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
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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
Gábor Kassay received his Ph.D. thesis at the Babes-Bolyai University in Cluj-Napoca, Romania, under the supervision of József Kolumbán in 1994. He is a Professor in Mathematics at the same University, with more than 75 published research papers, several books and book-chapters in the larger area of nonlinear analysis, and more than 1500 citations. Gábor Kassay delivered many invited and plenary talks, was session organizer and guest of honor at prestigious international conferences. He has more than 35 coauthors and collaborators from all over the world. He is currently the supervisor of the Research Group of Analysis and Optimization accredited by the Faculty of Mathematics and Computer Science of the Babes-Bolyai University. Between 2002 and 2004 he was an associate professor of Eastern Mediterranean University in Famagusta, Cyprus.
Vicen?iu D. Radulescu received his Ph.D. at the Université Pierre et Marie Curie (Paris 6) in 1995 under the supervision of Haim Brezis. In 2003 he defended his Habilitation Mémoire at the same university. Radulescu is Professor at the AGH University of Science and Technology in Kraków, Leading Senior Researcher at the Institute of Mathematics, Physics and Mechanics in Ljubljana, Professorial Fellow at the "Simion Stoilow Mathematics Institute of the Romanian Academy, and Professor at the University of Craiova. He is the author of about 300 research papers in nonlinear analysis and several books, including Variational and Nonvariational Methods in Nonlinear Analysis and Boundary Value Problems (Kluwer, 2003), Singular Elliptic Problems: Bifurcation and Asymptotic Analysis (Oxford University Press, 2008), Problems in Real Analysis: Advanced Calculus on the Real Axis (Springer, 2009), Variational Principles in Mathematical Physics, Geometry and Economics: Qualitative Analysis of Nonlinear Equations and Unilateral Problems (Cambridge University Press, 2010), Nonlinear PDEs: Mathematical Models in Biology, Chemistry and Population Genetics (Springer, 2012), Partial Differential Equations with Variable Exponents: Variational Methods and Qualitative Analysis (CRC Press, 2015), Variational Methods for Nonlocal Fractional Problems (Cambridge University Press, 2016). He was a Highly Cited Researcher (2014). He was elected to the Accademia Peloritana dei Pericolanti (2014) and to the Accademia delle Scienze dell'Umbria (2017).