## Taiwanese Journal of Mathematics

### WEIGHTED QUASI-VARIATIONAL INEQUALITIES AND CONSTRAINED NASH EQUILIBRIUM PROBLEMS

#### 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.

#### Article information

Source
Taiwanese J. Math., Volume 10, Number 2 (2006), 361-380.

Dates
First available in Project Euclid: 18 July 2017

https://projecteuclid.org/euclid.twjm/1500403830

Digital Object Identifier
doi:10.11650/twjm/1500403830

Mathematical Reviews number (MathSciNet)
MR2208272

Zentralblatt MATH identifier
1098.49009

#### Citation

Ansari, Qamrul Hasan; Chan, Wai-Kit; Yang, Xiao-Qi. WEIGHTED QUASI-VARIATIONAL INEQUALITIES AND CONSTRAINED NASH EQUILIBRIUM PROBLEMS. Taiwanese J. Math. 10 (2006), no. 2, 361--380. doi:10.11650/twjm/1500403830. https://projecteuclid.org/euclid.twjm/1500403830

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