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.     

Some implications of pricing bundles

In this article, we consider a problem in which two suppliers can sell their respective products both individually and together as a bundle, and study the impact of bundle pricing. Four pricing models (centralized, decentralized, coop–comp, and comp–coop) are analyzed with regard to the competition formats and sequences. As one would expect, the firms are always better off when pricing decisions are centralized. However, rather surprisingly, we find that firms may be worse off if the bundle prices are set in a cooperative way; we provide analytical characterization of those instances. Numerical studies show that these insights also hold for some nonlinear demand. © 2013 Wiley Periodicals, Inc. Naval Research Logistics, 2013     

公安边防部队缉毒斗争中的博弈分析

当前,我国毒品犯罪活动呈现出集团化、隐秘化、有组织化和跨国化等复杂特征,境内外社会环境、贩毒集团和执法者之间存在着彼此交错的关系,使得公安边防部队缉毒斗争面临着严峻的形势和挑战。在整合多位学者的理论观点和现实研究基础之上,基于博弈论的成熟理论,紧密结合公安边防部队缉毒斗争实际,构建了公安边防部队与贩毒集团之间的博弈模型,并对其进行深入分析,从微观角度为公安边防部队缉毒斗争实际提供有效参考和决策依据。     

联合作战中作战单元决策演化博弈研究

利用演化博弈理论,探讨了联合作战中担负相同作战任务的作战单元间其策略选择根据利益变化的演化过程,建立了复制动态方程并求得平衡点解,通过复制动态的相位图直观反映了博弈的演化稳定策略,并通过Malab软件对作战单元策略选择与收益关系进行了仿真,其行为选择的演化结果与相位图展示具有一致性。研究结论表明,收益大小及变化是作战单元策略改变的重要依据,最后针对提高作战单元间的策略稳定性提出对策建议.     

基于博弈论计算机网络对抗问题研究

针对日益普遍和多样的网络攻击行为,如何对网络各种攻防过程进行分析已逐渐成为热点研究方向。在对计算机网络对抗问题复杂性表现和产生根源进行探讨基础上,从完全信息静态博弈、完全信息动态博弈、不完全信息静态博弈、不完全信息动态博弈4个视角,对计算机网络对抗问题进行分类论述,对各解决方法进行了综合比较,并对今后的研究进行了展望。     

Information disclosure with endogenous channel structure

This article investigates the firms' optimal quality information disclosure strategies in a supply chain, wherein the supplier may encroach into the retail channel to sell products directly to end consumers. We consider two disclosure formats, namely, retailer disclosure (R-C) and supplier disclosure (S-C), and examine the optimal disclosure format from each firm's perspective. We show that either firm prefers to delegate the disclosure option to its partner when the supplier cannot encroach. However, the threat of supplier encroachment dramatically alters the firm's preference of disclosure. The supplier may prefer the S-C format to the R-C format when the entry cost is low and the disclosure cost is high to achieve a higher quality information transparency. Meanwhile, the retailer may prefer the R-C format to the S-C format when the entry cost is intermediate to deter the possible encroachment of the supplier. In this sense, the firms' preferences of disclosure format can be aligned due to the threat of supplier encroachment. The consumer surplus is always higher under the S-C format while either disclosure format can lead to a higher social welfare. We also consider an alternative scenario under which the supplier encroaches after the product quality information is disclosed. An interesting observation appears that the supplier may encroach when the product quality is low but foregoes encroachment when the product quality gets higher.     

非对称Colonel Blotto博弈模型下的多信道功率分配抗干扰

针对智能干扰条件下传输速率固定的通信系统多信道功率分配问题,建立了非对称Colonel Blotto博弈模型。在完全信息条件下,推导出了各种功率预算约束下通信方和干扰方的等效单信道最优功率分配策略,进而证明了通信方和干扰方存在唯一混合纳什均衡策略,并求得了纳什均衡收益。基于等效单信道最优功率分布,提出了一种多重扫描直接列元素交换算法,可以快速构建多信道混合功率分配矩阵,且相比于线性规划方法,可适应更多的信道数和更广的功率分布范围。通过数值仿真,验证了所提多信道混合功率分配矩阵构造算法的有效性及多信道功率分配策略的最优性。     

Capacity games for partially complementary products under multivariate random demands

In this study, we consider n firms, each of which produces and sells a different product. The n firms face a common demand stream which requests all their products as a complete set. In addition to the common demand stream, each firm also faces a dedicated demand stream which requires only its own product. The common and dedicated demands are uncertain and follow a general, joint, continuous distribution. Before the demands are realized, each firm needs to determine its capacity or production quantity to maximize its own expected profit. We formulate the problem as a noncooperative game. The sales price per unit for the common demand could be higher or lower than the unit price for the dedicated demand, which affects the firm's inventory rationing policy. Hence, the outcome of the game varies. All of the prices are first assumed to be exogenous. We characterize Nash equilibrium(s) of the game. At the end of the article, we also provide some results for the endogenous pricing. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 59: 146–159, 2012     

临近空间防空导弹制导律

基于临近空间防空导弹,在拦截高空高速大机动目标的条件下,对导弹的制导律进行了研究。给出了微分对策制导律的理论知识及其具体算法,通过Simulink工具进行模块化建模,并将制导律模型引入导弹六自由度模型中进行仿真,对比分析导弹飞行轨迹和需用过载,表明微分对策制导律要比常用的比例导引制导律更优。