Course:

Network Economics

Professor Anna Nagurney
John F. Smith Memorial Professor
Isenberg School of Management
University of Massachusetts
Amherst, MA 01003
nagurney@gbfin.umass.edu

This course introduces and develops the concept of network economics as a powerful tool for decision-making today. It provides the foundations of networks both as an intuitive tool and graphical medium as well as a rigorous methodological one for the formulation, qualitative analysis, and computation of solutions to economic equilibrium problems. Hence, it considers both physical networks such as transportation networks, whose structure maps into nodes, links, and flows, and abstract networks, whose network mapping is not intuitively obvious.

The course traces the history of networks in the global economy and demonstrates how a variety of economic problems are concerned with flows over space and time where the flows may be of commodities, humans, money, and/or informational. It provides the basic theory of networks and overviews the fundamental theory of mathematical programming, specifically, optimization theory and variational inequality theory, to enable the formulation and solution of the network problems. The course also surveys effective computational algorithms which take advantage of the underlying network structure of the problems.

The course then describes specific applications which underly the network economy including traffic network and spatial price equilibrium problems. Other applications include: oligopolistic market equilibrium problems, migration equilibrium problems, financial equilibrium problems as well as knowledge and environmental networks. A variety of policy instruments, along with their ramifications are explored in these contexts. The course provides a solid introduction to the subject.

More advanced topics are subsequently studied which focus on network economics in today's Information Age. These include: multicriteria decision-making with applications to teleshopping and telecommuting as well as supply chain networks with electronic commerce.

This course is taught in lecture format with many additional examples given in class as well as time for discussion. Textbook: Network Economics: A Variational Inequality Approach, 1999, revised and second edition, Anna Nagurney, Kluwer Academic Publishers, Boston, Massachusetts. The textbook, as well as additional reading materials, will be made available to the students through the appropriate library. Professor Nagurney's new book, Supernetworks: Decision-Making for the Information Age, 2002, co-authored with June Dong, Edward Elgar Publishers, Cheltenham, England, will also be made available for coverage of the advanced course topics.

OUTLINE OF LECTURES (Note that some of the background material will be interspersed throughout the lectures as needed by the specific applications.) Hence, below are topics that will be covered, but not necessarily in the order given. For example, much of the theoretical material in topics 2, 3, and 4 below will be incorporated into the subsequent topical lectures. Also, a topic may requre several class sessions for appropriate coverage of the material.

The formal lectures are posted on the web: http://supernet.som.umass.edu and can be downloaded from that site by scrolling to "Fulbright Lectures."

LECTURE TOPICS

1. Introduction

Overview of Network Economics, its History, and its Importance in Economics Today

Basics of Nonlinear Programming Theory
Basics of Network Theory

Basic Qualitative Theory
Relationship to Optimization Problems and Other Classical
Mathematical Programming Problems
Sensitivity Analysis

The General Iterative Scheme - Projection and Relaxation Methods
The Modified Projection Method
Decomposition Methods - Serial and Parallel

Introduction and History
The Standard Model
The Extended Model
Multimodal Models
The Elastic Demand Model

The Classical Model
Asymmetric and Multicommodity Models
Models with Policy Interventions
Relationship Between Traffic Network and Spatial Price Equilibrium

Nash Equilibrium
The Classical Model
Spatial Models
Relationship to Spatial Price Equilibrium

Overview of Environmental Issues and Policies
Spatial Oligopoly with Permits
Qualitative Properties

Conceptualization and History
Basic Models

The Costless Model
Model with Migration Costs
Model with Class Transformations

Walrasian Price Equilibrium
Network Equilibrium Equivalence
Sensitivity Analysis

Portfolio Optimization as a Network Flow Problem
Multi-Sector, Multi-Instrument Financial Equilibrium
Policy Interventions

Multicriteria Decision-Making on Networks
Equilibrium Concepts
Application to Teleshopping and Telecommuting Decision-Making

Extension of Multicriteria Decision-Making to Decision-Making Over Space and Over Time
Application to Telecomuting versus Commuting Decision-Making

Introduction to Supply Chains and Network Agents
Electronic Commerce: B2B and B2C
Network Equilibrium
Applications and Extensions