Abstract
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 of WQVIP and constrained Nash equilibrium problems for vector valued functions are derived.
Original language | English |
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Pages (from-to) | 361-380 |
Number of pages | 20 |
Journal | Taiwanese Journal of Mathematics |
Volume | 10 |
Issue number | 2 |
DOIs | |
Publication status | Published - 1 Jan 2006 |
Keywords
- Constrained Nash equilibrium problem
- Quasi-equilibrium problem
- System of vector quasi-variational inequalities
- System of weighted quasi-variational inequalities
- Weighted constrained Nash equilibrium problem
- Weighted quasi-variational inequalities
ASJC Scopus subject areas
- General Mathematics