On the stability of the solution for multiobjective generalized games with the payoffs perturbed |
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Authors: | QQ Song LS Wang |
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Institution: | a College of Science, China Agricultural University, Beijing 100083, PR Chinab College of Science, Guilin University of Technology, Guilin 541004, PR China |
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Abstract: | This paper studies the stability of weakly Pareto-Nash and Pareto-Nash equilibrium for multiobjective generalized games with the payoff perturbed. Using a simple characterization of the weakly Pareto-Nash solution, we obtain a generic continuous result concerning weakly Pareto-Nash solution mapping. Examples are given to show that Pareto-Nash equilibrium mapping is neither upper semicontinuous nor lower semicontinuous. Through seeking the sub-mapping, we prove that most multiobjective generalized games have at least one essential Pareto-Nash solution. |
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Keywords: | Multiobjective generalized games Essential set Pareto-Nash equilibrium |
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