This dissertation consists of seven chapters. An overview of the motivation for, contributions, and background literature to the research that I have conducted is provided in Chapter 1. Chapter 2 provides a thorough review of the methodologies, foundational models and theories, including variational inequality theory and Projected Dynamical Systems (PDS) theory, that this research is based on.
In Chapter 3 of the dissertation, according to the discussion of Section 1.3, I consider an Internet with a service-oriented architecture, in which content and network providers interact and compete in prices and quality of services. There are two models, a basic model and a general one. The methodology is inspired, for the first model, by Altman, Legout, and Xu (2011) and, for the second model, by El Azouzi, Altman, and Wynter (2003). Altman, Legout, and Xu (2011) studied the effect of side payments, while taking into account the different levels of quality offered by a network provider in the Internet with one content provider, one network provider, and one demand market.
With a basic model, I complete Altman, Legout, and Xu (2011)’s model by including the quality of both providers into the demand function and assuming a production cost function for the content provider. El Azouzi, Altman, and Wynter (2003) modeled an oligopoly market of content providers and one network provider in a bi-criteria Nash equilibrium competition between content providers. Their model restricts the network to one network provider and quality for only the content providers’ service. Therefore, it cannot reveal the competition among the network providers for users. In contrast, my model overcomes these limitations by including multiple providers, multiple users (demand markets), and demands as a function of the prices and quality levels of all
providers. On top of that, this model presents a general framework for modeling alternative cost functions and demand functions associated with the services and the demand markets. This chapter is based on Saberi, Nagurney, and Wolf (2014).
I develop a projected dynamical system model of a service-oriented Internet in Chapter 4. Such dynamical systems were introduced by Dupuis and Nagurney (1993) and have been used in a variety of applications from transportation, spatial economic and oligopolistic market problems (see Nagurney and Zhang (1996), Nagurney (1999), and the references therein) to supply chain network problems (cf. Nagurney (2006a), Nagurney, Cruz, and Toyasaki (2008), and Cruz (2008)) and finance (see Nagurney (2008)). In addition, PDSs have been applied in population games by Sandholm (2010) and in neuroscience by Girad et al. (2008). More recently, PDSs have been utilized to capture the dynamics of oligopolistic competition with the inclusion of quality (see Nagurney and Li (2014a)) and to model the dynamics of a service-oriented Internet with only quality associated with content provision by Nagurney et al. (2013a), and also to capture that associated with network provision by Nagurney and Wolf (2014).
Here, for the first time, I model the dynamics of both price and quality competition of both content providers and of network providers. This work is an attempt to complete both the latter models in terms of price setting while considering quality of service for both content and network provision. The continuous-time dynamic model that I propose describes the evolution of prices charged by the content providers and the network providers, as well as their quality levels of content and network transport provision, respectively. I provide qualitative results, including stability analysis, and also present a discrete-time algorithm for iterative computation and tracking of the prices and quality levels until a stationary point, equivalent to an equilibrium state is achieved. This work extends and completes the static Internet network economic model of Saberi, Nagurney, and Wolf (2014) by describing the underlying dynamic
behavior, accompanied by qualitative analysis, and with the provision of additional numerical examples. This chapter is based on Nagurney et al. (2014a).
In Chapter 5 of the dissertation, I formulate a competitive oligopoly market of Internet network providers, motivated by ChoiceNet (cf. Wolf et al. (2012) and Wolf et al. (2014)), although not limited to it, and the economic relationships among them. The entities are able to offer different network services and to create contracts for their users according to the users’ desires and needs. The model developed in this chapter is straightforward enough to understand for both users and network providers and creates an opportunity to control the total charge for a communication by a modification of the parameters. The users/demand markets select contracts based on three main criteria: the amount of usage contracted per period of time (the usage rate) during the contract duration, the quality level of service, and the contract duration. Here I consider a reserved usage amount per unit of time. The earlier work on the network economic game theoretical modeling of future Internet architectures focused on introducing quality, with an emphasis on service provision, which is maintained through network transport/provision in Nagurney et al. (2013a), and also on capturing the behavior of both content providers and network providers, with the latter competing on price and quality in Nagurney and Wolf (2014). In Nagurney et al. (2014a), the dynamics are associated with content and network provider competition where consumers respond to the prices and the quality of both content provision and network provision. Here, in contrast, my goal is to extend the game theoretical modeling of competitive network providers and services by including not only quality of service but also contract durations as strategic variables, in addition to the reserved usage rates. This chapter is based on Nagurney et al. (2015b).
In Chapter 6, I focus on the development of game theory models in both equilibrium and dynamic settings for a supply chain network with multiple manufacturers and
multiple freight service providers handling freight transportation. The decision-makers including manufacturers and freight service providers at each echelon are competing in both prices and quality. Quality of the product is traced along the supply chain with consumers differentiating among the products offered by manufacturers.
Also, quality of freight service shipment is accounted for in the model. Heretofore, the integration of price and quality competitive behavior with both manufacturers and freight service providers has not been examined in a rigorous theoretical and computationally tractable framework. This framework is inspired, in part, by the work of Nagurney et al. (2013a) and Saberi, Nagurney, and Wolf (2014). The former studied a network economic game theory model of a service-oriented Internet with choices and quality competition. In addition, Saberi, Nagurney, and Wolf (2014) proposed a network economic game theory model of service-oriented Internet architectures with price and quality competition between content and network providers. Here, I allow for multiple modes of transportation and each freight service provider can have a different number of mode options. I consider a mode in a general way in that it can correspond to intermodal transportation. This chapter is based on Nagurney et al.
(2015a).
Finally, Chapter 7 summarizes the obtained results and presents the conclusions.
Suggestions and directions for future research are also presented.
CHAPTER 2
METHODOLOGIES
This chapter provides an overview of some of the fundamental theories and methodologies that are utilized in this dissertation. I first recall variational inequality theory, which is utilized throughout this dissertation as the basic methodology, and is applied in Chapters 3 to 6. Variational inequality theory is a powerful methodology that can be applied to numerous problems to solve network economic equilibrium models and is applied in this dissertation to analyze the equilibria of price and quality competition in the Internet and in supply chain networks.
After the review of variational inequality theory, I present projected dynamical systems theory, which is used in Chapters 4 and 6, to analyze the associated dynamics.
Following that, I discuss the relationships between variational inequalities and game theory as well as the qualitative properties of the variational inequality model of Nash equilibrium. Finally, I recall the Euler method, which is induced by the general iterative scheme of Dupuis and Nagurney (1993) and employed in this dissertation to solve variational inequalities and projected dynamical systems. It is a computational algorithm and provides discrete-time realizations of the continuous-time adjustment processes associated with projected dynamical systems.
Further details and proofs of theorems concerning variational inequalities and projected dynamical systems can be found in Nagurney (1999), Dupuis and Nagurney (1993), and Nagurney and Zhang (1996).