Equilibrium Problems and Applications

Equilibrium Problems and Applications develops a unified variational approach to deal with single-valued, set-valued and quasi-variational equilibrium problems. The authors develop original results in relationship with classical contributions to the field of equilibrium problems. The content is mainly developed in the general setting of topological vector spaces and 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.

Presents a rigorous mathematical analysis of Nash equilibrium type problemsDevelops generic models relevant to mathematical economics and quantitative modeling of game theory, aiding economists to understand vital material without having to wade through complex proofsReveals a number of surprising interactions among various equilibria topics, enabling readers to identify a common and unified approach to analysis Illustrates the deep features shared by several types of nonlinear problems

1. Preliminaries and basic mathematical tools 2. An overview on equilibrium problems 3. Mathematical tools for solving equilibrium problems 4. Existence of solutions of equilibrium problems 5. Well-posedness for the equilibrium problems 6. Variational principles and variational analysis for the equilibrium problems 7. Applications to sensitivity of parametric equilibrium problems 8. Applications to Nash equilibrium 9. Applications to mathematical economics 10. Applications to variational inequalities and related topics 11. Regularization and numerical methods for equilibrium problems