Equilibrium Models and Variational Inequalities

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Overview

The concept of equilibrium plays a central role in various applied sciences, such as physics (especially, mechanics), economics, engineering, transportation, sociology, chemistry, biology and other fields. If one can formulate the equilibrium problem in the form of a mathematical model, solutions of the corresponding problem can be used for forecasting the future behavior of very complex systems and, also, for correcting the the current state of the system under control.

This book presents a unifying look on different equilibrium concepts in economics, including several models from related sciences.

- Presents a unifying look on different equilibrium concepts and also the present state of investigations in this field
- Describes static and dynamic input-output models, Walras, Cassel-Wald, spatial price, auction market, oligopolistic equilibrium models, transportation and migration equilibrium models
- Covers the basics of theory and solution methods both for the complementarity and variational inequality problems
- The methods are illustrated by applications and exercises to economic equilibrium models

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Editorial Reviews

From the Publisher

"By presenting a unifying view on equilibrium concepts in economics in an accessible and elegant way, this book fills an important gap in the xisting literature. It is recommended to researchers and graduate students working in theoretical aspects of mathematical equilibrium and/or applications to economic equilibrium models. However, a careful selection from the topics of the book together with necessary simplifications could also be used in an undergraduate course."--Mathematical Reviews

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Product Details

  • ISBN-13: 9780444530301
  • Publisher: Elsevier Science
  • Publication date: 3/1/2007
  • Series: Mathematics in Science and Engineering Series , #210
  • Edition description: New Edition
  • Pages: 252
  • Product dimensions: 0.63 (w) x 6.14 (h) x 9.21 (d)

Table of Contents

Preface
Contents
List of Figures
1. Introduction
Part I : Models
2. Linear Models in Economics
3. Linear Dynamic Models of an Economy
4. Optimization and Equilibria
5. Nonlinear Economic Equilibrium Models
6. Transportation and Migration Models
Part II : Complementarity Problems
7. Complementarity with Z Properties
8. Applications
9. Complementarity with P Properties
10. Applications
Part III: Variational Inequalities
11. Theory of Variational Inequalities
12. Applications
13. Projection Type Methods
14. Applications of the Projection Methods
15. Regularization Methods
16. Direct Iterative Methods for Monotone Variational Inequalities
17. Solutions to Exercises
Bibliography
Index
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