Variational Inequality Theory

Abstract

Equilibrium is a concept central to the analysis of economic phenomena. Methodologies that have been applied to the formulation, qualitative analysis, and computation of economic equilibria have included systems of equations, optimization theory, complementarity theory, as well as fixed point theory. In this chapter the foundations for the theory of variational inequalities are established and the relationship of this methodology to other existing equilibrium analysis tools identified. Variational inequality theory will be utilized throughout the book as the fundamental methodology in synthesizing network economic equilibrium models operating under a spectrum of behavioral mechanisms and ranging from spatial price equilibrium problems and imperfectly competitive oligopolistic market equilibrium problems to general financial equilibrium problems.