Strategic Defense And Attack For Series And Parallel Reliability Systems: Rejoinder

In our original comment, we showed that Hausken's characterization of Nash equilibrium is invalid for much of the parameter space examined and provided necessary conditions for his solution to hold. Most of the comments in his reply are either tangential or irrelevant. However, several of the claims made in the reply reveal continuing misunderstandings and gaps in his understanding. In this rejoinder, we briefly clarify the fundamental issues.     

Noncooperative cost spanning tree games with budget restrictions

We extend the noncooperative game associated with the cost spanning tree problem introduced by Bergantiños and Lorenzo (Math Method Oper Res 59(2004), 393–403) to situations where agents have budget restrictions. We study the Nash equilibria, subgame perfect Nash equilibria, and strong Nash equilibria of this game. © 2008 Wiley Periodicals, Inc. Naval Research Logistics 2008     

Constant risk aversion in stochastic contests with exponential completion times

This article analyzes a class of stochastic contests among multiple players under risk‐averse exponential utility. In these contests, players compete over the completion of a task by simultaneously deciding on their investment, which determines how fast they complete the task. The completion time of the task for each player is assumed to be an exponentially distributed random variable with rate linear in the player's investment and the completion times of different players are assumed to be stochastically independent. The player that completes the task first earns a prize whereas the remaining players earn nothing. The article establishes a one‐to‐one correspondence between the Nash equilibrium of this contest with respect to risk‐averse exponential utilities and the nonnegative solution of a nonlinear equation. Using the properties of the latter, it proves the existence and the uniqueness of the Nash equilibrium, and provides an efficient method to compute it. It exploits the resulting representation of the equilibrium investments to determine the effects of risk aversion and the differences between the outcome of the Nash equilibrium and that of a centralized version.© 2016 Wiley Periodicals, Inc. Naval Research Logistics 66:4–14, 2019     

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     

两类新的Nash平衡点的精选

本文从系统的观点出发,对n-人非合作对策的解点作了探讨,提出了两类新的Nash平衡点的精选,并证明了其存在性。这两种Nash平衡点分别称之为第一类Nash平衡点和第二类Nash平衡点。第一类Nash平衡点具有冒险性,第二类Nash平衡点具有保守性,二者都满足整体上的最优性。     

Inducing coordination in supply chains through linear reward schemes

Decentralized decision‐making in supply chain management is quite common, and often inevitable, due to the magnitude of the chain, its geographical dispersion, and the number of agents that play a role in it. But, decentralized decision‐making is known to result in inefficient Nash equilibrium outcomes, and optimal outcomes that maximize the sum of the utilities of all agents need not be Nash equilibria. In this paper we demonstrate through several examples of supply chain models how linear reward/penalty schemes can be implemented so that a given optimal solution becomes a Nash equilibrium. The examples represent both vertical and horizontal coordination issues. The techniques we employ build on a general framework for the use of linear reward/penalty schemes to induce stability in given optimal solutions and should be useful to other multi‐agent operations management settings. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

Strategic defense and attack for series and parallel reliability systems: reply 1 to comment 1

Kovenock and Roberson's [2011] comment provides initial work which has the potential, when suitably extended, to advance the research frontier. Kovenock and Roberson's paper consists of three sections. The first section is an interesting introduction. The second section, titled ‘Model and Main Result,’ provides no contribution beyond Hausken [2008a]. It consists of Equations (1)–(10) which are equivalent to equations developed by Hausken, and Equation (11) which is equivalent to the utility requirements u???0 and U???0 provided after Equation (17) in Hausken. The third section provides interesting ideas about mixed-strategy equilibria that can be extended in future research.     

On the set of (perfect) equilibria of a bimatrix game

This article provides a new approach to the set of (perfect) equilibria. With the help of an equivalence relation on the strategy space of each player. Nash sets and Selten sets are introduced. The number of these sets is finite and each of these sets is a polytope. As a consequence the set of (perfect) equilibria is a finite union of polytopes. © 1994 John Wiley & Sons. Inc.     

