异类值多目标二人零和约束矩阵对策及求解方法

矩阵对策是对策理论的一个重要分支。本文根据多目标决策和模糊对策理论,研究了支付值是异类值情况下的多目标二人零和约束矩阵对策问题。文章基于不同的排序方法将直觉模糊值、三角直觉模糊数和区间直觉模糊数的多目标对策清晰化,然后根据理想点法求解多目标规划问题。通过一个数值实例说明了该方法的有效性和实用性。     

模糊二人零和对策的纳什均衡求解

用三角模糊数刻画二人零和对策支付值的不确定性,提出了计算模糊二人零和对策纳什均衡解的多目标规划方法.给出了一种基于区间数比较的三角形模糊数排序方法,根据该方法将模糊二人零和对策转化为多目标线性规划.通过一个数值实例说明了该方法的有效性和实用性.     

模糊值二人零和对策的Nash均衡策略

我们将在Ramik定义的模糊最大序关系基础上研究模糊环境中的二人零和对策。在非对称模糊数基础上,引入模糊环境中的几种Nash均衡策略,讨论各种均衡策略存在的充要条件。并引入含参变量确定性矩阵对策及其均衡策略的概念,讨论含参变量确定性矩阵对策的Nash均衡策略和模糊值矩阵对策的均衡策略的关系。     

支付值为直觉模糊集的矩阵对策的线性规划求解方法

研究支付值为直觉模糊集的矩阵对策的求解方法.提出了支付值为直觉模糊集的矩阵对策的定义,并根据多目标优化的帕雷托最优解的概念定义了直觉模糊矩阵对策解的概念.进一步根据解的定义,证明了求此对策问题的解转化为求线性规划问题的最优解.通过一个数值实例说明了该方法的有效性和实用性.     

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.     

具有风险偏好的梯形直觉模糊双矩阵对策模型及解法

在对策问题中,行动方案的选择不可避免的需要对预期支付值(收益值)进行估计和排序,且选择结果往往受到现实局中人风险偏好程度的影响.因此,该文针对局中人具有风险偏好及支付值为梯形直觉模糊的双矩阵对策进行了模型及求解方法的探讨.首先,提出了具有风险偏好的梯形直觉模糊数排序方法,再利用双线性规划求解方法,对梯形直觉模糊双矩阵对策进行求解.最后以企业营销策略选择为例,表明了该方法的有效性和实用性.     

直觉模糊支付合作对策的核仁解

本文主要研究支付值为直觉模糊集的合作对策问题及其模糊核仁解.首先定义了直觉模糊集的得分函数和精确函数,并给出其排序方法,得到基于直觉模糊集的合作对策模型和适合这种模型的相应定义,同时提出了直觉模糊核仁解的概念;其次运用新的排序方法将求核仁解的问题转化为求解双目标非线性规划问题;最后通过实例分析验证了该方法的可行性和有效性。     

连续区间策略下二人零和对策问题研究

考虑连续区间策略下的二人零和对策问题,研究其均衡策略的存在性。首先分析了完全信息下的二人零和对策问题,证明了该问题均衡策略的存在性并给出求解方法。然后进一步研究了收益函数不确定的不完全信息二人零和对策问题,在各局中人都认为对方是风险厌恶型的假设下,分析该类对策纯策略均衡的存在性,并通过研究纯策略均衡存在的充要条件给出判断并寻找纯策略均衡解的方法。最后给出一个数值算例,验证本文所提出方法的可行性。     

多目标线性生产规划的模糊联盟对策

研究多目标生产规划的模糊联盟对策的求解问题,提出了求解多目标模糊联盟对策的Shapley值方法.通过建立多目标线性生产规划的模糊联盟对策模型,提出了多目标对策转化为多个单目标对策的权重分析法.结合多目标线性生产规划问题的实例,给出不同权重系数下局中人合作的利益分配策略.     

B矩阵对策

提出了一类局中人都设定有得失控制值的二人零和有限对策,即B矩阵对策.引入了稳妥策略、弱稳妥策略等概念.给出了B矩阵对策的数学模型、有关理论和求解方法.最后,还给了一个计算例子.     

