The construction of functions that simultaneously generalize weighted means and OWA operators is an interesting topic that has received special attention in recent years. Due to the properties they satisfy, one of the most interesting generalization are SUOWA operators, which have been widely studied in the literature. In a recent paper, a new generalization has been introduced, the Semi-SUOWA operators, which have a close relationship with SUOWA operators. The main aim of this paper is to analyze the games associated with Semi-SUOWA operators. In this respect, we give conditions under which we can guarantee the monotonicity of these games. Moreover, we establish some relationships between some games associated with SUOWA and Semi-SUOWA operators and show the pointwise convergence of certain games.
