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

  • Pradeep Dubey
  • Rahul Garg
  • Bernard De Meyer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4286)


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.


Social Network Nash Equilibrium Invariant Measure Pure Strategy Strategic Game 
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  1. 1.
    Domingos, P., Richardson, M.: Mining the network value of customers. In: Proceedings of the Seventh ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, San Francisco, USA, pp. 57–66 (August 2001)Google Scholar
  2. 2.
    Dubey, P., Garg, R., De Meyer, B.: Competing for customers in a social network. Stony Brook Working Paper (WP 06-1) (August 2006),
  3. 3.
    Jackson, M.: The economics of social networks. In: Blundell, R., Newey, W., Persson, T. (eds.) Proceedings of the 9th World Congress of the Econometric Society. Cambridge University Press, Cambridge (2005)Google Scholar
  4. 4.
    Moore, C.N.: Summability of series. The American Mathematical Monthly 39(2), 62–71 (1932)CrossRefMathSciNetGoogle Scholar
  5. 5.
    Richardson, M., Domingos, P.: Mining knowledge-sharing sites for viral marketing. In: Proceedings of the Seventh ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, Edmonton, Alberta, Canada, pp. 61–70 (July 2002)Google Scholar
  6. 6.
    Scott, J.: Social Network Analysis: A Handbook, 2nd edn. Sage Publications, London (2000)Google Scholar
  7. 7.
    Shapiro, C., Varian, H.R.: Information Rules: A Strategic Guide to the Network Economy. Harvard Business School Press (November 1998)Google Scholar
  8. 8.
    Shy, O.: The Economics of Network Industries. Cambridge University Press, Cambridge (2001)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Pradeep Dubey
    • 1
    • 2
  • Rahul Garg
    • 3
  • Bernard De Meyer
    • 2
    • 4
  1. 1.Center for Game TheoryStony Brook UniversityUSA
  2. 2.Cowles FoundationYale UniversityUSA
  3. 3.IBM India Research LabNew DelhiIndia
  4. 4.Cermsem, Univesité Paris 1ParisFrance

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