大博弈中Nash均衡的存在性

研究了具有任意多个局中人的非合作博弈(大博弈)中Nash均衡的存在性.将1969年Ma的截口定理推广得到新的截口定理.用这个新的截口定理进一步证明了:1)大博弈中Nash均衡的存在性;2)纯策略集为紧度量空间而且支付函数为连续函数时,连续大博弈中混合策略Nash均衡的存在性.并且存在性定理推出了2010年Salonen的结果,即此研究结果较Salonen的结论更具普遍意义.     

不确定下广义博弈强Berge均衡的存在性

本文基于不确定下的非合作博弈NS均衡给出了不确定下广义非合作博弈强Berge均衡与广义多目标弱Pareto强Berge均衡的定义,利用Fan-Glicksberg不动点定理证明了不确定下广义非合作博弈强Berge均衡与不确定下广义多目标弱Pareto强Berge均衡存在性定理.     

轻微利他弱Pareto-Nash均衡

2008年,Marco和Morgan在正规型博弈中引入轻微利他均衡和友好均衡的概念.利用轻微利他的思想,研究多目标博弈.证明轻微利他弱Pareto-Nash均衡的存在性定理,进一步地讨论轻微利他弱Pareto-Nash均衡和本质均衡的关系.     

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.     

多主从群体博弈中合作均衡的存在性

基于Scarf,Kajii关于n-人非合作博弈中的合作均衡存在性定理,越来越多的研究表明,对非合作博弈的合作均衡研究是有必要的.本文综合Sandholm的群体博弈模型以及Yang和Ju证明的多主从博弈的合作均衡存在性定理,旨在详细研究多主从群体博弈的合作均衡.首先,在多主从群体博弈中引入合作均衡的概念,并通过Kajii...     

模糊二人非合作对策的简单Berge均衡

研究模糊二人非合作对策的简单Berge均衡的存在性.基于Zimmermann处理模糊多目标线性规划的观点和Zhukovskii提出的简单Berge均衡概念,定义了模糊二人非合作对策的简单Berge均衡并借助于Ky Fan不等式证明其存在性.     

非紧集上不连续函数的Ky Fan不等式及其等价形式和应用

证明了非紧集上不具有任何连续性的函数弱Ky Fan点的存在性,给出了在函数只具非常弱的连续性和凸性条件下非紧集上Ky Fan不等式解的存在性,并给出它的两种等价形式.作为应用:(1)得到Ky Fan截口定理和Fan-Browder不动点定理的推广;(2)应用于博弈理论,得到几个新的Nash平衡存在性定理.     

信息集广义多目标博弈弱Pareto-Nash平衡点的存在性和稳定性

首先把信息集的概念引入到多目标博弈, 建立了信息集广义多目标博弈模型, 并指出了信息集广义多目标博弈以广义多目标博弈、广义n人非合作博弈、一般n人非合作博弈为特例, 然后用Fan-Glicksberg不动点定理证明了信息集广义多目标博弈弱Pareto-Nash平衡点的存在性, 最后在本质解和强本质解的意义下, 分别研究了信息集广义多目标博弈弱Pareto-Nash平衡点的通有稳定性和强本质连通区的存在性.     

年龄分布下种群资源开发动态博弈的Nash均衡

研究具有年龄结构的种群资源开发中的动态博弈问题.应用~Kakutani~多值映射不动点定理证明了Nash均衡的存在性,借助切锥－法锥和共轭系统技巧刻画了均衡策略.结果表明,在一定条件下,均衡策略具有Bang-Bang结构.     

超级模数博弈的存在性

本文定义了一类在有序Banach空间上的超模博弈,并利用著名的Birkhoff不动点定理证明了有序Banach空间上超模博弈Nash均衡的存在性.     

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.     

弱伪连续向量值函数及其在多目标博弈中的应用

基于对弱伪连续实值函数的研究, 提出向量值函数关于锥的弱伪连续定义, 并建立了向量值函数$R_+^k$弱伪连续与实值函数弱伪连续的对应关系. 作为弱伪连续向量值函数的应用, 给出了弱伪连续下的向量值Ky Fan点的存在性定理, 并通过该定理证明了伪连续向量值支付下的多目标博弈弱Pareto-Nash平衡点的存在性定理.     

Existence and stability of solutions for maximal element theorem on Hadamard manifolds with applications

In this paper, maximal element theorem on Hadamard manifolds is established. First, we prove the existence of solutions for maximal element theorem on Hadamard manifolds. Further, we prove that most of problems in maximal element theorem on Hadamard manifolds (in the sense of Baire category) are essential and that, for any problem in maximal element theorem on Hadamard manifolds, there exists at least one essential component of its solution set. As applications, we study existence and stability of solutions for variational relation problems on Hadamard manifolds, and existence and stability of weakly Pareto-Nash equilibrium points for n-person multi-objective games on Hadamard manifolds.     

多目标博弈平衡点存在性定理的推广

以向量值KyFan不等式的推广为基础,讨论支付函数为向量形式的n人非合作多目标博弈弱Pareto-Nash平衡点存在性条件,将多目标博弈平衡点存在性定理中策略空间的紧性,支付函数的凸性等条件减弱.     

Essential Components of the Set of Weakly Pareto-Nash Equilibrium Points for Multiobjective Generalized Games in Two Different Topological Spaces

In this paper, we study the existence and essential components of the set of weakly Pareto-Nash equilibrium points for multiobjective generalized games in two different uniform topological spaces. We obtain some new existence theorems. Examples show that the results are not identical in two different topological spaces.The author thanks two referees for careful reading of the paper and helpful comments.     

一个新的弱Pareto-Nash均衡点存在性结果

研究了多目标广义对策问题,通过Brouwer-Schauder-Tychonoff不动点定理,建立了弱Pareto-Nash均衡点的存在性结果,最后,通过一个例子,说明结果是新的、不能被已有的存在性结果所包含.     

On the stability of the solution for multiobjective generalized games with the payoffs perturbed

This paper studies the stability of weakly Pareto-Nash and Pareto-Nash equilibrium for multiobjective generalized games with the payoff perturbed. Using a simple characterization of the weakly Pareto-Nash solution, we obtain a generic continuous result concerning weakly Pareto-Nash solution mapping. Examples are given to show that Pareto-Nash equilibrium mapping is neither upper semicontinuous nor lower semicontinuous. Through seeking the sub-mapping, we prove that most multiobjective generalized games have at least one essential Pareto-Nash solution.     

一种n人静态博弈纯策略纳什均衡存在性判别法

本首先给出了n人静态博弈纯策略纳什均衡存在的充要条件。然后给出n人静态博弈纯策略纳什均衡存在性的一种判别方法。最后在判别纯策略纳什均衡存在的条件下，给出判定该静态博弈存在多少纯策略纳什均衡以及哪些纯策略组合是纯策略纳什均衡(解)的方法。     

Sufficient conditions for Nash equilibria inN-person games over reflexive Banach spaces

Sufficient conditions are obtained for the existence of Nash equilibrium points inN-person games when the strategy sets are closed, convex subsets of reflexive Banach spaces. These conditions require that each player's cost functional is convex in that player's strategy, weakly continuous in the strategies of the other players, weakly lower semicontinuous in all strategies, and furthermore satisfies a coercivity condition if any of the strategy sets is unbounded. The result is applied to a class of linear-quadratic differential games with no information, to prove that equilibrium points exist when the duration of these games is sufficiently small.This work was supported by a Commonwealth of Australia, Postgraduate Research Award.