Competing for Customers in a Social Network
AbstractThere 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 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. 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 valuations of clients are anonymous.
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Bibliographic InfoPaper provided by Stony Brook University, Department of Economics in its series Department of Economics Working Papers with number 06-01.
Date of creation: 2006
Date of revision:
Other versions of this item:
- 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.
- Pradeep Dubey & Rahul Garg & Bernard De Meyer, 2006. "Competing for Customers in a Social Network," Levine's Bibliography 321307000000000685, UCLA Department of Economics.
- A14 - General Economics and Teaching - - General Economics - - - Sociology of Economics
- C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
- D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
- D21 - Microeconomics - - Production and Organizations - - - Firm Behavior: Theory
- L1 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance
- L2 - Industrial Organization - - Firm Objectives, Organization, and Behavior
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- Pradeep Dubey & Rahul Garg & Bernard De Meyer, 2013. "Competing for Customers in a Social Network (R)," Department of Economics Working Papers 13-01, Stony Brook University, Department of Economics.
- Pradeep Dubey & Rahul Garg & Bernard De Meyer, 2012. "Competing for Customers in a Social Network," Department of Economics Working Papers 12-10, Stony Brook University, Department of Economics.
- 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.
- 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.
- Pradeep K. Dubey & Rahul Garg & Bernard De Meyer, 2012. "Competing for Customers in a Social Network (R)," Levine's Working Paper Archive 786969000000000526, David K. Levine.
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