In this paper, we introduce a weighted equilibrium problem over product of sets and a system of weighted equilibrium problems for vector-valued bifunctions and show that both have the same solution set. Further, we introduce the concept of normalized solution of the system of weightedequilibrium problems and give its relationship with the solutions of systems of vector equilibrium problems. Furthermore, several kinds of weighted monotonicities are defined for the family of vector-valued bifunctions. Using fixed-point theorems, we establish some existence theorems for these problems. The concepts and results presented in this paper extend and unify a number of previously known corresponding concepts and results in the literature.
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