Decentralized admission control of a queueing system: A game‐theoretic model

Consider a distributed system where many gatekeepers share a single server. Customers arrive at each gatekeeper according to independent Poisson processes with different rates. Upon arrival of a new customer, the gatekeeper has to decide whether to admit the customer by sending it to the server, or to block it. Blocking costs nothing. The gatekeeper receives a reward after a customer completes the service, and incurs a cost if an admitted customer finds a busy server and therefore has to leave the system. Assuming an exponential service distribution, we formulate the problem as an n‐person non‐zero‐sum game in which each gatekeeper is interested in maximizing its own long‐run average reward. The key result is that each gatekeeper's optimal policy is that of a threshold type regardless what other gatekeepers do. We then derive Nash equilibria and discuss interesting insights. © 2003 Wiley Periodicals, Inc. Naval Research Logistics 50: 702–718, 2003.     

Resource allocation in an asymmetric technology race with temporary advantages

We consider two opponents that compete in developing asymmetric technologies where each party's technology is aimed at damaging (or neutralizing) the other's technology. The situation we consider is different than the classical problem of commercial R&D races in two ways: First, while in commercial R&D races the competitors compete over the control of market share, in our case the competition is about the effectiveness of technologies with respect to certain capabilities. Second, in contrast with the “winner‐takes‐all” assumption that characterizes much of the literature on this field in the commercial world, we assume that the party that wins the race gains a temporary advantage that expires when the other party develops a superior technology. We formulate a variety of models that apply to a one‐sided situation, where one of the two parties has to determine how much to invest in developing a technology to counter another technology employed by the other party. The decision problems are expressed as (convex) nonlinear optimization problems. We present an application that provides some operational insights regarding optimal resource allocation. We also consider a two‐sided situation and develop a Nash equilibrium solution that sets investment values, so that both parties have no incentive to change their investments. © 2012 Wiley Periodicals, Inc. Naval Research Logistics 59: 128–145, 2012     

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     

Contracts and coordination: Supply chains with uncertain demand and supply

Considering a supply chain with a supplier subject to yield uncertainty selling to a retailer facing stochastic demand, we find that commonly studied classical coordination contracts fail to coordinate both the supplier's production and the retailer's procurement decisions and achieve efficient performance. First, we study the vendor managed inventory (VMI) partnership. We find that a consignment VMI partnership coupled with a production cost subsidy achieves perfect coordination and a win‐win outcome; it is simple to implement and arbitrarily allocates total channel profit. The production cost subsidy optimally chosen through Nash bargaining analysis depends on the bargaining power of the supplier and the retailer. Further, motivated by the practice that sometimes the retailer and the supplier can arrange a “late order,” we also analyze the behavior of an advance‐purchase discount (APD) contract. We find that an APD with a revenue sharing contract can efficiently coordinate the supply chain as well as achieve flexible profit allocation. Finally, we explore which coordination contract works better for the supplier vs. the retailer. It is interesting to observe that Nash bargaining solutions for the two coordination contracts are equivalent. We further provide recommendations on the applications of these contracts. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 305–319, 2016     

Purchase and retrieval competition for seasonal produce

We study the competition problem of purchase and multiretrieval of perishable seasonal produce, where wholesalers purchase and stock their products in the first period, and then retrieve and sell them in subsequent periods. We first consider the duopoly case and assume that the prices are exogenous and fluctuate. In each period, after the price realization, the wholesalers retrieve some stock from their warehouses to satisfy their demands. One wholesaler's unsatisfied customers can switch to another and be satisfied by its left retrieved products. Any unsold retrieved stock has no salvage value and any unsatisfied demand is lost. The unretrieved stock is carried to the next period at a perishable rate. The wholesalers compete for the substitute demand by determining their own purchase and retrieval quantities. We show the existence and uniqueness of a pure-strategy Nash equilibrium, and that the Nash equilibrium strategy has the simple “sell-down-to” structure. We also consider the general N-person game and show the existence of the Nash equilibrium, and characterize the structure of the equilibrium strategy for the symmetric case. In addition, we consider the case with endogenous prices, and show that the problem reduces to a repeated newsvendor game with price and inventory competition. We derive the conditions under which a unique Nash equilibrium exists and characterize the equilibrium strategy. Finally, we conduct numerical studies to examine the impacts of the model parameters on the equilibrium outcomes and to generate managerial insights.     

