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

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	E-pub ahead of print - 4 Dec 2023

Bibliographical note

Publisher Copyright:
© 2023 Elsevier B.V.

Keywords

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

Access to Document

10.1016/j.cam.2023.115720License: Unspecified

Cite this

@article{5c1e3fdd502b4e638140570dca3a206a,

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

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.",

keywords = "Vector optimization, Berge{\textquoteright}s maximum theorem, Weierstrass theorem, Generalized multiobjective games, Berge's maximum theorem",

author = "{Cotrina Asto}, {John Edwin} and Fabi{\'a}n Flores-Baz{\'a}n",

note = "Publisher Copyright: {\textcopyright} 2023 Elsevier B.V.",

year = "2023",

month = dec,

day = "4",

doi = "10.1016/j.cam.2023.115720",

language = "English",

volume = "442",

journal = "Journal of Computational and Applied Mathematics",

issn = "0377-0427",

publisher = "Elsevier",

}

TY - JOUR

T1 - Existence of Nash equilibria for generalized multiobjective games through the vector extension of Weierstrass and Berge maximum theorems

AU - Cotrina Asto, John Edwin

AU - Flores-Bazán, Fabián

PY - 2023/12/4

Y1 - 2023/12/4

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.

KW - Vector optimization

KW - Berge’s maximum theorem

KW - Weierstrass theorem

KW - Generalized multiobjective games

KW - Berge's maximum theorem

UR - http://www.scopus.com/inward/record.url?scp=85179072008&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/fe198bcd-5bdb-3d40-a7e5-e3c2faf20570/

U2 - 10.1016/j.cam.2023.115720

DO - 10.1016/j.cam.2023.115720

M3 - Article in a journal

SN - 0377-0427

VL - 442

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

M1 - 115720

ER -

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

Abstract

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

Cite this