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.     

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.     

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     

Discretization of the continuous ambush game

This article further considers the two‐person continuous ambush game introduced by Ruckle. This article extends the work of Ruckle, Baston and Bostock, and Lee by considering the game for a general number of barriers. By supplanting optimal strategies from a discretized version of the game, we show that there always exists a value for the game, which, furthermore, can be found using linear programming techniques. Further to this, we show that the discrete ambush game considered by Garnaev has the same value as a continuous game, allowing many new results to be obtained in both games. © 2003 Wiley Periodicals, Inc. Naval Research Logistics 50: 515–529, 2003     

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.     

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.     

Initial point search on weighted trees

An initial point search game on a weighted graph involves a searcher who wants to minimize search and travel costs seeking a hider who wants to maximize these costs. The searcher starts from a specified vertex 0 and searches each vertex in some order. The hider chooses a nonzero vertex and remains there. We solve the game in which the graph is a simple tree, and use this solution to solve a search game on a tree in which each branch is itself a weighted graph with a certain property, and the searcher is obliged to search the entire branch before departing. © 1994 John Wiley & Sons, Inc.     

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.     

基于成品油有限竞争市场的军油筹措战略研究

对国家成品油市场进行分析,认为目前国内成品油市场是典型的双寡头垄断有限竞争市场。通过对成品油市场主体厂商行为博弈的讨论,得出产量博弈的状况近期不会出现,价格博弈将使企业走入囚徒困境的结论。根据分析针对性地提出军油筹措战略,为相关决策提供参考。     

A price leadership method for solving the inspector's non-constant-sum game

An inspector's game is a non-constant-sum two-person game in which one player has promised to perform a certain duty and the other player is allowed to inspect and verify occasionally that the duty has indeed been performed. A solution to a variant of such a game is given in this paper, based on the assumption that the inspector can announce his mixed strategy in advance, if he so wishes, whereas the other player, who has already given his promise, cannot threaten by explicitly saying that he will not keep his word.     

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.     

基于贝叶斯混合博弈的空袭火力资源分配决策模型

从博弈论的角度出发研究空袭火力资源的分配问题,针对空袭编队和防空火力单元攻防对抗过程中存在的不确定性、静态性以及动态性,建立基于贝叶斯混合博弈的空袭对抗火力分配模型。通过构造贝叶斯混合博弈树,采用逆向回溯法分别建立不同的博弈分析模型,利用混合粒子群算法求解那什均衡。仿真结果表明:以博弈论为背景研究空袭作战火力分配问题,符合真实的作战坏境,有效性好,有较高的理论应用价值。     

论寓教于乐的教学理念与设计

“寓教于乐”是一种理想的教育教学目标，也是大学教学改革的重点，教育游戏的出现为教学拓宽了道路，实践着“寓教于乐”的理念。通过参阅大量文献资料，对教育游戏的概念与现状进行了阐述，并提出了教育游戏的设计理念与策略，为教育游戏的设计提供指导和帮助。     

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.     

The discrete evasion game with three-move lag

The discrete evasion game with three-move lag, formulated over 30 years ago, was one of the earliest games with time-lag complications. This game remains unsolved even though it is well known that the game has a value. In this article we obtain an upper bound for the value by constructing a strategy which consists of 400 conditional probabilities for the minimizing player. This is believed to be the best upper bound known.     

Localization of optimal strategies in certain games

Assume the payoffs of a matrix game are concave in the index of the maximizing player. That player is shown to have an optimal strategy which uses at most two consecutive pure strategies, identifiable through approximate solution of a related continuous game. Generalizations are given, and the results are applied to a motivating hidden-target model due to Shapley. © 1994 John Wiley & Sons, Inc.     

基于对策论的C4ISR系统作战效能评估方法

C4ISR系统在现代战争中的重要作用使得其评价问题得到了前所未有的重视.但C4ISR系统的复杂性使得大多研究仅限于其自身效能,而对使用效能特别是作战效能的评估则关注较少.通过对C4ISR系统效能评估的分析和研究,提出了一种基于对策论的C4ISR系统作战效能评估方法,利用矩阵对策构建不同作战策略的效能评估模型,实现了对抗环境中C4ISR系统作战效能的动态评估,并给出了模型的分析与求解方法.     

Congestion tolls: Equilibrium and optimality

An example of a network with flow costs depending on congestion is presented for which no system of tolls and subsidies exists which can ensure that all equilibria in the game of route selection are Pareto optimal.