Pro-Banach代数在Banach空间上的延拓表示

详细研究了pro-Banach代数及其表示,证明了有序pro-Banach代数在具有闭的正锥的有序Banach空间上的非退化正的连续表示可唯一延拓到其不同的中心化子代数上.     

抽象二阶周期边值问题解的存在性

研究了有序Banach空间中二阶周期边值问题解的存在性,利用凸锥理论与上、下解方法,获得了解的存在性结果.     

Diestel-Faires定理在局部凸空间中的推广

通过Banach 空间与局部凸空间的对比,将Banach 空间上的Diestel-Faires 定理在局部凸空间上进行推广。进一步给出了局部凸空间上的Orlicz-Pettis定理与推论。     

Banach空间值弱Garsia型鞅空间及其原子分解

定义了Banach空间值弱Garsia型鞅空间和三种类型原子,证明了Banach空间值弱Garsia型鞅空间上的四个原子分解定理,并利用这些定理,得到Banach空间值弱Garsia型鞅空间的互相嵌入关系,其结果与Banach空间的凸性和光滑性有密切关系.     

非自反Banach空间中的度量投影

该文给出非自反Banach空间中一类超平面上度量投影的表达式．在近严格凸Banach空间中,研究了它们的连续性．对于对偶Banach空间X*,给出弱*闭子集上度量投影的一些连续性结果．     

自反Banach空间中Ky Fan点的存在性

本文对自反Banach空间证明了一个Ky Fan点的存在性定理,作为它的应用,对非合作博弈的Nash平衡点及变分不等式的解给出了几个存在性定理.     

Banach值鞅变换算子的有界性

本文运用Banach值鞅不等式和鞅空间的相互嵌入关系．讨论了Banach空间值鞅空间上鞅变换算子L的有界性．并给出了鞅变换算子的有界性与Banach空间几何性质的关系．     

Banach空间闭超平面上度量投影的连续性

该文给出Banach空间X的对偶空间X~*中闭超平面上度量投影的表达式,并在Banach空间中研究了闭超平面上度量投影的连续性.     

有序Banach空间非线性Robin边值问题正解的存在性

讨论有序Banach空间E中的非线性Robin边值问题正解的存在性,通过非紧性测度的估计技巧与凝聚映射的不动点指数理论获得该问题正解的存在性结果.     

加权Banach空间中指数函数系完备的稳定性（英文）

本文研究了加权Banach空间中指数函数系完备的稳定性问题.利用解析函数扰动的方法,获得了加权Banach空间中指数函数系完备的稳定性若干结果,推广了现有有限区间Banach空间上的经典结果.     

An application of optimization theory to the study of equilibria for games: a survey

This contribution is a survey about potential games and their applications. In a potential game the information that is sufficient to determine Nash equilibria can be summarized in a single function on the strategy space: the potential function. We show that the potential function enable the application of optimization theory to the study of equilibria. Potential games and their generalizations are presented. Two special classes of games, namely team games and separable games, turn out to be potential games. Several properties satisfied by potential games are discussed and examples from concrete situations as congestion games, global emission games and facility location games are illustrated.     

On some families of cooperative fuzzy games

In a fuzzy cooperative game the players may choose to partially participate in a coalition. A fuzzy coalition consists of a group of participating players along with their participation level. The characteristic function of a fuzzy game specifies the worth of each such coalition. This paper introduces well-known properties of classical cooperative games to the theory of fuzzy games, and studies their interrelations. It deals with convex games, exact games, games with a large core, extendable games and games with a stable core.     

不确定性下强Berge均衡的存在性

在已知不确定参数变化的范围下,研究了非合作博弈与广义非合作博弈的强Berge均衡的存在性,基于强Berge均衡与不确定性下非合作博弈的强Nash均衡的概念,给出了不确定参数下非合作博弈与广义非合作博弈的强Berge均衡的定义,并利用Fan-Glicksberg不动点定理证明其存在性,最后用算例验证其可行性.     

Values for Interior Operator Games

The aim of this paper is to study a new class of cooperative games called interior operator games. These games are additive games restricted by antimatroids. We consider several types of cooperative games as peer group games, big boss games, clan games and information market games and show that all of them are interior operator games. Next, we analyze the properties of these games and compute the Shapley, Banzhaf and Tijs values.     

Reductions of interval noncooperative games

Noncooperative games of a finite number of persons with interval-valued payoff functions are considered. The concept of an equilibrium situation is introduced. A reduction of such games to deterministic noncooperative games is proposed. Properties of the reduced games are discussed. Interval antagonistic and bimatrix games are examined, and illustrative examples are considered.     

Approximating the least core value and least core of cooperative games with supermodular costs

We study the approximation of the least core value and the least core of supermodular cost cooperative games. We provide a framework for approximation based on oracles that approximately determine maximally violated constraints. This framework yields a 3-approximation algorithm for computing the least core value of supermodular cost cooperative games, and a polynomial-time algorithm for computing a cost allocation in the 2-approximate least core of these games. This approximation framework extends naturally to submodular profit cooperative games. For scheduling games, a special class of supermodular cost cooperative games, we give a fully polynomial-time approximation scheme for computing the least core value. For matroid profit games, a special class of submodular profit cooperative games, we give exact polynomial-time algorithms for computing the least core value as well as a least core cost allocation.     

Two characterizations of the consistent egalitarian solution and of the core on NTU games

In this paper, we provide two characterizations in the context of NTU games: of the consistent egalitarian solution and of the core. The first characterization is based on reduced games and contraction and expansion independence. The second one is based on reduced games and sub-reduced games.     

An average lexicographic value for cooperative games

For games with a non-empty core the Alexia value is introduced, a value which averages the lexicographic maxima of the core. It is seen that the Alexia value coincides with the Shapley value for convex games, and with the nucleolus for strongly compromise admissible games and big boss games. For simple flow games, clan games and compromise stable games an explicit expression and interpretation of the Alexia value is derived. Furthermore it is shown that the reverse Alexia value, defined by averaging the lexicographic minima of the core, coincides with the Alexia value for convex games and compromise stable games.     

集合对策边缘解的公理化方法

本文将单调集合对策边缘解推广到一般集合对策上,利用三个公理,确定了集合对策边缘解的唯—性．在证明唯—性的过程中,引进了单调集合对策将集合对策进行分解．证明过程与Aarts等人的方法完全不一样,在某些地方吸收了Young的有关思想．