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”

John Cotrina, Fabián Flores-Bazán

Research output: Contribution to journalNotepeer-review

Abstract

This note qualifies some results in Cotrina and Flores-Bazán (2024) on the ‘Finite intersection property’. We remind the essential role of this property for proving our results. In this note, we recall the statement of this property. We then specify the restrictive conditions that should be provided. An example proves the interest of this note revising some points in Cotrina and Flores-Bazán. Furthermore, it is showed that a class of generalized Nash equilibrium problems can be viewed as a particular case of a vector optimization problem, whose vector-valued function always possesses the Finite intersection property on its natural domain. Thus, the existence of a generalized Nash equilibrium will be a consequence of our Berge-type theorem and the Kakutani fixed point theorem, being it more general than those existing in recent literature, as shown by our examples.

Original languageEnglish
Article number115971
Number of pages5
JournalJournal of Computational and Applied Mathematics
Volume449
DOIs
StatePublished - 15 Oct 2024

Bibliographical note

Publisher Copyright:
© 2024 Elsevier B.V.

Keywords

  • Berge's maximum theorem
  • Generalized multiobjective games
  • Vector optimization

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