A network economic game theory model of a service-oriented internet with choices and quality competition

  • Anna Nagurney
  • Dong Li
  • Tilman Wolf
  • Sara Saberi


This paper develops a new dynamic network economic model of Cournot-Nash competition for a service-oriented Internet in the case of service differentiation and quality competition. Each service provider seeks to maximize its own profit by determining its service volumes and service quality. We utilize variational inequality theory for the formulation of the governing Nash equilibrium as well as for the computational approach. We then construct the projected dynamical systems model, which provides a continuous-time evolution of the service providers service volumes and service quality levels, and whose set of stationary points coincides with the set of solutions to the variational inequality problem. We recall stability analysis results using a monotonicity approach and construct a discrete-time version of the continuous-time adjustment process, which yields an algorithm, with closed form expressions at each iteration. The algorithm is then utilized to compute the solutions to several numerical examples. A sensitivity analysis is also conducted.


Game theory Service differentiation Quality competition Service-oriented internet Variational inequalities Projected dynamical systems 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Arrow, K., & Hurwicz, L. (1977). Studies in resource allocation processes. New York: Cambridge University Press.CrossRefGoogle Scholar
  2. 2.
    Baake, P., & Wichmann, T. (1999). On the economics of internet peering. Netnomics, 1(1), 89–105.CrossRefGoogle Scholar
  3. 3.
    Cerf, V.G., & Kahn, R.E. (1974). A protocol for packet network intercommunication. IEEE Transactions on Communications, COM-22(5), 637–648.CrossRefGoogle Scholar
  4. 4.
    Clark, D.D. (1988). The design philosophy of the DARPA Internet protocols. In Proceedings of ACM annual conference of the special interest group on data communication (SIGCOMM) (pp. 106–114). Stanford, CA.Google Scholar
  5. 5.
    Dafermos, S., & Nagurney, A. (1987). Oligopolistic and competitive behavior of spatially separated markets. Regional Science and Urban Economics, 17, 245–254.CrossRefGoogle Scholar
  6. 6.
    Dupuis, P., & Nagurney, A. (1993). Dynamical systems and variational inequalities. Annals of Operations Research, 44, 9–42.CrossRefGoogle Scholar
  7. 7.
    Faulhaber, G.R., & Hogendorn, C. (2000). The market structure of broadband telecommunications. The Journal of Industrial Economics, 48(3), 305–329.Google Scholar
  8. 8.
    Fox, A., Gribble, S.D., Chawathe, Y., Brewer, E.A., Gauthier, P. (1997). Cluster-based scalable network services. In ACM SIGOPS operating systems review (Vol. 31, pp. 7891). ACM.Google Scholar
  9. 9.
    Gabay, D., & Moulin, H. (1980). On the uniqueness and stability of Nash equilibria in noncooperative games. In Applied stochastic control of econometrics and management science. North-Holland, Amsterdam, The Netherlands.Google Scholar
  10. 10.
    Gibbons, R., Mason, R., Steinberg, R. (2000). Internet service classes under competition. IEEE Journal on Selected Areas in Communications, 18(12), 2490–2498.CrossRefGoogle Scholar
  11. 11.
    McKnight, L., & Bailey, J. (1997). Internet economics: when constituencies collide in cyberspace. Internet Computing, IEEE, 1(6), 30–37.CrossRefGoogle Scholar
  12. 12.
    Nagurney, A. (1999). Network economics: a variational inequality approach second and revised editon. Boston, Massachusetts: Kluwer Academic Publishers.Google Scholar
  13. 13.
    Nagurney, A. (2010). Supply chain network design under profit maximization and oligopolistic competition. Transportation Research E, 46, 281–294.CrossRefGoogle Scholar
  14. 14.
    Nagurney, A., Dupuis, P., Zhang D. (1994). A dynamical systems approach for network oligopolies and variational inequalities. Annals of Regional Science, 28, 263–283.CrossRefGoogle Scholar
  15. 15.
    Nagurney, A., & Yu, M. (2012). Sustainable fashion supply chain management under oligopolistic competition and brand differentiation. International Journal of Production Economics, 135, 532–540.CrossRefGoogle Scholar
  16. 16.
    Nagurney, A., Yu, M., Qiang, Q. (2011). Supply chain network design for critical needs with outsourcing. Papers in Regional Science, 90, 123–142.CrossRefGoogle Scholar
