Existence of Nash equilibria for generalized multiobjective games through the vector extension of Weierstrass and Berge maximum theorems

John Edwin Cotrina Asto; Fabián Flores-Bazán

doi:10.1016/j.cam.2023.115720

Existence of Nash equilibria for generalized multiobjective games through the vector extension of Weierstrass and Berge maximum theorems

John Edwin Cotrina Asto, Fabián Flores-Bazán

Producción científica: Contribución a una revista › Artículo de revista › revisión exhaustiva

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Resumen

In this work, we deal with a vector extension of the generalized the Weierstrass and Berge maximum theorems, notably in mathematical economics. This is carried out by introducing the notions of transfer continuity and pseudo-continuity for those functions. Here the preference relation is given via a closed convex cone, having possibly empty interior. As a consequence, we present an existence of strong-Nash equilibria for generalized multiobjective games, and the Rosen model is revisited.

Idioma original	Inglés
Número de artículo	115720
Publicación	Journal of Computational and Applied Mathematics
Volumen	442
Fecha en línea anticipada	4 dic. 2023
DOI	https://doi.org/10.1016/j.cam.2023.115720
Estado	Publicada - 1 may. 2024

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© 2023 Elsevier B.V.

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A note on the Finite intersection property in “Existence of Nash equilibria for generalized multiobjective games through the vector extension of Weierstrass and Berge maximum theorems”
Cotrina, J. & Flores-Bazán, F., 15 oct. 2024, En: Journal of Computational and Applied Mathematics. 449, 5 p., 115971.
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Existence of Nash equilibria for generalized multiobjective games through the vector extension of Weierstrass and Berge maximum theorems. / Cotrina Asto, John Edwin; Flores-Bazán, Fabián.
En: Journal of Computational and Applied Mathematics, Vol. 442, 115720, 01.05.2024.

Producción científica: Contribución a una revista › Artículo de revista › revisión exhaustiva

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N2 - In this work, we deal with a vector extension of the generalized the Weierstrass and Berge maximum theorems, notably in mathematical economics. This is carried out by introducing the notions of transfer continuity and pseudo-continuity for those functions. Here the preference relation is given via a closed convex cone, having possibly empty interior. As a consequence, we present an existence of strong-Nash equilibria for generalized multiobjective games, and the Rosen model is revisited.

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KW - Berge’s maximum theorem

KW - Weierstrass theorem

KW - Generalized multiobjective games

KW - Berge's maximum theorem

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Existence of Nash equilibria for generalized multiobjective games through the vector extension of Weierstrass and Berge maximum theorems

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A note on the Finite intersection property in “Existence of Nash equilibria for generalized multiobjective games through the vector extension of Weierstrass and Berge maximum theorems”

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