Capacity allocation with traditional and Internet channels

In this paper we study a capacity allocation problem for two firms, each of which has a local store and an online store. Customers may shift among the stores upon encountering a stockout. One question facing each firm is how to allocate its finite capacity (i.e., inventory) between its local and online stores. One firm's allocation affects the decision of the rival, thereby creating a strategic interaction. We consider two scenarios of a single‐product single‐period model and derive corresponding existence and stability conditions for a Nash equilibrium. We then conduct sensitivity analysis of the equilibrium solution with respect to price and cost parameters. We also prove the existence of a Nash equilibrium for a generalized model in which each firm has multiple local stores and a single online store. Finally, we extend the results to a multi‐period model in which each firm decides its total capacity and allocates this capacity between its local and online stores. A myopic solution is derived and shown to be a Nash equilibrium solution of a corresponding “sequential game.” © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

The Banzhaf value and communication situations

Myerson 3 and 4 proposed and characterized a modification of the Shapley value in the context of communication situations. In this paper we propose several characterizations of the extension of the Banzhaf value proposed by Owen 7 to communication situations. In particular we characterize this value with the properties of fairness, isolation, and pairwise merging. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

基于合作博弈的智能集群自主聚集研究

智能集群是指由大量智能体构成、采用自组织策略协作完成任务的群体。以无人车集群系统协同监视再入体着靶过程为任务背景,开展智能集群自组织策略的关键技术研究。设计了无人车集群执行再入体着靶协同监视的集群行为模式,提出了基于合作博弈的智能集群自组织策略,各智能体以实现群体聚集为“合作目标”,以降低自身能量消耗为“竞争目标”,开展博弈,基于微粒群算法规划局部路径,最终使群体系统涌现出聚集行为。仿真实验验证了设计的自主聚集策略的有效性。     

Non‐zero‐sum nonlinear network path interdiction with an application to inspection in terror networks

A simultaneous non‐zero‐sum game is modeled to extend the classical network interdiction problem. In this model, an interdictor (e.g., an enforcement agent) decides how much of an inspection resource to spend along each arc in the network to capture a smuggler. The smuggler (randomly) selects a commodity to smuggle—a source and destination pair of nodes, and also a corresponding path for traveling between the given pair of nodes. This model is motivated by a terrorist organization that can mobilize its human, financial, or weapon resources to carry out an attack at one of several potential target destinations. The probability of evading each of the network arcs nonlinearly decreases in the amount of resource that the interdictor spends on its inspection. We show that under reasonable assumptions with respect to the evasion probability functions, (approximate) Nash equilibria of this game can be determined in polynomial time; depending on whether the evasion functions are exponential or general logarithmically‐convex functions, exact Nash equilibria or approximate Nash equilibria, respectively, are computed. © 2017 Wiley Periodicals, Inc. Naval Research Logistics 64: 139–153, 2017     

Bullwhip and reverse bullwhip effects under the rationing game

When an unreliable supplier serves multiple retailers, the retailers may compete with each other by inflating their order quantities in order to obtain their desired allocation from the supplier, a behavior known as the rationing game. We introduce capacity information sharing and a capacity reservation mechanism in the rationing game and show that a Nash equilibrium always exists. Moreover, we provide conditions guaranteeing the existence of the reverse bullwhip effect upstream, a consequence of the disruption caused by the supplier. In contrast, we also provide conditions under which the bullwhip effect does not exist. In addition, we show that a smaller unit reservation payment leads to more bullwhip and reverse bullwhip effects, while a large unit underage cost results in a more severe bullwhip effect. © 2017 Wiley Periodicals, Inc. Naval Research Logistics 64: 203–216, 2017     

多舰对抗研究

研究了海上军事实战模式抽象出的一追二和一二对抗的两大问题。解决一追二问题的方法共讨论了三种：初始角的平分线航向法、瞬时角的平分线航向法、中点轨迹法。给出了确定性的数学模型、以及选代计算方法。一二对抗问题的结论可以由—一对抗问题的结论经过迭加而得到。而—一对抗问题的解决是以定性微分对策的双边极值原理为基础展开的。     

可靠性鉴定中 Bayes 方法的运用

本文论述可靠性鉴定的Bayes方法。文中讨论了成败型和寿命型两种模型。给出了可靠性鉴定方法及可能犯的两种错误的概率计算公式。论述中,充分注意了工程实践中出现的问题,并提出了处置方法。     

A new kind of fictitious play

Gass, Zafra, and Qiu (1996) introduce a modified version of fictitious play for matrix games where only the more successful player's strategy is retained. This paper introduces additional modifications that appear to converge faster. © 2001 John Wiley & Sons, Inc.* Naval Research Logistics 48: 270–280, 2001     

New results on a Ruckle problem in discrete games of ambush

This article deals with a two‐person zero‐sum game in which player I chooses in integer interval [1, N] two integer intervals consisting of p and q points where p + q < N, and player II chooses an integer point in [1, N]. The payoff to player I equals 1 if the point chosen by player II is at least in one of the intervals chosen by player II and 0 otherwise. This paper complements the results obtained by Ruckle, Baston and Bostock, Lee, Garnaev, and Zoroa, Zoroa and Fernández‐Sáez. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48: 98–106, 2001     

Rendezvous search when marks are left at the starting points

Leaving marks at the starting points in a rendezvous search problem may provide the players with important information. Many of the standard rendezvous search problems are investigated under this new framework which we call markstart rendezvous search. Somewhat surprisingly, the relative difficulties of analysing problems in the two scenarios differ from problem to problem. Symmetric rendezvous on the line seems to be more tractable in the new setting whereas asymmetric rendezvous on the line when the initial distance is chosen by means of a convex distribution appears easier to analyse in the original setting. Results are also obtained for markstart rendezvous on complete graphs and on the line when the players' initial distance is given by an unknown probability distribution. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48: 722–731, 2001