Maximal element with applications to Nash equilibrium problems in Hadamard manifolds

被引：3

作者：

Lu, Hai-Shu ^{[1
]}

Li, Rong ^{[1
]}

Wang, Zhi-Hua ^{[1
]}

机构：

[1] Jiangsu Univ Technol, Sch Business, Changzhou, Peoples R China

来源：

OPTIMIZATION | 2019年 / 68卷 / 08期

关键词：

Hadamard manifold; maximal element; Nash equilibrium; generalized game; PROXIMAL POINT ALGORITHM; VARIATIONAL-INEQUALITIES; EXISTENCE; THEOREMS; MINIMAX;

D O I：

10.1080/02331934.2019.1647197

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

The purpose of this paper is to study the existence of maximal elements with applications to Nash equilibrium problems for generalized games in Hadamard manifolds. By employing a KKM lemma, we establish a new maximal element theorem in Hadamard manifolds. As applications, some existence results of Nash equilibria for generalized games are derived. The results in this paper unify, improve and extend some known results from the literature.

引用

页码：1491 / 1520

页数：30

共 47 条

[1] [Anonymous], 1976, Differential Geometry of Curves and Surfaces
[2] Market power in water markets
Ansink, Erik
Houba, Harold
[J]. JOURNAL OF ENVIRONMENTAL ECONOMICS AND MANAGEMENT, 2012, 64 (02) : 237 - 252
[3] Coincidence and maximal element theorems and their applications to generalized equilibrium problems and minimax inequalities
Balaj, Mircea
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2008, 68 (12) : 3962 - 3971
[4] Equivalent forms of a generalized KKM theorem and their applications
Balaj, Mircea
Lin, Lai-Jiu
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2010, 73 (03) : 673 - 682
[5] An Existence Result for the Generalized Vector Equilibrium Problem on Hadamard Manifolds
Batista, E. E. A.
Bento, G. C.
Ferreira, O. P.
[J]. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2015, 167 (02) : 550 - 557
[6] Chavel I., 1993, RIEMANNIAN GEOMETRY, V108
[7] Equilibrium problems in Hadamard manifolds
Colao, Vittorio
Lopez, Genaro
Marino, Giuseppe
Martin-Marquez, Victoria
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2012, 388 (01) : 61 - 77
[8] Debreu's social equilibrium existence theorem
Dasgupta, Partha Sarathi
Maskin, Eric S.
[J]. PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 2015, 112 (52) : 15769 - 15770
[9] The study of maximal elements, fixed points for Ls-majorized mappings and their applications to minimax and variational inequalities in product topological spaces
Deguire, P
Tan, KK
Yuan, GXZ
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1999, 37 (07) : 933 - 951
[10] Existence of solutions for quasi-equilibrium problems in noncompact topological spaces
Ding, XP
[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2000, 39 (3-4) : 13 - 21

← 1 2 3 4 5 →