New product introduction against a predator: A bilevel mixed‐integer programming approach

We consider a scenario with two firms determining which products to develop and introduce to the market. In this problem, there exists a finite set of potential products and market segments. Each market segment has a preference list of products and will buy its most preferred product among those available. The firms play a Stackelberg game in which the leader firm first introduces a set of products, and the follower responds with its own set of products. The leader's goal is to maximize its profit subject to a product introduction budget, assuming that the follower will attempt to minimize the leader's profit using a budget of its own. We formulate this problem as a multistage integer program amenable to decomposition techniques. Using this formulation, we develop three variations of an exact mathematical programming method for solving the multistage problem, along with a family of heuristic procedures for estimating the follower solution. The efficacy of our approaches is demonstrated on randomly generated test instances. This article contributes to the operations research literature a multistage algorithm that directly addresses difficulties posed by degeneracy, and contributes to the product variety literature an exact optimization algorithm for a novel competitive product introduction problem. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2009     

联合补充博弈的费用分摊

就一个仓库、多个零售商,对联合订货费用函数的模型进行分析,给出了一个求解最佳订货周期的多项式时间的算法,且算法的时间复杂性为O（nlogn）。利用文献[8]中的技巧,给出了该库存博弈的核。     

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.     

改进博弈论的舰载无人机编队协同对海突击目标分配

目标分配问题是UAV自主控制的重要问题。针对舰载无人机编队协同对海突击目标分配问题,首先建立了基于离散动态贝叶斯网络的目标价值评估模型,在此基础上构建了舰载无人机编队的益损值矩阵,设计了舰载无人机编队协同对海突击目标分配的决策函数,提出了一种基于改进博弈论的目标分配方法,为4种不同约束条件下的目标分配问题分别设计了算法。最后对所建立的目标价值评估模型和改进博弈论的目标分配算法进行了实例仿真,仿真结果表明了模型和算法的可行性和有效性。     

The solution to an open problem for a caching game

In a caching game introduced by Alpern et al. (Alpern et al., Lecture notes in computer science (2010) 220–233) a Hider who can dig to a total fixed depth normalized to 1 buries a fixed number of objects among n discrete locations. A Searcher who can dig to a total depth of h searches the locations with the aim of finding all of the hidden objects. If he does so, he wins, otherwise the Hider wins. This zero‐sum game is complicated to analyze even for small values of its parameters, and for the case of 2 hidden objects has been completely solved only when the game is played in up to 3 locations. For some values of h the solution of the game with 2 objects hidden in 4 locations is known, but the solution in the remaining cases was an open question recently highlighted by Fokkink et al. (Fokkink et al., Search theory: A game theoretic perspective (2014) 85–104). Here we solve the remaining cases of the game with 2 objects hidden in 4 locations. We also give some more general results for the game, in particular using a geometrical argument to show that when there are 2 objects hidden in n locations and n→∞, the value of the game is asymptotically equal to h/n for h≥n/2. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 23–31, 2016     

Timing of information acquisition in a competitive environment

This article investigates the impact of timing on sellers' information acquisition strategies in a duopoly setting. Market uncertainty is captured by a representative consumer who has a private taste for the product's horizontal attribute, and both sellers can acquire this information either before (ex‐ante acquisition) or after (ex‐post acquisition) observing their own product qualities. We identify several conflicting effects of information acquisition that vary significantly in its timing and market characteristics. In the monopoly scenario, information acquisition is unambiguously beneficial and ex‐ante acquisition is the dominant option, because it helps a seller not only design the proper product but also craft better pricing strategy. By contrast, when there is competition, information acquisition eliminates the buffer role of market uncertainty and leads to the fiercest production or pricing competition, which makes the subsequent effects of acquisition detrimental, and a seller's payoff is nonmonotonic in terms of its acquisition cost. Moreover, compared with the ex‐ante information acquisition, ex‐post information acquisition normally generates higher sellers' equilibrium payoffs by postponing the timing of acquisition and maintaining product differentiation. Nonetheless, ex‐post information acquisition also provides the seller with greater acquisition incentive and occasionally makes him worse off than that in the ex‐ante scenario. Thus, in a competitive environment, having the option of information acquisition and flexibility in its timing can be both detrimental and irresistible. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 3–22, 2016     

A strategic model for state compliance verification

The theory of directed graphs and noncooperative games is applied to the problem of verification of State compliance to international treaties on arms control, disarmament and nonproliferation of weapons of mass destruction. Hypothetical treaty violations are formulated in terms of illegal acquisition paths for the accumulation of clandestine weapons, weapons‐grade materials or some other military capability. The paths constitute the illegal strategies of a sovereign State in a two‐person inspection game played against a multi‐ or international Inspectorate charged with compliance verification. The effectiveness of existing or postulated verification measures is quantified in terms of the Inspectorate's expected utility at Nash equilibrium. A prototype software implementation of the methodology and a case study are presented. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 260–271, 2016     

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。     

航天器轨道追逃态势分析的水平集方法

航天器轨道追逃是当前航天动力学与控制领域的研究热点。针对轨道追逃定性问题开展研究,提出了一种综合运用降维动力学模型和后向可达集的航天器近距离轨道追逃态势分析方法,以支撑任务可行性分析;通过在视线旋转坐标系下推导博弈系统降维动力学模型,建立近距离追逃定性问题模型,减少了状态空间维度;使用目标集的后向可达集描述捕获区并划分追逃状态空间,基于水平集方法建立可达集在降维动力学模型中演化的动态HJI(Hamilton-Jacobi-Isaacs)偏微分方程,并设计WENO-TVD求解器数值计算HJI方程终值问题粘性解,完成了追逃目标集的准确描述并避免了可能出现的终端奇异现象。通过不同推力构型的追逃场景数值仿真验证了方法的有效性,展现了一次计算批量化处理初始态势的功能。     

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.