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

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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.

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Cotrina, J., & Flores-Bazán, F. (2024). Existence of Nash equilibria for generalized multiobjective games through the vector extension of Weierstrass and Berge maximum theorems. Journal of Computational and Applied Mathematics, 442. https://doi.org/10.1016/j.cam.2023.115720

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