集值映射的Nash平衡点的存在定理

本文引入了集值映射的Nash平衡点的概念，它以通常的Nash平衡点及Loose Nash平衡点为特例，并在紧和非紧的假设下，得到集值映射的Nash平衡点的存在定理，其中在非紧的情况下使用escaping序列的定义．     

多目标对策的弱Pareto-Nash平衡点集的稳定性研究

通过定义多目标对策的加权Nash平衡点集,得出它和对应对策的弱Pareto-Nash平衡点集之间的关系,证明了在一定条件下的多目标对策的弱Pareto-Nash平衡点集的稳定性.     

集值Fredholm映射及其拓扑度

本文推广C~1-Fredholm映射的概念到上半连续集值映射的情形,并对零指标的集值Fredbolm映射及其集值紧摄动建立拓扑度理论。§1.集值Fredholm映射设X是C~0-Banach流形,模空间为Banach空间E,图册为A=     

集值保通（CO）映射的上半连续性

本义讨论了集值映射是保通（ＣＯ）映射以及保通（ＣＯ）映射是上半连续映射的一些充分条件。     

锥拟凸集值映射与集值映射的锥半连续性

本文借助锥界集定义了一种新的锥拟凸集值映射,并且利用广义Minkowski泛函讨论了锥半连续及锥外上半连续集值映射的锥拟凸性．     

一类迭代方程的集值解

该文将文献 [9] 中关于一类集值迭代方程解的存在性的结果推进到更广范围的一类集值映射. 作者还研究了解对已知集值映射的连续依赖性.     

图象拓扑下的Ky Fan引理解集的本质连通区及其在对策论上的应用

本文在集值映射的图象拓扑意义下,证明了赋范线性空间中的Ky Fan引理的解集的本质连通区的存在性,由此得到一类对策的Nash平衡点集的本质连通区的存在性.     

含约束集值映射超有效解集的连通性

在局部凸拓扑线性空间中给出了含约束集值映射超有效解的连通性定理,当目标函数及约束映射为锥弧连通的集值映射时,其超有效解集是连通的.     

关于无限对策Nash平衡点集的本质连通区

证明了任意纯策略集是紧度量空间和支付函数连续的n人无限非合作对策存在 Nash平衡点集的本质连通区．     

不确定条件下n人非合作博弈均衡点集的通有稳定性

基于经典博弈模型的Nash均衡点集的通有稳定性和具有不确定参数的n人非合作博弈均衡点的概念,探讨了具有不确定参数博弈的均衡点集的通有稳定性.参照Nash均衡点集稳定性的统一模式,构造了不确定博弈的问题空间和解空间,并证明了问题空间是一个完备度量空间,解映射是上半连续的,且解集是紧集（即usco（upper semicontinuous and compact-valued）映射）,得到不确定参数博弈模型的解集通有稳定性的相关结论.     

System of Generalized Vector Quasi-Equilibrium Problems with Applications to Fixed Point Theorems for a Family of Nonexpansive Multivalued Mappings

In this paper, we establish the existence theorems of the generalized vector quasi-equilibrium problems. From some existence theorem, we establish fixed point theorems for a family of lower semicontinuous or nonexpansive multivalued mappings. We also obtain the existence theorems of system of mixed generalized vector variational-like inequalities and existence theorems of the Debreu vector equilibrium problems and the Nash vector equilibrium problems.     

Fixed point theorems and their applications to theory of Nash equilibria

In this paper we prove fixed point theorems for set-valued mappings in products of posets. Applications to the theory of Nash equilibria are presented.     

抽象凸空间中集值映射的不动点定理及其应用

A new fixed point theorem and the selection property for upper semi-continuous set-valued mappings in abstract convexity space are established. As their applications the existence of Nash equilibrium for n-person non-cooperative generalized games is proved.     

On extremal solutions of inclusion problems with applications to game theory

A recursion principle, generalized iteration methods and the axiom of choice are applied to prove the existence of extremal fixed points of set-valued mappings in posets, extremal solutions of an inclusion problem, and extremal Nash equilibria for a normal-form game.     

Coincidence Theorems with Applications to Minimax Inequalities, Section Theorem, Best Approximation and Multiobjective Games in Topological Spaces

Some new coincidence theorems involving admissible set-valued mappings are proved in general noncompact topological spaces. As applications, some new minimax inequalities, section theorem, best approximation theorem, existence theorems of weighted Nash equilibria and Pareto equilibria for multiobjective games are given in general topological spaces.     

Several extensions of the Abian–Brown Fixed Point Theorem and their applications to extended and generalized Nash equilibria on chain-complete posets

In this paper, we provide several extensions of the Abian–Brown Fixed Point Theorem from single-valued mappings to set-valued mappings on chain-complete posets. Then we examine some non-monetized, non-cooperative games where both the collections of the strategies and the ranges of the utilities for the players are posets. By applying the extensions of the Abian–Brown Fixed Point Theorem and by applying the order-preserving property of mappings, we prove some existence theorems of extended and generalized Nash equilibria for non-monetized, non-cooperative games on chain-complete posets.     

An Ekeland’s variational principle for set-valued mappings with applications

In this paper, we obtain a general Ekeland’s variational principle for set-valued mappings in complete metric space, which is different from those in [G.Y. Chen, X.X. Huang, Ekeland’s ε-variational principle for set-valued mapping, Mathematical Methods of Operations Research 48 (1998) 181–186; G.Y. Chen, X.X. Huang, S.H. Hou, General Ekeland’s Variational Principle for Set-Valued Mappings, Journal of Optimization Theory and Applications 106 (2000) 151–164; S.J. Li, W.Y. Zhang, On Ekeland’s variational Principle for set-valued mappings, Acta Mathematicae Application Sinica, English Series 23 (2007) 141–148]. By the result, we prove some existence results for a general vector equilibrium problem under nonconvex and compact or noncompact assumptions of its domain, respectively. Moreover, we give some equivalent results to the variational principle.     

集值映射空间上的自然映射(英文)

In this paper,we discuss the continuities of some natural mappings on pointcompact continuous set-valued mapping spaces with compact-open topology and obtain the properties of set-valued injective mappings,set-valued diagonal mappings,induced mappings,set-valued evaluation mappings,set-valued topological sum mappings and set-valued topological product mappings.     

A selection theorem for a new class of set-valued maps

A new class of set-valued maps that includes all upper and lower semicontinuous set-valued maps is introduced. For this class, a selection theorem having applications in the theory of differential inclusions is presented. Translated fromMatematicheskie Zametki, Vol. 66, No. 4, pp. 503–507, October, 1999.