二人零和连续对策上的判断与最优策略间的关系

引进了二人零和连续对策上的判断，判断块以及在判断下的最优策略等概念．研究了判断下的最优策略集与经典最优策略集之间的关系，得到了一些在理论上有趣而且有用的结果．     

效用理论在再保险中的应用

本文在Ｂｏｒｃｈ（１９９０）提出的再保险市场模型基础上讨论了效用理论在再保险中的应用,证明了最优再保险策略的充分及必要条件,并讨论了最优再保险策略的性质     

从树型集上最优停止问题到一般偏序集上最优停止问题

本文讨论了树型集上与偏序集上最优停止问题两者间的关系，证明了最优策略与最优控制变量的一一对应关系，从而导出最优策略．可在最优控制变量中取到．     

线性二次高斯系统的奇异对策

本文讨论量测噪声协方差阵和控制作用加权阵可能退化时的二次高斯系统的二人零和随机对策,给出了统一适用的次优策略,当系统成为非退化时,次优策略就收敛到最优策略.     

报酬无界的连续时间折扣马氏决策规划

本文讨论了报酬函数夫界，转移速率族一致有界，状态空间和行动集均可数的连续时间折扣马氏决策规划，文中引入了一为新的无界报酬函数，并在一新的马氏策略类中，证明了有界报酬下成立的所有结果。讨论了最优策略的结构，得到了该模型策略为最优的一个充要条件。     

模糊矩阵对策

本文考虑了三种类型的模糊矩阵对策问题，提出了最优解集和对策值对价值标准的连续依赖性，对策双方最优策略的可调和性等概念，得到了一些基本结果。模糊矩阵对策；价值标准；连续依赖性；可调和性     

连续对策之判断下的最优策略集

本文引进连续对策上的判断块、判断准确、判断下的最优策略集等概念，得到了如下几个主要结果：1.判断下的最优策略集是一个局部凸空间的非空有界闭凸集；2.两个判断下的最优策略集相等的充要条件是这两个判断位于同一判断块中；3.若局中人判断准确，则在一次性对策下不论他使用此判断下的那一个最优策略（不论是纯的还是混合的），都可无风险地取得最优赢得。     

高校提高综合实力与教师之间的博弈

建立了学校与教师之间的主从微分博弈,证明主从双方最优策略的存在唯一性及其性质.并讨论从方初始值变化时,对其最优策略及主方效用的影响程度.给出主从双方最优策略的求解方法.     

伪造风险损失欺诈博弈与最优保险合同设计

运用不完全信息动态博弈和机制设计的有关理论，建立了伪造风险损失欺诈博弈模型，研究了伪造风险损失欺诈博弈问题的纳什均衡及其保险双方的最优博弈策略。在此基础上，得出了使保险人的期望利润为零的保险定价公式，讨论了基于保险双方最优博弈策略的最优保险合同形式，证明了基于保险双方最优博弈策略的保险合同是部分保险。     

一类多步矩阵对策上的计策问题

以有序树为工具,研究了可以描述连环计,诱敌深入等多步矩阵对策上的一类计策模型.在不考虑信息环境的封闭对策系统中,及局中人对每一步矩阵对策的赢得矩阵,两个局中人的策略集合以及局中人的理性等的了解都是局中人的共同知识的假定下,提出了局中人的最优计策链及将计就计等概念,研究了局中人中计和识破计策的固有概率,讨论了局中人在什么情况下最好主动用计,在什么情况下最好从动用计以及求解最优计策等问题.     

Differential inclusions with unbounded right-hand side: Existence and relaxation theorems

For a conflict-controlled dynamical system whose motion is described by neutraltype functional differential equations in Hale’s form and for a quality index that evaluates the motion history realized up to the terminal instant of time, we consider a differential game in the class of control-with-guide strategies. We construct an approximating differential game in the class of pure positional strategies in which the motion of a conflict-controlled system is described by ordinary differential equations and the quality index is terminal. We show that the value of the approximating game gives the value of the original game in the limit, and that the optimal strategies in the original game can be constructed by using the optimal motions of the approximating game as guides.     

