Computational Methods for Equilibrium Problems with Micro-Level Data

University Of Maryland, College Park, College Park MD

Investigators

Abstract

The objective of this work is to examine systems with micro-level data for which an equilibrium of some sort is to be reached. One important example is the Gas Systems Analysis Model (GSAM), a modular, reservoir-based model of the North American natural gas system developed for the U. S. Department of Energy. In its current form, GSAM is a large-scale nonlinear program that computes estimates of market equilibrium prices, quantities, flows, and other values based on the notion of maximizing total surplus less transportation costs. Unlike the classical approach in which supply curves are known in closed form, GSAM builds supply curves from the "bottom up" using a data base of over 17,000 natural gas reservoirs taking into account both the interregional as well as intertemporal interdependence of these curves. While this "bottom up" feature provides a good deal of realism, it renders the equilibrium computations much more difficult due to the lack of closed form supply curves. The proposed work has two main objectives. First, analyze the GSAM market equilibrium problem more generally by noting the functional relationships between seasonal market prices (Lagrange multipliers) and demand for gas, storage activity levels, investment decisions, etc. using the variational inequality problem (VIP) and nonlinear complementarity problem (NCP) formats. The second main task is to develop efficient methods to reach a solution to GSAM-type problems exploiting the particular problem structure. Iterative methods from optimization and equation solving is used to develop appropriate algorithms for this task. Due to recent advances in information technology, it is now possible to model the activities of individual agents in rather complicated systems. Examples of applications in scientific and engineering settings using micro-level data abound. While simulations of these systems can be rather elaborate using for example, complicated "if-then" type rules, determining equilibrium behavior of the system in a rigorous manner can be challenging. Part of the difficulty is due to a lack of closed form expressions for describing the system. The proposed work will examine one such system in its general form and develop both a theory for equilibrium as well as efficient mathematical algorithms to compute such a solution. The anticipated impact of this work is to greatly advance the state of the art in solving large-scale equilibrium problems that use micro-level data for modeling the economic behavior of individual agents. This is significant since many similar systems are now modeled that contain no closed form expressions for key elements but for which an equilibrium solution is desirable.