Essential components of the set of weakly Pareto-Nash equilibrium points |
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| Institution: | Department of Mathematics, Guizhou University Guiyang, Guizhou 550025, P.R. China;Department of Applied Mathematics, Zhejiang University Hangzhou, Zhejiang 310027, P.R. China;Department of Science and Technology of Guizhou Province Guiyang, Guizhou 550002, P.R. China |
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| 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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