Equilibrium Problems and Applications

Gábor Kassay, Vicențiu Rădulescu

• Publisher: Academic Press
• Year: 2018
• Print ISBN: 9780128110294
• eBook ISBN: 9780128110300
• Topic: Economics
• Subtopic: Econometrics
• Index: Economics

Equilibrium Problems and Applications develops a unified variational approach to deal with single-valued, set-valued and quasi-equilibrium problems. The authors promote original results in relationship with classical contributions to the field of equilibrium problems. The content evolved in the general setting of topological vector spaces and it lies at the interplay between pure and applied nonlinear analysis, mathematical economics, and mathematical physics. This abstract approach is based on tools from various fields, including set-valued analysis, variational and hemivariational inequalities, fixed point theory, and optimization. Applications include models from mathematical economics, Nash equilibrium of non-cooperative games, and Browder variational inclusions. The content is self-contained and the book is mainly addressed to researchers in mathematics, economics and mathematical physics as well as to graduate students in applied nonlinear analysis. - A rigorous mathematical analysis of Nash equilibrium type problems, which play a central role to describe network traffic models, competition games or problems arising in experimental economics - Develops generic models relevant to mathematical economics and quantitative modeling of game theory, aiding economists to understand vital material without having to wade through complex proofs - Reveals a number of surprising interactions among various equilibria topics, enabling readers to identify a common and unified approach to analysing problem sets - Illustrates the deep features shared by several types of nonlinear problems, encouraging readers to develop further this unifying approach from other viewpoints into economic models in turn

Table of contents

• Cover image
• Title page
• Table of Contents
• Copyright
• Dedication
• About the Authors
• Preface
• Acknowledgments
• Chapter 1: Preliminaries and Basic Mathematical Tools
• Chapter 2: An Overview on Equilibrium Problems
• Chapter 3: Mathematical Tools for Solving Equilibrium Problems
• Chapter 4: Existence of Solutions of Equilibrium Problems
• Chapter 5: Well-Posedness for the Equilibrium Problems
• Chapter 6: Variational Principles and Variational Analysis for the Equilibrium Problems
• Chapter 7: Applications to Sensitivity of Parametric Equilibrium Problems
• Chapter 8: Applications to Nash Equilibrium
• Chapter 9: Applications to Mathematical Economics
• Chapter 10: Applications to Variational Inequalities and Related Topics
• Chapter 11: Regularization and Numerical Methods for Equilibrium Problems
• Appendix A: Ekeland Variational Principle
• Appendix B: Minimization Problems and Fixed Point Theorems
• Appendix C: Nonsmooth Clarke Theory and Generalized Derivatives
• Appendix D: Elements of Szulkin Critical Point Theory
• Bibliography
• Index