2013

Dissertation

Ph.D.

#### Degree Granting Department

Mathematics and Statistics

#### Keywords

Adaptive Expectation, Agent-Based Modeling Simulation, Local Network Externality, Principle of Network Externality

#### Abstract

The network externality function plays a very important role in the study of economic network industries. Moreover, the consumer group dynamic interactions coupled with network externality concept is going to play a dominant role in the network goods in the 21st century. The existing literature is stemmed on a choice of externality function with certain quantitative properties. The utility function coupled with the network externality function is used to investigate static properties of rational equilibrium. The aim of this work is to systematically initiate a development of quantitative effects of the concept of network externality and its influence on the characteristics of network market equilibrium.

We introduce several basic concepts, notably, network externality process and network goods. Formulating a principle of network externality, we developed a mathematical dynamic model (1) for the network externality process. A closed form solution of the mathematical model was determined and analyzed (2). The presented qualitative and quantitative analysis provides a systematic and unified way of constructing the existing network externality function. The solution process is called "Generalized Network Externality Function (GNEF)". Moreover, our study of quantitative description, parametric representation of attributes and sensitivity analysis of network externality process provides a tool for planning, policy and performance for network goods (3).

In the absence of desired data set, we presented an illustration to exhibit the significance of GNEF. We used two types of data sets on the US banking asset and deposit. Employing nonlinear regression methods and data sets, we developed statistical models for the US banking asset and deposit, and constructed two normalized the US banking deposit models (4). Finally, using the concept of theory of relative growth and GNEF (4), we developed two dynamic models for the network externality for the US banking asset with respect to the US banking deposit as a financial market share (5).

Incorporating the GNEF (2) in the consumer utility function, a concept of market share adjustment function is introduced and utilized to develop dynamic models for existing rational and static expectation processes (6). In fact, the role and scope of dynamic models of market share adjustment process are extended to the well-known adaptive expectation and its extension process (7). Using a fixed point theorem and the method of upper and lower solutions of discrete time processes, the existence of equilibrium states of developed dynamic models of market share adjustment processes are established in a systematic way (8). Furthermore, the qualitative properties (stability and oscillatory) of equilibrium states are investigated in terms of model and speed of adjustment parameters. Moreover, the system parameter space is decomposed according to qualitative properties (stability, instability and oscillatory) and the type of expectation processes.

Very recently, the idea of local network externality is utilized to characterize the rational equilibrium (under fulfilled expectation assumptions). From the study on two-scale network dynamic model of human mobility process an eco-socio-culture interactions, we note that heterogeneity in the network goods consumer community generates a local network externality. Furthermore, dynamic models of adaptive expectation processes (6,7) for network goods provide tool to extend the characterization of rational equilibrium study to static, current and lagged adaptive types equilibriums. Here, we treat the consumer decision to be a dynamic process. We formulate a dynamic structural representation of a consumer network structure, structure of utility function and decision rule under the influence of local network externality concept (9). For the consumer network structure, we generalize the one-dimensional Hotelling location line model to multi-dimensional location (10). This formulation generates a mathematical model for a consumer decision dynamic process (11). The byproduct of the dynamic model leads to an agent-based simulation model (12). The simulation model is employed to investigate different types of consumer decision dynamic market equilibriums. Moreover, prototype illustrations are given to exhibit the association between network attributes and its market equilibriums.

We extend the work of two firms (duopoly) into multi-firms (oligopoly and monopolistic competition). This work shed light on the policies for manager to meet performance goal of their firm in network goods industry.

In future, we propose to extend this work to incorporate random fluctuations, to remove restrictions and the local and global economic framework in the 21st century.

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