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1.
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.  相似文献   

2.
矩阵计策的支撑解系   总被引:12,自引:0,他引:12  
姜殿玉 《经济数学》2001,18(1):33-37
令[aij]n×n是二人零和对策的支付矩阵.局中人1可用其"计策"得到最大支付a=max{aij|1≤i≤n,1≤j≤n},然而,一个开放问题是如何找到全体计策解,本文首先引进计策解系的一种特殊类型--支撑解系.然后研究支撑解系的特征、性质、代数结构.最后给出寻找全体基本支撑解系的一个算法.  相似文献   

3.
矩阵对策的两个注记   总被引:6,自引:1,他引:5  
设(x*,y*)是以A=[aij]m×n为赢得矩阵G的对策解,则当局中人1,2各自独立地使用其最优策略x*=(x*1,x*2,…,xmn),y*=(y*1,y*2,…,y*n)时,局中人1的赢得期望为对策值v*=x*Ay*T.若局中人双方使用使得方差D(x*,y*)=∑∑(aij-v*)2x*iy*j达最小的对策解(x*,y*),则其赢得靠近v*的概率达到最大.以O记使方差达到最小的对策解的集合.若O满足(x(1),y(1)),(x(2),y(2))∈O蕴涵(x(1),y(2)),(x(2),y(1))∈O,则说O是可换的.本文首先证明了若矩阵对策G有纯解,则O是可换的.然后证明了如果限定局中人1在其混合扩充策略集的一个非空紧凸子集X中选取策略,那么存在X的一个非空紧子集O(X),它是有限个非空互不相交紧凸集之并,使得只要局中人1使用O(X)中的策略,那么在最坏的情况下可以取得最好的赢得.  相似文献   

4.
基于一个历史实例及假定:①三步矩阵对策中赢得矩阵都不变,②每步都是局中人1先行动,③对于每步对策,局中人2观测不到对手究竟使用了何策略;但局中人1可以观测到对手所用的策略,建立了三步矩阵对策上的无中生有计(《三十六计》中的第七计)的对策模型.研究了当局中人2中计,半识破和完全识破对手的无中生有计时的赢得和所用的策略的情况.并用上述实例对模型作了说明.  相似文献   

5.
连续对策之判断下的最优策略集   总被引:7,自引:0,他引:7  
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。  相似文献   

6.
矩阵对策的公平性研究   总被引:3,自引:1,他引:2  
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。  相似文献   

7.
本文用刺激性(感)来描述游戏一个零和对策的两个局中人的风险性和侥幸取胜性,游戏不同的零和对策可能有不同的刺激感,刺激性越大,对策结果的公平性越小;反之亦然,本文解决了如下问题;(1)刺激性和公平性的数学描述是什么?(2)局中人如何保证他们的一局对策的对策结果是最公平的或最有刺激感的?(3)如果两个局中人希望对策结果尽量公平或尽量有刺激感,他们最好从给定的连续对策中选择哪个?  相似文献   

8.
对于正方形[0,2]×[0,2]上的连续对策,将局中人的非纯策略(概率分布函数)的导数称为这个局中人的策略密度(概率密度函数).建立了这种连续对策的最大熵理论.主要证明了当每个局中人都没有最优纯策略时,具有最大熵的最优策略密度集合的非空紧凸性,研究了最优策略密度的最大熵,给出一类带有最大熵的连续对策.  相似文献   

9.
罗尔定理是说,若f(x)满足:(1)在闭区间[a,b]上连续,(2)在开区间(a,b)内可导,(3)区间端点处的值相等,即f(a)=f(b),则至少存在一点,使得.如果将定理的条件(2)改成f(x)在(a,b)内右导数存在,其它两条不变,是否也存在一点,使得呢?一般不可以.考察函数.显然,(1)f(X)在上连续,切我们有下面定理:定理若函数f(x)在闭区间上连续;在开区间(a,b)内右导数存在且连续(即:存在且连续);且f(a)=f(b),则至少存在一点,使得证明由f(x)在[a,b]上连续,必取到最大值M,最小值m,这样只有两种情形…  相似文献   

