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We introduce two new concepts of the vector-valued generalized single deviation property and the vector-valued positive generalized single deviation property for discontinuous multiobjective games. Then, some new existence theorems of weakly Pareto-Nash equilibria for discontinuous multiobjective games are established. Moreover, we prove that most of the discontinuous multiobjective games are essential with perturbed payoffs in the sense of Baire category.

Existence and stability of weakly Pareto-Nash equilibria for discontinuous multiobjective games