一个组合对策问题的解

本文求解如下的组合对策问题:设有一堆棋子,总数N 是奇数,甲乙两人轮流取子,每人每次可取一颗、二颗,最多可取s 颗,但不能不取,直至取完后分别来数甲乙两人所取棋子的总数,总数为奇数者获胜。站在甲的立场上考虑获胜的策略,文中解决了如下两个问题:(Ⅰ)总数N 应是什么样的奇数,甲才有获胜策略;(Ⅱ)当N 一定时,甲应采取什么样的策略取子,才能获胜。     

Efficiency of equilibria in restricted uniform machine scheduling with total weighted completion time as social cost

In the last decade, there has been much progress in understanding scheduling problems in which selfish jobs aim to minimize their individual completion time. Most of this work has focused on makespan minimization as social objective. In contrast, we consider as social cost the total weighted completion time, that is, the sum of the agent costs, a standard definition of welfare in economics. In our setting, jobs are processed on restricted uniform parallel machines, where each machine has a speed and is only capable of processing a subset of jobs; a job's cost is its weighted completion time; and each machine sequences its jobs in weighted shortest processing time (WSPT) order. Whereas for the makespan social cost the price of anarchy is not bounded by a constant in most environments, we show that for our minsum social objective the price of anarchy is bounded above by a small constant, independent of the instance. Specifically, we show that the price of anarchy is exactly 2 for the class of unit jobs, unit speed instances where the finite processing time values define the edge set of a forest with the machines as nodes. For the general case of mixed job strategies and restricted uniform machines, we prove that the price of anarchy equals 4. From a classical machine scheduling perspective, our results establish the same constant performance guarantees for WSPT list scheduling. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012     

Lateral capacity exchange and its impact on capacity investment decisions

We study the problem of capacity exchange between two firms in anticipation of the mismatch between demand and capacity, and its impact on firm's capacity investment decisions. For given capacity investment levels of the two firms, we demonstrate how capacity price may be determined and how much capacity should be exchanged when either manufacturer acts as a Stackelberg leader in the capacity exchange game. By benchmarking against the centralized system, we show that a side payment may be used to coordinate the capacity exchange decisions. We then study the firms' capacity investment decisions using a biform game framework in which capacity investment decisions are made individually and exchange decisions are made as in a centralized system. We demonstrate the existence and uniqueness of the Nash equilibrium capacity investment levels and study the impact of firms' share of the capacity exchange surplus on their capacity investment levels.© 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

基于博弈论的装备采办成本控制问题研究

从武器装备采办的理论需求出发,以博弈论为理论工具,对武器装备采办过程中的生产成本控制问题进行了分析;建立了基于激励的生产成本控制模型,并对成本控制模型的特点进行了分析和解释;针对军方在激励合同执行过程中有可能出现的2类错误,对成本控制模型进行了优化。在非对称信息条件下,优化后的成本控制模型不但能有效减少2类错误的发生,而且可提高军方装备采办效用,减少代理方合同风险。     

基于博弈论的装备采购定价激励模型

不同的定价方式和定价参数的选择对于承包商会起到不同程度的激励作用。为提高装备采购效益,在承包商追求效用最大化假设的基础上,建立了装备采购完全信息动态博弈模型。对价格、成本、承包商努力程度和承包商效用之间的关系进行了研究,证明了成本分担和固定价格的定价方式能够有效激励承包商提高自身努力水平降低成本,并提出了2种定价方式的参数定量计算方法。     

对抗仿真中防空导弹微分对策模型研究

针对防空导弹与目标的空间对抗,建立了防空导弹微分对策空间对抗模型,并推算得到了最优策略,运用自适应神经网络评判方法对模型进行求解,通过给定条件下的仿真证明了该算法的有效性,显示了该模型可应用于防空导弹与目标的空间对抗问题。     

基于博弈论的C~4ISR系统监视与侦察功能模型

监视与侦察已成为现代C4ISR系统的重要组成部分,传统的监视与侦察系统效能分析方法存在模型难以建立、结果不准确等问题,很难量化其与作战效果之间的影响。在对基于Lanchester方程的C4ISR系统建模方法进行研究的基础上,提出了反映监视与侦察功能的Lanchester方程模型,并引入博弈论分析了战场上信息的不对称对交战结果的影响,克服了描述C4ISR系统的Lanchester方程没有考虑作战单元、对手和环境间的动态交互以及数学结构简单的缺点。仿真结果验证了模型的有效性。     

Should competing firms reveal their capacity?

In this article, we explore when firms have an incentive to hide (or reveal) their capacity information. We consider two firms that aim to maximize profits over time and face limited capacity. One or both of the firms have private information on their own capacity levels, and they update their beliefs about their rival's capacity based on their observation of the other firm's output. We focus on credible revelation mechanisms—a firm may signal its capacity through overproduction, compared to its myopic production levels. We characterize conditions when high‐capacity firms may have the incentive and capability to signal their capacity levels by overproduction. We show that prior beliefs about capacity play a crucial, and surprisingly complex, role on whether the firm would prefer to reveal its capacity or not. A surprising result is that, despite the fact that it may be best for the high‐capacity firm to overproduce to reveal its capacity when capacity information is private, it may end up with more profits than if all capacity information were public knowledge in the first place. © 2013 Wiley Periodicals, Inc. Naval Research Logistics, 2013     

Efficient distributions of arms‐control inspection effort

A rule that constrains decision‐makers is enforced by an inspector who is supplied with a fixed level of inspection resources—inspection personnel, equipment, or time. How should the inspector distribute its inspection resources over several independent inspectees? What minimum level of resources is required to deter all violations? Optimal enforcement problems occur in many contexts; the motivating application for this study is the role of the International Atomic Energy Agency in support of the Treaty on the Non‐Proliferation of Nuclear Weapons. Using game‐theoretic models, the resource level adequate for deterrence is characterized in a two‐inspectee problem with inspections that are imperfect in the sense that violations can be missed. Detection functions, or probabilities of detecting a violation, are assumed to be increasing in inspection resources, permitting optimal allocations over inspectees to be described both in general and in special cases. When detection functions are convex, inspection effort should be concentrated on one inspectee chosen at random, but when they are concave it should be spread deterministicly over the inspectees. Our analysis provides guidance for the design of arms‐control verification operations, and implies that a priori constraints on the distribution of inspection effort can result in significant inefficiencies. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2004.     

Reconciling strategic studies … with itself: a common framework for choosing among strategies

Three distinct, and seemingly irreconcilable, schools of thought are identified within the strategic studies literature. One which searches for “universal principles of war,” a second, “context-dependent,” approach that seeks to embed each instance of warfare within its concurrent social, political, technological milieu and, finally a “paradoxical logic” school, which equates strategy with the generation of uncertainty. The author offers some intuitive concepts from non-cooperative game theory to develop a “dominate-mix” approach to strategy choice. In doing so, he helps to reconcile these disparate approaches and provides a simple framework to assist researchers in framing military decisions as well as to assist planners in choosing among strategies.