| In this dissertation, I considered various novel extensions of network equilibrium problems both in static and in dynamic settings from modeling, qualitative analysis, and computational perspectives. For each problem, I identified the network structure, described the behavior of the network agents involved, presented the formulations, derived the equilibrium conditions, established the qualitative properties, and proposed the appropriate algorithm for computations. A variety of numerical examples were provided for illustration of the models presented.; First, I proposed a multilevel network perspective for the conceptualization of the dynamics underlying supply chains in the presence of competition. Rather than being formulated over a single network, as was done by Nagurney, Dong, and Zhang (2002) and Nagurney et al (2002), who proposed static models of supply chain networks under competition, the multilevel network consisted of: the logistical network, the informational network, and the financial network. The network agents, in turn, consisted of the manufacturers, the retailers, and the consumers located at the demand markets.; Next, I studied financial network equilibrium problems with intermediation in a static setting and described the disequilibrium dynamics as well. I considered an economy consisting of three types of agents: those with sources of funds, intermediaries, and the consumers located at demand markets corresponding to the uses of funds. Subsequently, I generalized the modeling framework to incorporate the impact of electronic transactions on the financial networks with intermediation. The modeling framework captured both competition and cooperation, and included transaction costs which brought a greater degree of realism to the study of financial intermediation. In order to capture the influence of the decision-makers' risk attitudes upon the financial network equilibrium, I further developed a value function approach in which the risk for each decision-maker was penalized by a variable weight.; The models and computational methods were based on the methodologies of variational inequality theory for the study of the statics (cf. Nagurney (1999)) and projected dynamical systems for the dynamics (cf. Nagurney and Zhang (1996)).; I concluded this dissertation with a summary of the modeling framework developed and provided suggestions for possible future extensions. |
