Stability of Weakly Pareto-Nash Equilibria and Pareto-Nash Equilibria for Multiobjective Population Games
نویسندگان
چکیده
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. Firstly, the set of weakly Pareto-Nash equilibria is proven to be upper semicontinuous and further generically continuous with payoff functions perturbed. 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.
منابع مشابه
Multiobjective Games and Determining Pareto-Nash Equilibria
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