Abstract
In this paper, we first give a generalization of Ky Fan's inequality to vector-valued functions. We prove that, for every vector-valued function (satisfying some continuity and convexity conditions), there exists at least one essential component of the set of its Ky Fan's points. As applications, we show that, for every multiobjective game (satisfying some continuity and convexity conditions), there exists at least one essential component of the set of its weakly Pareto-Nash equilibrium points.
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