军事欺骗战法分析的数学方法-理论*

针对军事欺骗战法定量分析困难的问题，采用基于贝叶斯统计推断和博弈均衡分析的数学方法在理论上为解决此难题提供了一种可行的方法。该方法首先定义基本概率矩阵，然后根据贝叶斯原理为交战双方构造用于统计推断的主观概率矩阵，并在由两个主观概率矩阵元素构成的偏序链与实施军事欺骗机会之间建立了对应关系。再将此关系推广到基本概率矩阵，即是否存在实施军事欺骗的机会将由基本概率矩阵元素构成的偏序链决定。数学分析表明：对于2×2基本概率矩阵，这样的偏序链长度为3、总数为8，通过对这些偏序链的分析。可以为军事欺骗战法的研究和运用提供科学依据。     

军事欺骗战法分析的数学方法-应用*

针对军事欺骗战法定量分析困难的问题,采用基于贝叶斯统计推断和博弈均衡分析的数学方法,在理论上为解决此难题提供了一种可行的方法.该方法首先定义基本概率矩阵,然后根据贝叶斯原理为交战双方构造用于统计推断的主观概率矩阵,并在由两个主观概率矩阵元素构成的偏序链与实施军事欺骗机会之间建立对应关系,再将此关系推广到基本概率矩阵,即是否存在实施军事欺骗的机会将由基本概率矩阵元素构成的偏序链决定.对理论成果的初步应用表明:通过分析由战场情报信息构成的基本概率矩阵的偏序链,可以科学地运用军事欺骗和反军事欺骗战法.     

军事欺骗战法分析的数学方法-应用

针对军事欺骗战法定量分析困难的问题,采用基于贝叶斯统计推断和博弈均衡分析的数学方法,在理论上为解决此难题提供了一种可行的方法。该方法首先定义基本概率矩阵,然后根据贝叶斯原理为交战双方构造用于统计推断的主观概率矩阵,并在由两个主观概率矩阵元素构成的偏序链与实施军事欺骗机会之间建立对应关系,再将此关系推广到基本概率矩阵,即是否存在实施军事欺骗的机会将由基本概率矩阵元素构成的偏序链决定。对理论成果的初步应用表明：通过分析由战场情报信息构成的基本概率矩阵的偏序链,可以科学地运用军事欺骗和反军事欺骗战法。     

Network routing for insurgency: An adversarial risk analysis framework

Problems in counterterrorism and corporate competition have prompted research that attempts to combine statistical risk analysis with game theory in ways that support practical decision making. This article applies these methods of adversarial risk analysis to the problem of selecting a route through a network in which an opponent chooses vertices for ambush. The motivating application is convoy routing across a road network when there may be improvised explosive devices and imperfect intelligence about their locations. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011     

The matrix game derived from the many-against-many battle

The many-against-many battle, which is a variant of the Friedman's one-against-many battle, is formulated as a two-person constant-sum game. It is shown that the matrix which expresses this game has a saddle point. Some cases are presented in which the payoff matrix of the game can be reduced. Finally, some parametrically special cases are analyzed.     

突袭敌方指挥所兵力需求仿真

甲方以特种部队突袭乙方师(旅)指挥所的行动是未来渡海登岛作战中的重要内容,能大大加快战役进程.战前通过侦察已知对方实力,通过作战模拟的方法确定规定时间内完成任务所需派遣特种部队的规模有决定性意义.采用指数-Lanchester理论模拟作战过程,在考虑气象、士气因素对作战过程影响的基础上,以甲方在消灭乙方50%有生力量后作战结束,通过MATLAB7 0仿真工具得出在一定的作战想定条件下甲方需要投入兵力的综合战斗力指数.     

One-person games of economic survival

This paper discusses the one-person economic survival game model with a discrete probability distribution for the contribution to surplus variable. The general game model and strategies in these games are examined, and necessary conditions which an undominated, stationary strategy must satisfy are obtained. For a special class of these games a mathematical formulation of the value of the game is given, and examples and theorems which relate to undominated strategies in this class are presented. This paper, in some sense, is a sequel to a portion of a paper by Shubik and Thompson [7] which appeared in this journal.     

An attack-defense game with matrix strategies

This paper presents the results and the method of analysis for an attack-defense game involving allocation of resources. Each player is assumed to have several different types of resources to be divided in optimal fashion among a fixed set of targets. The payoff function of the game is convex. The “No Soft-Spot” principle of M. Dresher, and the concept of the generalized inverse of a matrix are used to determine optimal strategies for each player and the value of the game.     

