Computational Management Science

, Volume 11, Issue 4, pp 475–502 | Cite as

A Cournot–Nash–Bertrand game theory model of a service-oriented Internet with price and quality competition among network transport providers

  • Anna Nagurney
  • Tilman Wolf
Original Paper


This paper develops a game theory model of a service-oriented Internet in which profit-maximizing service providers provide substitutable (but not identical) services and compete with the quantities of services in a Cournot–Nash manner, whereas the network transport providers, which transport the services to the users at the demand markets, and are also profit-maximizers, compete with prices in Bertrand fashion and on quality. The consumers respond to the composition of service and network provision through the demand price functions, which are both quantity and quality dependent. We derive the governing equilibrium conditions of the integrated game and show that it satisfies a variational inequality problem. We then describe the underlying dynamics, and provide some qualitative properties, including stability analysis. The proposed algorithmic scheme tracks, in discrete-time, the dynamic evolution of the service volumes, quality levels, and the prices until an approximation of a stationary point (within the desired convergence tolerance) is achieved. Numerical examples demonstrate the modeling and computational framework.


Network economics Game theory Oligopolistic competition Service differentiation Quality competition  Cournot–Nash equilibrium Service-oriented Internet Bertrand competition Variational inequalities Projected dynamical systems 



This research was supported, in part, by the National Science Foundation (NSF) grant CISE #1111276, for the NeTS: Large: Collaborative Research: Network Innovation Through Choice project awarded to the University of Massachusetts Amherst. This support is gratefully acknowledged. The authors thank Ilia Baldine, Ken Calvert, Rudra Dutta, Jim Griffioen, George Rouskas, and Dong Li and Sara Saberi for many helpful discussions. The authors also acknowledge the helpful comments and suggestions of three anonymous reviewers on earlier versions of this paper.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of Operations and Information Management, Isenberg School of ManagementUniversity of MassachusettsAmherstUSA
  2. 2.School of Business, Economics and LawUniversity of GothenburgGothenburgSweden
  3. 3.Department of Electrical and Computer EngineeringUniversity of MassachusettsAmherstUSA

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