On Nash Equilibrium Strategy of Two-person Zero-sum Games with Trapezoidal Fuzzy Payoffs

In this paper, we investigate Nash equilibrium strategy of two-person zero-sum games with fuzzy payoffs. Based on fuzzy max order, Maeda and Cunlin constructed several models in symmetric triangular and asymmetric triangular fuzzy environment, respectively. We extended their models in trapezoidal fuzzy environment and proposed the existence of equilibrium strategies for these models. We also established the relation between Pareto Nash equilibrium strategy and parametric bi-matrix game. In addition, numerical examples are presented to find Pareto Nash equilibrium strategy and weak Pareto Nash equilibrium strategy from bi-matrix game.     

Correlated equilibria in some classes of two-person games

A correlated equilibrium in a two-person game is “good” if for everyNash equilibrium there is a player who prefers the correlated equilibrium to theNash equilibrium. If a game is “best-response equivalent” to a two-person zero-sum game, then it has no good correlated equilibria. But games which are “almost strictly competitive” or “order equivalent” to a two-person zero-sum game may have good correlated equilibria.     

On a dynamic fractional game

Consider a two-person zero-sum game constructed by a dynamic fractional form. We establish the upper value as well as the lower value of a dynamic fractional game, and prove that the dual gap is equal to zero under certain conditions. It is also established that the saddle point function exists in the fractional game system under certain conditions so that the equilibrium point exists in this game system.     

Stationary,completely mixed and symmetric optimal and equilibrium strategies in stochastic games

In this paper, we address various types of two-person stochastic games—both zero-sum and nonzero-sum, discounted and undiscounted. In particular, we address different aspects of stochastic games, namely: (1) When is a two-person stochastic game completely mixed? (2) Can we identify classes of undiscounted zero-sum stochastic games that have stationary optimal strategies? (3) When does a two-person stochastic game possess symmetric optimal/equilibrium strategies? Firstly, we provide some necessary and some sufficient conditions under which certain classes of discounted and undiscounted stochastic games are completely mixed. In particular, we show that, if a discounted zero-sum switching control stochastic game with symmetric payoff matrices has a completely mixed stationary optimal strategy, then the stochastic game is completely mixed if and only if the matrix games restricted to states are all completely mixed. Secondly, we identify certain classes of undiscounted zero-sum stochastic games that have stationary optima under specific conditions for individual payoff matrices and transition probabilities. Thirdly, we provide sufficient conditions for discounted as well as certain classes of undiscounted stochastic games to have symmetric optimal/equilibrium strategies—namely, transitions are symmetric and the payoff matrices of one player are the transpose of those of the other. We also provide a sufficient condition for the stochastic game to have a symmetric pure strategy equilibrium. We also provide examples to show the sharpness of our results.     

基于Choquet积分的直觉模糊联盟合作博弈的Shapley值

本文针对联盟是直觉模糊集的合作博弈Shapley值进行了研究.通过区间Choquet积分得到直觉模糊联盟合作博弈的特征函数为区间数,并研究了该博弈特征函数性质。根据拓展模糊联盟合作博弈Shapley值的计算方法,得到直觉模糊联盟合作博弈Shapley值的计算公式,该计算公式避免了区间数的减法。进一步证明了其满足经典合作博弈Shapley值的公理性。最后通过数值实例说明本文方法的合理性和有效性。     

基于联合作战兵力配置的非合作博弈研究

基于联合作战实体定量分析的作战能力指数组合期望效用,研究了联合作战任务兵力配置问题,建立了二人零和参数博弈模型,并讨论了模型构建的理论依据与算法.     

Perfect information two-person zero-sum markov games with imprecise transition probabilities

Based on an extension of the controlled Markov set-chain model by Kurano et al. (in J Appl Prob 35:293–302, 1998) into competitive two-player game setting, we provide a model of perfect information two-person zero-sum Markov games with imprecise transition probabilities. We define an equilibrium value for the games formulated with the model in terms of a partial order and then establish the existence of an equilibrium policy pair that achieves the equilibrium value. We further analyze finite-approximation error bounds obtained from a value iteration-type algorithm and discuss some applications of the model.