具有策略偏好的模糊双矩阵对策模型及其应用

针对局中人对策略有偏好、支付值模糊的双矩阵对策给出了一种具体的求解方法,首先根据加权算子集结得到局中人的策略偏好向量、利用模糊数排序方式将模型转化为清晰的双矩阵对策,再利用粒子群优化算法求解.最后以雷达电子对抗为例,建立了具有策略偏好的模糊双矩阵对策的作战效能评估模型,研究结果对于双方资源分配,提高作战效能具有一定的军...     

An inspection game: Taking account of fulfillment probabilities of players' aims

This paper deals with an inspection game of customs and a smuggler. The customs can take two options of assigning a patrol or not. The smuggler has two strategies of shipping its cargo of contraband or not. Two players have several opportunities to take actions during a limited number of days. When both players do, there are some possibilities that the customs captures the smuggler and, simultaneously, the smuggler possibly makes a success of the smuggling. If the smuggler is captured or there remain no days for playing the game, the game ends. In this paper, we formulate the problem into a multi‐stage two‐person zero‐sum stochastic game and investigate some characteristics of the equilibrium solution, some of which are given in a closed form in a special case. There have been some studies so far on the inspection game. However, some consider the case that the smuggler has only one opportunity of smuggling or the perfect‐capture case that the customs can certainly arrest the smuggler on patrol, and others think of a recursive game without the probabilities of fulfilling the players' purposes. In this paper, we consider the inspection game taking account of the fulfillment probabilities of the players' aims. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

基于三方动态博弈模型的网络生存防御策略优化配置

针对网络攻防环境中防御方以提高系统生存能力为目的所进行的最优生存防御策略的选取问题,提出了一种基于完全信息动态博弈理论的生存防御策略优化配置算法。将恶意攻击方、故障意外事件及防御方作为博弈的参与人,提出了一种混合战略模式下的三方动态博弈模型,对博弈的主要信息要素进行了说明,以混合战略纳什均衡理论为基础,将原纳什均衡条件式的表达式转化为可计算数值结果的表达式,并据此增加了近似的概念,最后,将提出的模型和近似纳什均衡求解算法应用到一个网络实例中,结果证明了模型和算法的可行性和有效性。     

Modified fictitious play

We describe a modification of Brown's fictitious play method for solving matrix (zero-sum two-person) games and apply it to both symmetric and general games. If the original game is not symmetric, the basic idea is to transform the given matrix game into an equivalent symmetric game (a game with a skew-symmetric matrix) and use the solution properties of symmetric games (the game value is zero and both players have the same optimal strategies). The fictitious play method is then applied to the enlarged skew-symmetric matrix with a modification that calls for the periodic restarting of the process. At restart, both players' strategies are made equal based on the following considerations: Select the maximizing or minimizing player's strategy that has a game value closest to zero. We show for both symmetric and general games, and for problems of varying sizes, that the modified fictitious play (MFP) procedure approximates the value of the game and optimal strategies in a greatly reduced number of iterations and in less computational time when compared to Brown's regular fictitious play (RFP) method. For example, for a randomly generated 50% dense skew-symmetric 100 × 100 matrix (symmetric game), with coefficients |a_ij| ≤ 100, it took RFP 2,652,227 iterations to reach a gap of 0.03118 between the lower and upper bounds for the game value in 70.71 s, whereas it took MFP 50,000 iterations to reach a gap of 0.03116 in 1.70 s. Improved results were also obtained for general games in which the MFP solves a much larger equivalent symmetric game. © 1996 John Wiley & Sons, Inc.     

A continuous submarine versus submarine game

This paper analyzes, from a game-theoretic standpoint, the simultaneous choice of speeds by a transitor and by an SSK which patrols back and forth perpendicular to the transitor's course. Using idealized acoustic assumptions and a cookie-cutter detection model which ignores counterdetection, we are able to present the problem as a continuous game, and to determine an analytic solution. The results indicate that with these assumptions, there are conditions under which neither a “go fast” nor a “go slow” strategy is optimal. The game provides a good example of a continuous game with a nontrivial solution which can be solved effectively.     

