一类多元决策问题

讨论一类多元决策问题.运用对策论的分析方法和初等推理方法,在特定的条件下,得到了诸决策方获胜的充分必要条件.本文所讨论的问题具有一定的应用背景.     

一类多对多随机格斗的获胜概率

为了计算出多对多随机格斗的获胜概率,首先推导出多对多随机格斗的状态转移速率,然后应用拉普拉斯变换的性质,分别计算出在不带搜索和带搜索两种情形下,三对二随机格斗中双方各自获胜概率的实用公式.     

集群搜索-规避对抗对策的概念和性质

讨论了集群搜索-规避对抗对策的概念，明确了对策双方的策略与最优策略的定义，给出了对策的支付函数及对策的解，讨论了最优策略及对策值的存在性。     

一类搜索型随机格斗的获胜概率研究

把随机过程分析引入Lanchester方程就形成了随机格斗理论.运用随机格斗理论研究了潜艇协同隐蔽攻击水面舰艇编队获胜概率的数学模型,利用状态转移图和Laplace变换的性质推导出了2对2搜索型随机格斗中双方的获胜概率公式,并结合潜艇协同隐蔽攻击水面舰艇的实际,计算分析了格斗双方的获胜概率.利用这一公式可以得到概率上的精确解,能够被用来定量评估潜艇协同隐蔽攻击水面舰艇编队的作战效能.     

172相互独立事件同时发生的概率(第一课时)

1创设情境,提出问题 1.1创设情境 (动画)画面背景:擂台.横幅:解题大赛,奖品丰厚. 比赛双方:诸葛亮VS臭皮匠团队 比赛规则:各位参赛选手必须独立解题;团队中有一人解出即为团队获胜.     

可转移效用下的动态模糊联盟的广义核心解

利用模糊数学相关理论,对具有可转移效用的模糊合作对策进行了研究.采用调整相应系数的方法给出了此类对策的广义核心解和广义稳定集的概念,讨论了它们之间的关系.提出一种新的分配方案—不将联盟总收益分配给所有局中人,而保留一部分从而实现收益的再分配.该成果解决了对策传统解在现实应用中的局限性,特别是对现实生活中的资源再分配问题具有一定的参考和应用价值.     

广义对称对策的核仁

Schmeidler于1969年提出了核仁的概念,并把它作为合作对策的一种解,同时证明了核仁对每个对策存在唯一,且连续地依赖于对策的特征函数.1977年,Justman运用点到集映射讨论了一般n人合作对策的核仁求解问题.1981年,Dragan从平衡集入手,在理论上给出了通过解一系列线性规划而求出n人合作对策的核仁的一种算法.但是,实际上有效而可行的求解一般合作对策的核仁的算法还没有.然而,也有许多人对某类     

图的边对策着色和边对策色数

本文介绍了边对策着色,讨论了图G的边对策着色的性质.对几种特殊图类进行了讨论,分别确定链图,圈图及与圈有关的图,扇图,Petersen图的边对策色数.     

“三局两胜、五局三胜”制公平吗？

在体育比赛中 ,一局定胜负 ,虽然比赛双方获胜的概率均为二分之一 ,但是由于实验的次数太少 ,偶然因素较多 ,不能较好地展示双方实力 ,故这种赛制难以使参赛者信服 ,不能展现胜者风范 .而比赛组织者普遍采用的“三局两胜”或“五局三胜”制决定胜负的方法 ,既令参赛选手满意 ,又被观众所接受 .那么 ,这种比赛制度公平吗 ?下面用概率的观点和知识加以阐述 .由于一场比赛前两位选手的水平或胜率是一个不可测的未知数 ,因此 ,赛事组织者理应撇开比赛中甲、乙双方的原有水平 ,而认为在一次比赛中甲、乙双方获胜的概率各为 ｐ=12 ,即在一局比赛中…     

多重因素约束下的网格搜索对策问题研究

首次基于搜索成本及搜索资源等限制因素,构造局中人面向多重约束条件的可行策略集合,建立相应的搜索空间;在给定搜索点权值的基础上,考虑搜索成本与搜索成功概率等因素,构造相应的支付函数,建立多重因素约束下的网格搜索对策模型.为简化模型求解,将对策论问题转化为约束最优化问题,求解约束问题获得最优值,转化为模型的对策值,并给出双方最优混合策略.最后,给出军事想定实例,说明上述模型的实用性及方法的有效性.     

