zbMATH — the first resource for mathematics

Network economics: a variational inequality approach. (English) Zbl 0873.90015
Advances in Computational Economics. 1. Dordrecht: Kluwer Academic Publishers. xxi, 326 p. (1993).
The subject is captured by the book’s title, “Network Economics: A variational inequality approach.” It is accurately and clearly written. Its statement of focus is an example: “Physical networks are pervasive in today’s society, be they in the form of transportation networks, telecommunication networks, energy pipelines, electric power networks, etc. Mathematical networks, on the other hand, may be used to represent not only physical networks but also interactions among economic agents. \(\ldots\) The identification of the network underlying an economic problem provides an added dimension to the analysis and computation of equilibria. For example, not only can the complexity of problems be more readily grasped through a graphical depiction, but issues of structural change and policy interventions may be addressed through modifications of the network.”
The book is successful in demonstrating these relationships and applications of network analysis. Based on a unified principle of analysis, it is an excellent text for students with a certain level of mathematical sophistication (good courses in matrix algebra and multivariate real analysis), whether in a lecture course or for self-study. The necessary tools of analysis, both variational analysis and the most common computational algorithms, are reviewed in the first two chapters. The remainder of the book contains a selection of self-contained applications of network analysis to a number of economic equilibrium problems.
These cover a broad range of economic problems: partial equilibrium analysis of perfect competition (spatial price equilibrium, traffic network equilibrium, and migration equilibrium); partial equilibrium analysis of imperfect competition (classical and spatial oligopoly models); general equilibrium analysis (Walrasian models, and financial models); and estimation (constrained matrices, and financial flow-of-funds problems). Each chapter (each of the topics in parentheses above corresponds to a chapter) contains detailed discussion of the computation of solutions to the problem, and several describe computational experience (in terms of computational resources required) for realistic problems. Examples of computation solutions are given, but not with realistic problems.
The book’s only weakness is the lack of a software and databank ‘companion’ to provide examples of realistic problems that the reader could load onto a computer and work out. One would expect that most lecturers in the field would have their own research to draw realistic examples from, but a data/software companion would be helpful for self-study.

91B50 General equilibrium theory
91B52 Special types of economic equilibria
90C90 Applications of mathematical programming
90-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to operations research and mathematical programming