Characterization of the nucleolus for a class of n-person games

An inductive procedure is given for finding the nucleolus of an n-person game in which all coalitions with less than n-1 players are totally defeated. It is shown that, for such a game, one of three things may occur: (a) all players receive the same amount; (b) each player receives his quota, plus a certain constant (which may be positive, nerative, or zero); (c) the weakest player receives one half his quota, and the other players divide the remaining profit according to the nucleolus of a similar (n-1)-person game. It is also shown that the nucleolus of such a game yields directly the nucleolus of each derived game. An example is worked out in detail.     

Revisiting inspection game and inspector leadership through reaction networks

The inspection game is a two-player noncooperative game that models a situation where an inspector verifies whether the inspectee complies with the rules (on the assumption that the inspectee has the tendency to violate at least one of the rules). The usual approach in the analysis of this game seeks to find an optimal strategic inspection scheme for each of the two players yielding favorable payoffs. Recently, there have been some developments in the study of such games that use a mathematical structure known as reaction network involving a set of molecular species and the existing reactions among these species. In this paper, we use a reaction network to analyze the inspection game giving an alternative way of modeling the social situation. The molecular species play the role of the players' decision moves and their resulting gain or loss, while the reactions are the encounters of the decisions of the players which, as expected, yield payoffs. We reexamine the dynamics of the inspection game through the lens of reaction network theory and consider various situations that call for more detailed analyses such as equal or unequal reaction rates and inspection leadership. Conditions concerning reaction rates, initial population of decision species, benefits, and costs are determined in order to identify strategies that yield better payoffs both for the inspector and inspectee. These results illustrate practical insights rooted from the formulated simple game models.     

关于二人零和对策混合鞍点的一个新的理论和算法

本文提出了向量优超的概念,给出了二人零和对策等价的定义,得到了二人零和对策等价的两个充要条件及三个充分条件并应用本文的理论,给出了二人零和对策混合鞍点的一个新算法。     

大班表演游戏中教师指导行为的研究

游戏是幼儿园基本活动,表演游戏是一种典型的游戏活动,可以促进幼儿想象力、语言肢体表达能力的发展,教师适宜指导可促进幼儿游戏水平的提高。运用观察法和访谈法对大班表演游戏中教师的指导行为进行研究,发现教师指导主题丰富且情绪态度积极,但也存在以下问题:教师指导频次较高;教师指导控制性强,权威性高;教师对幼儿鼓励少;指导多以教师身份进行,身份单一;对表演游戏理解不足等。提出弱化指导权威,树立师幼平等观念;强化“消极”等待,把握先观察后指导的原则;加强游戏理论学习,树立角色规范意识;多采用鼓励的指导态度等建议。     

On some stocxastic tactical antisubmarine games

Mathematical models of tactical problems in Hntisubmarine Warfare (ASW) are developed. Specifically, a game of pursuit between a hunter-killer force. player 1, and a possible submarine, player 2 is considered. The game consists of a sequence of moves and terminates when player 2 is tcaught or evades player 1. When the players move they observe the actual tactical configuration of the forces (state) and each player choosa-s a tactical plan from a finite collection. This joint choice of tactical plans determines an immediate payoff and a transition probability distribution over the states. Hence an expected payoff function is defined, Formally this game is a Terminating Stochastic Game (TSG). Shapley demonstrated the existence of a value and optimal strategies (solution), An iterative technique to approximate the solution to within desired accuracy is proposed. Each iteration of the technique is obtained by solving a set of linear programs. To introduce more realism into the game several variations of the TSG are also considered. One variation is a finite TSG and linear programming techniques are employed to find the solution.     

Estimation of strategies in a markov game

In this paper a two-person Markov game, in discrete time, and with perfect state information, is considered from the point of view of a single player (player A) only. It is assumed that A's opponent (player B) uses the same strategy every time the game is played. It is shown that A can obtain a consistent estimate of B's strategy on the basis of his past experience of playing the game with B. Two methods of deriving such an estimate are given. Further, it is shown that using one of these estimates A can construct a strategy for himself which is asymptotically optimal. A simple example of a game in which the above method may be useful is given.     

基于模糊双矩阵对策的作战效能评估模型

讨论了策略集清晰、支付值模糊的模糊双矩阵对策的一种求解方法，并以某型导弹混编群对抗ARM（反辐射导弹）及载机为案例进行研究，建立了基于模糊双矩阵对策的作战效能评估模型，研究结果对于双方资源分配，提高作战效能具有一定的军事应用价值。