Weighted quasi-variational inequalities and constrained Nash equilibrium problems

Q. H. Ansari, W. K. Chan, Xiaoqi Yang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

11 Citations (Scopus)


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 languageEnglish
Pages (from-to)361-380
Number of pages20
JournalTaiwanese Journal of Mathematics
Issue number2
Publication statusPublished - 1 Jan 2006


  • 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

  • Mathematics(all)

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