model, which enables us to compute NE in polynomial time. An important structural feature of NE is that, 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. We finally 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.

Suggested Citation

  • Bernard de Meyer & Pradeep K. Dubey & Rahul Garg, 2006. "Competing for Customers in a Social Network: The Quasi-linear Case," Post-Print hal-00367866, HAL.
    • Handle: RePEc:hal:journl:hal-00367866
    DOI: 10.1007/11944874_16
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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. 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.
    3. 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.
    4. Goyal, Sanjeev & Heidari, Hoda & Kearns, Michael, 2019. "Competitive contagion in networks," Games and Economic Behavior, Elsevier, vol. 113(C), pages 58-79.
    5. 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.
    6. 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).
    7. 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.
    8. 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).

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