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Competing for Customers in a Social Network (R)

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  • Pradeep Dubey

    ()
    (Department of Economics, Stony Brook University)

  • Rahul Garg

    ()
    (Opera Solutions, INDIA)

  • Bernard De Meyer

    ()
    (PSE-Univesite Paris 1, Paris, FRANCE)

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    Abstract

    There are many situations in which a customer's proclivity to buy the product of any rm depends heavily on who else is buying the same product. We model these situations as non-cooperative games in which rms market their products to customers located in a \social network". 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 rms, then there is a cut-o level above which high cost rms are blockaded at an NE, while the rest compete uniformly throughout the network. Otherwise rms could end up as regional monopolies. We also explore the relation between the connectivity of a customer and the money rms 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. When we allow for cost functions of rms to be convex, instead of just linear, NE need no longer be unique as we show via an example. But uniqueness is restored if there is enough competition between rms or if their valuations of clients are anonymous. Finally we develop a general model of nonlinear externalities and show that existence of NE remains intact.

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    File URL: http://www.sunysb.edu/economics/research/papers/2013/geb_rev7.pdf
    File Function: First version, 2013
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    Bibliographic Info

    Paper provided by Stony Brook University, Department of Economics in its series Department of Economics Working Papers with number 13-01.

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    Date of creation: Jul 2013
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    Handle: RePEc:nys:sunysb:13-01

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    Postal: Stony Brook, NY 11794-4384
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    Web page: http://www.stonybrook.edu/economics
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    1. Banerji, A. & Dutta, Bhaskar, 2009. "Local network externalities and market segmentation," International Journal of Industrial Organization, Elsevier, vol. 27(5), pages 605-614, September.
    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. Shy,Oz, 2001. "The Economics of Network Industries," Cambridge Books, Cambridge University Press, number 9780521805001, October.
    4. Bloch, Francis & Quérou, Nicolas, 2013. "Pricing in social networks," Games and Economic Behavior, Elsevier, vol. 80(C), pages 243-261.
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