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

Research output: Contribution to journal › Article in a journal › peer-review

7 Scopus citations

Abstract

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.

Original language	English
Article number	115720
Journal	Journal of Computational and Applied Mathematics
Volume	442
Early online date	4 Dec 2023
DOIs	https://doi.org/10.1016/j.cam.2023.115720
State	Published - 1 May 2024

Bibliographical note

Publisher Copyright:
© 2023 Elsevier B.V.

Keywords

Vector optimization
Berge’s maximum theorem
Weierstrass theorem
Generalized multiobjective games
Berge's maximum theorem

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10.1016/j.cam.2023.115720License: Unspecified

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AU - Flores-Bazán, Fabián

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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.

AB - 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

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KW - Generalized multiobjective games

KW - Berge's maximum theorem

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JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

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ER -

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

Abstract

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Keywords

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