Competing for customers in a social network

Bernard de Meyer (), Pradeep Dubey and Rahul Garg
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Bernard de Meyer: CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement
Rahul Garg: Opera Solution (India)

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Abstract: Customers' proclivities to buy products often depend heavily on who else is buying the same product. This gives rise to non-cooperative games in which firms sell to customers located in a ``social network''. Nash Equilibrium (NE) in pure strategies exist in general. In the quasi-linear case, NE are unique. If there are no a priori biases between customers and firms, 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 firms could end up as regional monopolies. The connectivity of a customer is related to the money firms spend on him. This 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 cost functions of firms are 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 firms 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.

Keywords: Social network; externalities; noncooperative game; Nash equilibrium. (search for similar items in EconPapers)
Date: 2014-07
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Citations: View citations in EconPapers (16)

Published in Journal of Dynamics and Games, 2014, 1 (3), pp.377 - 409. ⟨10.3934/jdg.2014.1.377⟩

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Related works:
Working Paper: Competing for customers in a social network (2014)
Working Paper: Competing for customers in a social network (2014)
Working Paper: Competing for Customers in a Social Network (R) (2013)
Working Paper: Competing for Customers in a Social Network (R) (2012)
Working Paper: Competing for Customers in a Social Network (R) (2012)
Working Paper: Competing for Customers in a Social Network (2012)
Working Paper: Competing for Customers in a Social Network (2006)
Working Paper: Competing for Customers in a Social Network (2006)
Working Paper: Competing for Customers in a Social Network (2006)
Working Paper: Competing for Customers in a Social Network (2006)
Working Paper: Competing for Customers in a Social Network (2006)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:pseptp:hal-01432210

DOI: 10.3934/jdg.2014.1.377

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