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

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 discretetime, 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.