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。     

The incentive effect of acceptance sampling plans in a supply chain with endogenous product quality

This article studies a firm that procures a product from a supplier. The quality of each product unit is measured by a continuous variable that follows a normal distribution and is correlated within a batch. The firm conducts an inspection and pays the supplier only if the product batch passes the inspection. The inspection not only serves the purpose of preventing a bad batch from reaching customers but also offers the supplier an incentive to improve product quality. The firm determines the acceptance sampling plan, and the supplier determines the quality effort level in either a simultaneous game or a Stackelberg leadership game, in which both parties share inspection cost and recall loss caused by low product quality. In the simultaneous game, we identify the Nash equilibrium form, provide sufficient conditions that guarantee the existence of a pure strategy Nash equilibrium, and find parameter settings under which the decentralized and centralized supply chains achieve the same outcome. By numerical experiments, we show that the firm's acceptance sampling plan and the supplier's quality effort level are sensitive to both the recall loss sharing ratio and the game format (i.e., the precommitment assumption of the inspection policy). © 2013 Wiley Periodicals, Inc. Naval Research Logistics, 2013     

Nonrobustness of the normal approximation of lead‐time demand in a (Q,R) system

For computing an optimal (Q, R) or kindred inventory policy, the current literature provides mixed signals on whether or when it is safe to approximate a nonnormal lead‐time‐demand (“LTD”) distribution by a normal distribution. The first part of this paper examines this literature critically to justify why the issue warrants further investigations, while the second part presents reliable evidence showing that the system‐cost penalty for using the normal approximation can be quite serious even when the LTD‐distribution's coefficient of variation is quite low—contrary to the prevalent view of the literature. We also identify situations that will most likely lead to large system‐cost penalty. Our results indicate that, given today's technology, it is worthwhile to estimate an LTD‐distribution's shape more accurately and to compute optimal inventory policies using statistical distributions that more accurately reflect the LTD‐distributions' actual shapes. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2003     

Timely exposure of a secret project: Which activities to monitor?

A defender wants to detect as quickly as possible whether some attacker is secretly conducting a project that could harm the defender. Security services, for example, need to expose a terrorist plot in time to prevent it. The attacker, in turn, schedules his activities so as to remain undiscovered as long as possible. One pressing question for the defender is: which of the project's activities to focus intelligence efforts on? We model the situation as a zero‐sum game, establish that a late‐start schedule defines a dominant attacker strategy, and describe a dynamic program that yields a Nash equilibrium for the zero‐sum game. Through an innovative use of cooperative game theory, we measure the harm reduction thanks to each activity's intelligence effort, obtain insight into what makes intelligence effort more effective, and show how to identify opportunities for further harm reduction. We use a detailed example of a nuclear weapons development project to demonstrate how a careful trade‐off between time and ease of detection can reduce the harm significantly.     

SOMALIA AND SOMALILAND

The authors consider the recent referral by the UN Security Council of the situation in the western region of Sudan (Darfur) for investigation and prosecution to the International Criminal Court. The paper focuses on the context of this referral, especially since the referral signals a capitulation by the United States of America (which had the power to veto the referral) in the face of worldwide pressure for the United Nations to take action against perpetrators of atrocities in Sudan. In considering the referral, the authors point out that the International Criminal Court has been handed a hot potato. Because it is one of the first cases that the court will hear, the spotlight will be on the court's effectiveness as an instrument of international criminal justice. Sudan is not party to the court's statute, however, and accordingly owes the court no obligation to cooperate in the investigation and prosecution of Sudanese offenders.     

Leadership at NATO: Secretary General Manfred Woerner and the Crisis in Bosnia

NATO's post-Cold War transformation, as well as the military alliance's decision to use force in Bosnia in 1994 and 1995, has been examined from multiple perspectives. Among an array of diplomatic, historical and political approaches, however, analysts have given little attention to the role played by NATO's top civilian leader in Brussels, the Secretary General. On the crisis in Bosnia, no research has been devoted to the leadership of Secretary General Manfred Woerner, who oversaw NATO as it moved toward aggressive military action in the Balkans. Using an approach that examines the Secretary General's leadership from three perspectives, this article provides the first assessment of Woerner's role in shaping alliance policy on Bosnia. The findings suggest that Woerner was a critical leader in influencing NATO decisions, which provides new explanations for NATO's conduct in the Balkans, and speaks to the broader literature on NATO's evolution after the Cold War.     

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