Local dense solutions for equilibrium problems with applications to noncooperative games. (2nd September 2021)

• Record Type: Journal Article
• Authors: Moradi, S.; Jafari, S.
• Is Part Of: Optimization. Volume 70:Number 9(2021)
• Page Start: 1987
• Page End: 2012
• Publication Date: 2021-09-02
• Subjects: Equilibrium problem -- locally segment-dense set -- set-valued mapping -- quasiconvexity -- topological vector space; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2020.1767614
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : In this work, we establish several results concerning the existence of solutions for set-valued and single-valued equilibrium problems in real Hausdorff topological vector spaces. Firstly we introduce some generalizations of convexity and continuity conditions to set-valued mappings and then apply them to special dense subsets of the domain to obtain the existence of local dense solutions of equilibrium problems. Then the existence of the global solutions follows from a condition that is weaker than semistrict quasiconvexity. Specifically, we give an existence theorem for noncooperative n -person games, under assumptions imposed on a locally segment-dense subset of the strategy set of each player.