Abstract
Using the method of generic continuity of set-valued mappings, this paper studies the stability of weakly Pareto-Nash and Pareto-Nash equilibria for multiobjective population games, when payoff functions are perturbed. More precisely, the paper investigates the continuity properties of the set of weakly Pareto-Nash equilibria and that of the set of Pareto-Nash equilibria under sufficiently small perturbations of payoff functions. Firstly, the set of weakly Pareto-Nash equilibria is proven to be upper semicontinuous and further generically continuous with the perturbed payoff functions. Secondly, examples are illustrated to show that the set of Pareto-Nash equilibria is neither upper semicontinuous nor lower semicontinuous. By seeking an upper semicontinuous sub-mapping, it is shown that the set of Pareto-Nash equilibria is partly upper semicontinuous and almost lower semicontinuous.
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This research is supported by the National Science Foundation of China (grant 11271098), the Guizhou Provincial Science and Technology Foundation (grant 20132116) and the Postgraduate Innovative Foundation of Guizhou University (grant 2014065).
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Yang, G., Yang, H. Stability of Weakly Pareto-Nash Equilibria and Pareto-Nash Equilibria for Multiobjective Population Games. Set-Valued Var. Anal 25, 427–439 (2017). https://doi.org/10.1007/s11228-016-0391-6
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DOI: https://doi.org/10.1007/s11228-016-0391-6