10.
本文通过在有向图上每个状态结点处定义合作函数,运用Berge C的关于图匕对策中策略的概念,在网格状有向图上考察部分合作动态对策.局中人在对策进程中将采取部分合作而不是完全合作,部分合作的主要特征是每个局中人的行为是合作行动与单独行动的组合.本文合作函数的设定允许局中人加入某个联盟之后再脱离该联盟,同时给出了有向图上部分合作对策的值、最优路径的算法及示例.  相似文献   

11.
We prove that if one or more players in a locally finite positional game have winning strategies, then they can find it by themselves, not losing more than a bounded number of plays and not using more than a linear-size memory, independently of the strategies applied by the other players. We design two algorithms for learning how to win. One of them can also be modified to determine a strategy that achieves a draw, provided that no winning strategy exists for the player in question but with properly chosen moves a draw can be ensured from the starting position. If a drawing- or winning strategy exists, then it is learnt after no more than a linear number of plays lost (linear in the number of edges of the game graph). Z. Tuza’s research has been supported in part by the grant OTKA T-049613.  相似文献   

12.
We consider the following modification of annihilation games called node blocking. Given a directed graph, each vertex can be occupied by at most one token. There are two types of tokens, each player can move only tokens of his type. The players alternate their moves and the current player i selects one token of type i and moves the token along a directed edge to an unoccupied vertex. If a player cannot make a move then he loses. We consider the problem of determining the complexity of the game: given an arbitrary configuration of tokens in a planar directed acyclic graph (dag), does the current player have a winning strategy? We prove that the problem is PSPACE-complete.  相似文献   

13.
We study a zero-sum stochastic game where each player uses both control and stopping times. Under certain conditions we establish the existence of a saddle point equilibrium, and show that the value function of the game is the unique solution of certain dynamic programming inequalities with bilateral constraints.  相似文献   

14.
Various models of 2-player stopping games have been considered which assume that players simultaneously observe a sequence of objects. Nash equilibria for such games can be found by first solving the optimal stopping problems arising when one player remains and then defining by recursion the normal form of the game played at each stage when both players are still searching (a 2 × 2 matrix game). The model considered here assumes that Player 1 always observes an object before Player 2. If Player 1 accepts the object, then Player 2 does not see that object. If Player 1 rejects an object, then Player 2 observes it and may choose to accept or reject it. It is shown that such a game can be solved using recursion by solving appropriately defined subgames, which are played at each moment when both players are still searching. In these subgames Player 1 chooses a threshold, such that an object is accepted iff its value is above this threshold. The strategy of Player 2 in this subgame is a stopping rule to be used when Player 1 accepts this object, together with a threshold to be used when Player 1 rejects the object. Whenever the payoff of Player 1 does not depend on the value of the object taken by Player 2, such a game can be treated as two optimisation problems. Two examples are given to illustrate these approaches.  相似文献   

15.
We present results concerning winning strategies and tactics in club games on ??λ. We show that there is generally no winning tactic for the player trying to get inside the club. The bound‐countable game turns out to be rather fruitful and adds to some previous results about the construction of elementary substructures and their localization in certain intervals. We show that Player II has a winning strategy in the bound‐countable game, thus establishing a new ZFC result. The applications given are new proofs for two cardinal diamonds and the impossibility of collapsing cardinals to ?2 under certain conditions (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

16.
A two-person zero-sum infinite dimensional differential game of infinite duration with discounted payoff involving hybrid controls is studied. The minimizing player is allowed to take continuous, switching and impulse controls whereas the maximizing player is allowed to take continuous and switching controls. By taking strategies in the sense of Elliott-Kalton, we prove the existence of value and characterize it as the unique viscosity solution of the associated system of quasi-variational inequalities.  相似文献   

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