Existence and stability of weakly Pareto-Nash equilibria for discontinuous multiobjective games

Abstract

We introduce two new concepts of the vector-valued generalized single deviation property and the vector-valued positive generalized single deviation property for discontinuous multiobjective games. Then, some new existence theorems of weakly Pareto-Nash equilibria for discontinuous multiobjective games are established. Moreover, we prove that most of the discontinuous multiobjective games are essential with perturbed payoffs in the sense of Baire category.

Keywords:

• Discontinuous multiobjective games
• weakly Pareto-Nash equilibrium
• generic stability

Mathematics subject classifications:

• 91A10
• 90C31

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant numbers 12061020, 71961003], the Science and Technology Foundation of Guizhou Province [grant numbers 20201Y284, 20205016, 2021088, [2021]5640], the Foundation of Guizhou University [grant numbers 201405, 201811]. The authors acknowledge these supports.