On a solution of the discrete resource allocation game

A discrete zero-sum two-person game of breaking attacks at defended posts (a Blotto game) is considered. An algorithm for finding a game solution in mixed strategies is described and generalized to games with budget constraints. In particular cases, explicit formulas for the value of the game and optimal strategies are obtained.     

信息披露中四方主体双边合谋的博弈分析

为了解决信息披露过程中的多个主体合谋损害投资者利益的问题,根据信息披露的过程,采用多人非合作博弈的方法构建了上市公司、媒体、会计事务所和监管机构参与双边合谋的博弈模型,均衡分析发现:每个局中人最优策略选择都取决于实现各自预期效用最大化的临界值.最后根据每个主体决策的临界值提出了治理合谋的政策建议.     

矩阵对策的公平性研究

众所周知，零和二人有限对策也称为矩阵对策。设做一个矩阵对策的两个局中人都希望对策结果尽可能公平。当两个局中人使用对策解中的策略进行对策时，如果对策结果最公平，那么这个对策解称为最优的。本文证明了最优对策解集的一些性质，然后给出矩阵对策公平度的概念并证明了它的一些有趣的性质。     

On stochastic programmed design of strategies in a differential game

A differential game /1–17/ is analyzed, in which the strategies form controls on the basis of information on the motion's history. The computation of this game's value is discussed, as also is the construction of optimal strategies on the basis of auxiliary programmed constructions which contain an artificially introduced random element. Thus, a method of stochastic programmed design, proposed in /18,19/ for differential games, is examined here from a certain general viewpoint.     

具有随机工资的养老金最优投资问题

在三种目标函数下, 研究了具有随机工资的养老金最优投资问题. 第一种是均值-方差准则, 第二种基于效用的随机微分博弈, 第三种基于均值-方差准则的随机微分博弈. 随机微分博弈问题中博弈的双方为养老金计划投资者和金融市场, 金融市场是博弈的虚拟手. 应用线性二次控制理论求得了三种目标函数下的最优策略和值函数的显式解.     

半马尔可夫对策

本文考虑半马尔可夫随机对策.在一定条件下,我们证明随机对策有值函数,两个局中人相对于折扣报酬都有最优策略.     

Zero-Sum Stochastic Games with Partial Information and Average Payoff

We consider a discrete time partially observable zero-sum stochastic game with average payoff criterion. We study the game using an equivalent completely observable game. We show that the game has a value and also we present a pair of optimal strategies for both the players.     

Alfa-cut based linear programming methodology for constrained matrix games with payoffs of trapezoidal fuzzy numbers

The purpose of this paper is to develop an effective methodology for solving constrained matrix games with payoffs of trapezoidal fuzzy numbers (TrFNs), which are a type of two-person non-cooperative games with payoffs expressed by TrFNs and players’ strategies being constrained. In this methodology, it is proven that any Alfa-constrained matrix game has an interval-type value and hereby any constrained matrix game with payoffs of TrFNs has a TrFN-type value. The auxiliary linear programming models are derived to compute the interval-type value of any Alfa-constrained matrix game and players’ optimal strategies. Thereby the TrFN-type value of any constrained matrix game with payoffs of TrFNs can be directly obtained through solving the derived four linear programming models with data taken from only 1-cut and 0-cut of TrFN-type payoffs. Validity and applicability of the models and method proposed in this paper are demonstrated with a numerical example of the market share game problem.     

Asymptotic behavior of continuous stochastic games

Summary The aim of this paper is to analyze the asymptotic behavior of the value functions of a continuous stochastic game as the number of stages grows to infinity or the discount factor approaches 1. After the setup of the problem we prove that, in both cases, the extrema of the value functions converge to the same limits. The convergence of the value functions is then obtained from the unicity of the solution of a functional problem and it is thus possible to design hypotheses that assure the convergence to a constant. This allows to assign a value to an undiscounted infinite-stage stochastic game in several senses and to show that optimal strategies are available for both players. Furthermore the boundedness of the remainders of the value function after removing the principal terms is analyzed, with appropriate hypotheses, and related to the existence of solutions of a Howard's type functional equation. This allows to show that for an infinite-stage undiscounted stochastic game optimal stationary strategies exist at least if this functional equation has some solution.