| Microeconomic equilibrium problems are intimately related to game theory, but the current state of knowledge for several types of microeconomic problems is limited. This dissertation rigorously addresses several of these problems from the standpoint of variational inequality theory. In addition to proving theoretical results about problem properties, important microeconomic implications are discussed when applicable. The individual chapters of this work focus on: (1) equilibrium existence for perfectly competitive capacity expansion problems with risk-averse players; (2) a comprehensive analysis of the application of Lemke's method to affine generalized Nash equilibrium problems; (3) the formulation and study of a unified power market model encompassing different microeconomic behavioral assumptions, capacity markets, emission permit auctions, and consumer surplus maximization; (4) an investigation of differential Nash games with mixed state-control constraints.;Although the presented results are applicable to a broad class of games that satisfy certain structural properties, electricity markets represent a key application area underlying several of the chapters and are specifically addressed in Chapter 4. As a whole, this dissertation should clearly illustrate how variational inequality theory can be used to analyze these applications and should provide the basis for the development of effective solution methodologies. It should also provide deeper insights into complex microeconomic games that cannot be described solely with demand and supply curves. Suggestions for additional research are provided at the end of each chapter to motivate future work in the respective domains. |