  17. 17.
    Nagurney, A., & Zhang, D. (1996). Projected dynamical systems and variational inequalities with applications. Boston, Massachusetts: Kluwer Academic publishers.CrossRefGoogle Scholar
  18. 18.
    Nash, J. (1950). Equilibrium points in n-person games. In Proceedings of the national academy of sciences, USA (Vol. 36, pp. 48–49).Google Scholar
  19. 19.
    Nash, J. (1951). Noncooperative games. Annals of Mathematics, 54, 286–298.CrossRefGoogle Scholar
  20. 20.
    Niyato, D., & Hossain, E. (2006). WLC04-5: bandwidth allocation in 4G heterogeneous wireless access networks: a noncooperative game theoretical approach. In Proceedings of IEEE global telecommunications conference (pp. 1–5). San Francisco, California, USA.Google Scholar
  21. 21.
    Njoroge, P., Ozdaglar, A., Stier, N., Weintraub, G. (2009). Competition, market coverage, and quality choice in interconnected platforms. In Proceedings of NetEcon09. Stanford, CA.Google Scholar
  22. 22.
    Njoroge, P., Ozdaglar, A., Stier, N., Weintraub, G. (2010). Weintraub. Investment in two sided markets and the net neutrality debate. Columbia University, Decision, Risk and Operations Working Papers Series, Tech. Rep. DRO-2010-05.Google Scholar
  23. 23.
    Okuguchi, K., & Szidarovszky, F. (1990). The theory of oligopoly with multi-product firms. In Lecture notes in economics and mathematical systems (p. 342). Berlin, Germany: Springer-Verlag.Google Scholar
  24. 24.
    Parzy, M., & Bogucka, H. (2010). QoS support in radio resource sharing with Cournot competition. In Proceedings of 2nd international workshop on cognitive information processing (pp. 93–98). Elba Island, Italy.Google Scholar
  25. 25.
    Postel, J. (1981a). Internet Protocol. RFC 791, Information Sciences Institute.Google Scholar
  26. 26.
    Postel, J. (1981b). Transmission Control Protocol. RFC 793, Information Sciences Institute.Google Scholar
  27. 27.
    Radonjic, V., Acimovic-Raspopovic, V., Kostic-Ljubisavljevic, A. (2011). Quality of experience in Cournot competition model for pricing next generation networks. In Proceedings of 5th international quality conference (pp. 363–370). Kragujevac, Serbia: University of Kragujevac.Google Scholar
  28. 28.
    Semret, N., Liao, R.F., Campbell, A.T., Lazar, A.A. (2000). Pricing, provisioning and peering: dynamic markets for differentiated internet services and implications for network interconnections. Selected Areas in Communications, IEEE Journal on, 18(12), 2499–2513.CrossRefGoogle Scholar
  29. 29.
    Shetty, N., Schwartz, G., Walrand, J. (2010). Internet QoS and regulations. IEEE/ACM Transactions on Networking, 18(6), 1725–1737.CrossRefGoogle Scholar
  30. 30.
    van Moorsel, A. (2001). Metrics for the internet age: quality of experience and quality of business.Google Scholar
  31. 31.
    Varian, H.R. (1996). Economic issues facing the Internet. Accessed 25 December 2012.
  32. 32.
    Vives, X. (1999). Oligopoly pricing: old ideas and new tools. Cambridge, Massachusetts: MIT Press.Google Scholar
  33. 33.
    Wolf, T. (2010). In-network services for customization in next generation networks. IEEE Network, 24(4), 6–12.CrossRefGoogle Scholar
  34. 34.
    Wolf, T., Grifoen, J., Calvert, K., Dutta, R., Rouskas, G., Baldine, I., Nagurney, A. (2012). Choice as a principle in network architecture. In SIGCOMM12. Helsinki, Finland.Google Scholar
  35. 35.
    Zhang, Z., Nabipay, P., Odlyzko, A., Gurin, R.A. (2010). Interactions, competition and innovation in a service-oriented internet: an economic model. In IEEE INFOCOM 2010 mini-conference (pp. 46–50). San Diego, CA.Google Scholar
  36. 36.
    Zhang, D., & Nagurney, A. (1995). On the stability of projected dynamical systems. Journal of Optimization Theory and its Applications, 85, 97–124.CrossRefGoogle Scholar
  37. 37.
    Zhang, K., Wang, Y., Shi, C., Wang, T., Feng, Z. (2011). A non-cooperative game approach for bandwidth allocation in heterogeneous wireless networks. In Proceedings of IEEE vehicular technology conference (pp. 1–5). San Francisco, California, USA.Google Scholar

Copyright information

© Springer Science+Business Media New York 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
  4. 4.IMDEA NetworksMadridSpain

Personalised recommendations