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.
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机译：在这篇论文中，我从建模，定性分析和计算的角度考虑了静态和动态环境中网络平衡问题的各种新颖扩展。对于每个问题，我确定了网络结构，描述了所涉及的网络代理的行为，提出了公式，得出了平衡条件，建立了定性性质，并提出了适合的计算算法。提供了许多数值示例来说明所呈现的模型。首先，我提出了一个多层次的网络视角，用于在存在竞争的情况下概念化供应链背后的动力。多层次网络不是像单一的网络那样由纳格尼，东和张（2002）以及纳格尼等人（2002）提出的，后者提出了竞争下的供应链网络的静态模型，而是由以下组成： ，信息网络和财务网络。网络代理商又由位于需求市场的制造商，零售商和消费者组成。接下来，我研究了在静态环境下具有中介作用的金融网络均衡问题，并描述了不均衡动态。我考虑了一种经济，它由三种类型的代理组成：具有资金来源，中介的代理，以及位于与资金使用相对应的需求市场上的消费者。随后，我概括了建模框架，以整合电子交易对金融网络的影响。该建模框架既包含竞争也包含合作，并包括交易成本，这为金融中介的研究带来了更大程度的现实性。为了捕获决策者的风险态度对金融网络均衡的影响，我进一步开发了一种价值函数方法，其中，每个决策者的风险都受到可变权重的惩罚。这些模型和计算方法基于变分不等式理论的方法论，以研究静力学（参见Nagurney（1999））和预测动力学的动力学系统（参见Nagurney and Zhang（1996））。最后，本文对开发的建模框架进行了总结，并为将来可能的扩展提供了建议。
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