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E-raamat: Equilibrium Models and Variational Inequalities

(Kazan State University, Kazan, Russia)
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Equilibrium Models and Variational InequalitiesSuurem pilt
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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

Arvustused

"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

Preface v
Contents ix
List of Figures
xiii
Introduction
1(10)
I. MODELS
11(66)
Linear Models in Economics
15(14)
Open input-output model
16(4)
Generalizations
20(2)
Closed input-output model
22(7)
Linear Dynamic Models of an Economy
29(10)
Extended dynamic input-output model
29(2)
The von Neumann model of an expanding economy
31(8)
Optimization and Equilibria
39(12)
Linear programming problems
39(4)
Economic interpretation of optimality conditions
43(2)
Economic interpretation of the solution method
45(6)
Nonlinear Economic Equilibrium Models
51(18)
Cassel-Wald type economic equilibrium models
51(1)
General price equilibrium models
52(3)
Spatial price equilibrium models
55(5)
Imperfectly competitive equilibrium models
60(9)
Transportation and Migration Models
69(8)
Network equilibrium models
69(5)
Migration equilibrium models
74(3)
II. COMPLEMENTARITY PROBLEMS
77(50)
Complementarity with Z Properties
81(14)
Classes of complementarity problems
81(2)
Classes of square matrices and their properties
83(5)
Complementarity problems with Z cost mappings
88(7)
Applications
95(10)
Input-output models
95(3)
Price equilibrium models
98(3)
A pure trade market model
101(1)
Price oligopoly models
102(3)
Complementarity with P Properties
105(10)
Existence and uniqueness results
105(6)
Solution methods for CP's with P properties
111(4)
Applications
115(12)
Walrasian price equilibrium models
115(6)
Oligopolistic equilibrium models
121(6)
III. VARIATIONAL INEQUALITIES
127(102)
Theory of Variational Inequalities
131(18)
Variational inequalities and related problems
131(12)
Existence and uniqueness results
143(6)
Applications
149(14)
Cassel-Wald equilibrium models
149(1)
Walrasian equilibrium models and their modifications
150(7)
Existence results in Walrasian equilibrium models
157(2)
Imperfect competition models
159(1)
Network and migration equilibrium models
160(3)
Projection Type Methods
163(18)
The classical projection method
163(7)
The projection methods with linesearch
170(7)
Modifications and extensions
177(4)
Applications of the Projection Methods
181(10)
Applications to variational inequalities
181(3)
Applications to systems of variational inequalities
184(7)
Regularization Methods
191(6)
The classical regularization method and its modifications
191(2)
The proximal point method
193(4)
Direct Iterative Methods for Monotone Variational Inequalities
197(8)
Extrapolation methods
197(5)
The ellipsoid method
202(3)
Solutions to Exercises
205(24)
Bibliography 229(3)
Index 232


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