Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Altman E, Rojas J, Wong S, Hanawal MK, Xu Y (2011) Proceedings of the ICST conference on game theory for networks, Shanghai
Bertrand J (1883) Theorie mathematique de la richesse sociale. Journal des Savants 67:499–508
Cournot AA (1838) Researches into the mathematical principles of the theory of wealth, English translation. MacMillan, London
Cruz JM (2008) Dynamics of supply chain networks with corporate social responsibility through integrated environmental decision-making. Eur J Oper Res 184:1005–1031
Dafermos S, Nagurney A (1987) Oligopolistic and competitive behavior of spatially separated markets. Reg Sci Urban Econ 17:245–254
Dupuis P, Nagurney A (1993) Dynamical systems and variational inequalities. Ann Oper Res 44:9–42
Dyaberi JM, Parsons B, Pai VS, Kannan K, Chen Y-FR, Jana R, Stern D, Varshavsky A (2012) Managing cellular congestion using incentives. IEEE Communications Magazine, pp 100–107
Gabay D, Moulin H (1980) On the uniqueness and stability of Nash equilibria in noncooperative games. In: Bensoussan A, Kleindorfer P, Tapiero CS (eds) Applied stochastic control of econometrics and management science. North-Holland, Amsterdam
Ha S, Sen S, Joe-Wong C, Im Y, Chiang N (2012) Tube: time-dependent pricing for mobile data. In: Proceedings of the ACM SIGCOMM 2012 conference on applications, technologies, architectures, and protocols for computer communication, SIGCOMM ’12. ACM, Helsinki, pp 247–258
He L, Walrand J (2005) Pricing differentiated internet services. In: Proceedings of INFOCOM, pp 195–204
Kausar N, Briscoe B, Crowcroft J (1999) A charging model for sessions on the internet. In: Leopold H, Garcia N (eds) European conference on multimedia applications, services and techniques (ECMAST’99), Lecture Notes in Computer Science. vol 1629. Springer, Berlin, pp 246–261
Kelly FP (1997) Charging and rate control for elastic traffic. Eur Trans Telecommun 8:33–37
Lv Q, Rouskas GN (2010) An economic model for pricing tiered network services. Ann Telecommun 65:147–161
MacKie-Mason J, Varian H (1995) Pricing the Internet—progress and misconceptions. In: Kahin B, Keller J (eds) Access to the Internet. MIT Press, Cambridge, pp 269–314
McKnight LW, Bailey JP (eds) (1997) Internet economics. MIT Press, Cambridge
Nagurney A (1999) Network economics: a variational inequality approach second and revised edition. Kluwer Academic Publishers, Boston
Nagurney A (2006) Supply chain network economics: dynamics of prices, flows, and profits. Edward Elgar Publishing, Cheltenham
Nagurney A (2010) Formulation and analysis of horizontal mergers among oligopolistic firms with insights into the merger paradox: a supply chain network perspective. Comput Manage Sci 7:377–410
Nagurney A, Dupuis P, Zhang D (1994) A dynamical systems approach for network oligopolies and variational inequalities. Ann Reg Sci 28:263–283
Nagurney A, Ke K, Cruz J, Hancock K, Southworth F (2002) Dynamics of supply chains: a multilevel (logistical/informational/ financial) network perspective. Environ Plan B 29:795–818
Nagurney A, Li D (2013) A dynamic network oligopoly model with transportation costs, product differentiation, and quality competition. Comput Econ (in press)
Nagurney A, Takayama T, Zhang D (1995) Massively parallel computation of spatial price equilibrium problems as dynamical systems. J Econ Dyn Control 18:3–37
Nagurney A, Wolf T, Li D, Saberi S (2013) A network economic game theory model of a service-oriented Internet with choices and quality competition. Netnomics (in press)
Nagurney A, Zhang D (1996) Projected dynamical systems and variational inequalities with applications. Kluwer Academic Publishers, Boston
Nash JF (1950) Equilibrium points in n-person games. Proc Natl Acad Sci USA 36:48–49
Nash JF (1951) Noncooperative games. Ann Math 54:286–298
Neely MJ (2007) Optimal pricing in a free market wireless network. In: Proceedings of IEEE INFOCOM
Njoroge P, Ozdaglar A, Stier N, Weintraub G (2009) Competition, market coverage, and quality choice in interconnected platforms. In: Proceedings of NetEcon09, Stanford
Odlyzko A (1999) Paris metro pricing for the Internet. In: Proceedings of the ACM conference on electronic commerce (EC’99), AM, pp 140–147
Ros D, Tuffin B (2004) A mathematical model of the Paris metro pricing scheme for charging packet networks. Comput Netw 46(1):73–85
Sen S, Joe-Wong C, Ha S, Chiang M (2012) Incentivizing time-shifting of data: a survey of time-dependent pricing for Internet access. IEEE Commun 50(11):91–99
Shakkottai S, Srikant R (2006) Economics of network pricing with multiple ISPs. IEEE/ACM Trans Netw 16(6):1233–1259
Shen H, Basar T (2007) Optimal nonlinear pricing for a monopolistic service provider with complete and incomplete information. IEEE ISAC 25(6):1216–1223
Varian H (1996) Economic issues facing the Internet. http://people.ischool.berkeley.edu/hal/Papers/econ-issues-internet.html
Varian HR (2001) The demand for bandwidth: evidence from the index project. In: Crandall RW, Alleman JH (eds) Broadband: should we regulate high-speed Internet access?. Aei-Brookings Joint Center for Regulatory Studies, American Enterprise Institute, Washington, DC, pp 39–56
Wolf T, Griffioen J, Calvert K, Dutta R, Rouskas G, Baldine I, Nagurney A (2012) Choice as a principle in network architecture. In: Proceedings of ACM SIGCOMM, Helsinki
Zhang Z-L, Nabipay P, Odlyzko A, Guerin R (2010) Mini-conference proceedings, San Diego
Zhang D, Nagurney A (1995) On the stability of projected dynamical systems. J Optim Theory Appl 85:97–124
Acknowledgments
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.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Nagurney, A., Wolf, T. A Cournot–Nash–Bertrand game theory model of a service-oriented Internet with price and quality competition among network transport providers. Comput Manag Sci 11, 475–502 (2014). https://doi.org/10.1007/s10287-013-0183-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10287-013-0183-5