Maximizing selections from the core of a cooperative game

A core selection is a function which for each cooperative game with non-empty core selects a subset, possibly a single element, of the core. In this paper, we study selections which maximize some function or binary relation on the core. We present an axiomatic characterization of such core selections, as well as a local characterization using duality which can be applied to investigate properties of core selections. We give an application of the local characterization to a question of coalitional monotonicity of core selections.     

Cooperative Hedging in Incomplete Markets

Abstract

The problem of (partial) hedging contingent claims for a single agent is well studied. This paper studies the problem for the multiagent case in incomplete markets. For this case, a cooperative hedging game is posed as follows: First, all agents contribute some money and collect the money together as the initial total capital, then invest the initial total capital in a trading strategy, and, finally, divide the terminal wealth of the trading strategy and each of them gets a part. We give a characterization of the optimal cooperative hedging strategy and prove that the core of the cooperative hedging game, as a cooperative game with side payment, is nonempty.     

A topological duality for posets

In this paper, we present a topological duality for partially ordered sets. We use the duality to give a topological construction of the canonical extension of a poset, and we also topologically represent the quasi-monotone maps, that is, maps from a finite product of posets to a poset that are order-preserving or order-reversing in each coordinate.     

Abstract subdifferentials and some characterizations of optimal solutions

We introduce and study the subdifferential of a function at a point, with respect to a primal-dual pair of optimization problems, which encompasses, as particular cases, several known concepts of subdifferential. We give a characterization of optimal solutions of the primal problem, in terms of abstract Lagrangians, and a simultaneous characterization of optimal solutions and strong duality, with the aid of abstract subdifferentials. We give some applications to unperturbational Lagrangian duality and unperturbational surrogate duality.We wish to thank H. J. Greenberg for discussions and valuable remarks on the subject of this paper, made during his visit in Bucharest, in May 1985, within the framework of the Cooperative Exchange Agreement between the National Academy of Sciences of the USA and the Romanian Academy of Sciences.     

On duality theory in multiobjective programming

In this paper, we study different vector-valued Lagrangian functions and we develop a duality theory based upon these functions for nonlinear multiobjective programming problems. The saddle-point theorem and the duality theorem are derived for these problems under appropriate convexity assumptions. We also give some relationships between multiobjective optimizations and scalarized problems. A duality theory obtained by using the concept of vector-valued conjugate functions is discussed.The author is grateful to the reviewer for many valuable comments and helpful suggestions.     

Chip-firing based methods in the Riemann–Roch theory of directed graphs

Baker and Norine proved a Riemann–Roch theorem for divisors on undirected graphs. The notions of graph divisor theory are in duality with the notions of the chip-firing game of Björner, Lovász and Shor. We use this connection to prove Riemann–Roch-type results on directed graphs. We give a simple proof for a Riemann–Roch inequality on Eulerian directed graphs, improving a result of Amini and Manjunath. We also study possibilities and impossibilities of Riemann–Roch-type equalities in strongly connected digraphs and give examples. We intend to make the connections of this theory to graph theoretic notions more explicit via using the chip-firing framework.     

Fuzzy extensions of bargaining sets and their existence in cooperative fuzzy games

Recently, the concept of classical bargaining set given by Aumann and Maschler in 1964 has been extended to fuzzy bargaining set. In this paper, we give a modification to correct some weakness of this extension. We also extend the concept of the Mas-Colell's bargaining set (the other major type of bargaining sets) to its corresponding fuzzy bargaining set. Our main effort is to prove existence theorems for these two types of fuzzy bargaining sets. We will also give necessary and sufficient conditions for these bargaining sets to coincide with the Aubin Core in a continuous superadditive cooperative fuzzy game which has a crisp maximal coalition of maximum excess at each payoff vector. We show that both Aumann-Maschler and Mas-Colell fuzzy bargaining sets of a continuous convex cooperative fuzzy game coincide with its Aubin core.     

On Linear Programming Duality and Necessary and Sufficient Conditions in Minimax Theory

In this paper we discuss necessary and sufficient conditions for different minimax results to hold using only linear programming duality and the finite intersection property for compact sets. It turns out that these necessary and sufficient conditions have a clear interpretation within zero-sum game theory. We apply these results to derive necessary and sufficient conditions for strong duality for a general class of optimization problems. The authors like to thank the comments of the anonymous referees for their remarks, which greatly improved the presentation of this paper.     

Computing all solutions of linear generalized Nash equilibrium problems

In this paper we consider linear generalized Nash equilibrium problems, i.e., the cost and the constraint functions of all players in a game are assumed to be linear. Exploiting duality theory, we design an algorithm that is able to compute the entire solution set of these problems and that terminates after finite time. We present numerical results on some academic examples as well as some economic market models to show effectiveness of our algorithm in small dimensions.