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Weighted quasi-variational inequalities and constrained Nash equilibrium problems. (English) Zbl 1098.49009
Summary: The weighted quasi-variational inequalities over product of sets (for short, WQVIP) and system of weighted quasi-variational inequalities (for short, SWQVI) are introduced. It is shown that these two problems are equivalent. A relationship between SWQVI and system of vector quasi-variational inequalities is given. The concept of normalized solutions of WQVIP and SWQVI is introduced. A relationship between solution (respectively, normalized solution) of SWQVI and solution of weighted constrained Nash equilibrium problem (respectively, normalized weight Nash equilibrium) is also given. The scalar quasi-equilibrium problem (for short, QEP), which includes WQVIP as a particular case, is also considered. By introducing the concept of densely pseudomonotonicity of bifunctions, the existence of a solution of QEP is established. As a consequence, existence results for solutions for WQVIP and constrained Nash equilibrium problems for vector value functions are derived.
49J40Variational methods including variational inequalities
90C29Multi-objective programming; goal programming
47J20Inequalities involving nonlinear operators