The value of losing control: Competition in markets for complements

When selling complementary products, manufacturers can often benefit from considering the resulting cross‐market interdependencies. Although using independent retailers makes it difficult to internalize these positive externalities, the ensuing double marginalization can mitigate within‐market competition. We use standard game theoretic analysis to determine optimal distribution channel strategies (through independent retailers or integrated) for competing manufacturers who participate in markets for complements. Our results suggest that a firm's optimal channel choice is highly dependent on its competitive positioning. A firm with a competitive advantage in terms of product characteristics (customer preferences) or production capabilities (cost) might benefit from selling through company‐controlled stores, allowing coordinated pricing across the two markets, whereas a less competitive firm might be better off using independent channel intermediaries to mitigate price competition. We consider two scenarios depending on whether the two firms make their distribution channel decisions sequentially or simultaneously. Although firms are unlikely to make such decisions at exactly the same instant, the simultaneous model also serves as a proxy for the scenario where firms decide sequentially, but where they cannot observe each other's strategic channel choices. For the sequential case, we find that the sequence of entry can have tremendous impact on the two firms'profits; whereas in some cases, the first mover can achieve substantially higher profits, we find that when the two markets are of sufficiently different size and only loosely related, a firm with a competitive advantage might be better off as a follower. Interestingly, our results suggest that, when the markets are of rather similar size, both firms are better off if they enter the industry sequentially. In those cases, the first entrant has incentive to reveal its planned channel strategies, and the follower has incentive to seek out and consider this information. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

Modified fictitious play

We describe a modification of Brown's fictitious play method for solving matrix (zero-sum two-person) games and apply it to both symmetric and general games. If the original game is not symmetric, the basic idea is to transform the given matrix game into an equivalent symmetric game (a game with a skew-symmetric matrix) and use the solution properties of symmetric games (the game value is zero and both players have the same optimal strategies). The fictitious play method is then applied to the enlarged skew-symmetric matrix with a modification that calls for the periodic restarting of the process. At restart, both players' strategies are made equal based on the following considerations: Select the maximizing or minimizing player's strategy that has a game value closest to zero. We show for both symmetric and general games, and for problems of varying sizes, that the modified fictitious play (MFP) procedure approximates the value of the game and optimal strategies in a greatly reduced number of iterations and in less computational time when compared to Brown's regular fictitious play (RFP) method. For example, for a randomly generated 50% dense skew-symmetric 100 × 100 matrix (symmetric game), with coefficients |a_ij| ≤ 100, it took RFP 2,652,227 iterations to reach a gap of 0.03118 between the lower and upper bounds for the game value in 70.71 s, whereas it took MFP 50,000 iterations to reach a gap of 0.03116 in 1.70 s. Improved results were also obtained for general games in which the MFP solves a much larger equivalent symmetric game. © 1996 John Wiley & Sons, Inc.     

Dynamic pricing and inventory control with learning

Optimal operating policies and corresponding managerial insight are developed for the decision problem of coordinating supply and demand when (i) both supply and demand can be influenced by the decision maker and (ii) learning is pursued. In particular, we determine optimal stocking and pricing policies over time when a given market parameter of the demand process, though fixed, initially is unknown. Because of the initially unknown market parameter, the decision maker begins the problem horizon with a subjective probability distribution associated with demand. Learning occurs as the firm monitors the market's response to its decisions and then updates its characterization of the demand function. Of primary interest is the effect of censored data since a firm's observations often are restricted to sales. We find that the first‐period optimal selling price increases with the length of the problem horizon. However, for a given problem horizon, prices can rise or fall over time, depending on how the scale parameter influences demand. Further results include the characterization of the optimal stocking quantity decision and a computationally viable algorithm. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 303–325, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10013     

An inspection game: Taking account of fulfillment probabilities of players' aims

This paper deals with an inspection game of customs and a smuggler. The customs can take two options of assigning a patrol or not. The smuggler has two strategies of shipping its cargo of contraband or not. Two players have several opportunities to take actions during a limited number of days. When both players do, there are some possibilities that the customs captures the smuggler and, simultaneously, the smuggler possibly makes a success of the smuggling. If the smuggler is captured or there remain no days for playing the game, the game ends. In this paper, we formulate the problem into a multi‐stage two‐person zero‐sum stochastic game and investigate some characteristics of the equilibrium solution, some of which are given in a closed form in a special case. There have been some studies so far on the inspection game. However, some consider the case that the smuggler has only one opportunity of smuggling or the perfect‐capture case that the customs can certainly arrest the smuggler on patrol, and others think of a recursive game without the probabilities of fulfilling the players' purposes. In this paper, we consider the inspection game taking account of the fulfillment probabilities of the players' aims. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

Special Forces for Counter Revolutionary Warfare: The South African Case

Special Forces have long formed a central part of counter-revolutionary warfare. In the South African case, between 1974 and 1990, these were central to Pretoria's regional strategies. Serving as the primary tool for inflicting punishment on any Frontline State that allowed the ANC and its allies basing rights, the Special Forces conducted sabotage, raids, bombings and assassinations throughout the Frontline States, alongside the Special Tasks contra-mobilization programmes throughout the region and internally. When these tools proved insufficient - especially internally - the security forces turned to the medical Special Forces, who were at the centre of South Africa's chemical and biological warfare programme, for assistance in incapacitating and killing the state's opponents. Overall, these units worked under the banner of the state's 'Total Counter-Revolutionary Strategy' and in co-operation with the more covert elements of the security forces (such as the Civil Co-operation Bureau, the SAP's Koevoet and C1 counter-intelligence units, and the Directorate of Covert Collection) involved in the direct-targeting of the state's opponents.     

The advantage of deeper pockets in Silverman's game on intervals

Silverman's game on (1, B) × (1, B) was analyzed by R. J. Evans, who showed that optimal strategies exist (and found them) only on a set of measure zero in the parameter plane. We examine the corresponding game on (1, B) × (1, D) with D > B, and show that optimal strategies exist in about half the parameter plane. Optimal strategies and game value are obtained explicitly. © 1995 John Wiley & Sons, Inc.     

Optimal pricing for a short life‐cycle product when customer price‐sensitivity varies over time

Technology products often experience a life‐cycle demand pattern that resembles a diffusion process, with weak demand in the beginning and the end of the life cycle and high demand intensity in between. The customer price‐sensitivity also changes over the life cycle of the product. We study the prespecified pricing decision for a product that exhibits such demand characteristics. In particular, we determine the optimal set of discrete prices and the times to switch from one price to another, when a limited number of price changes are allowed. Our study shows that the optimal prices and switching times show interesting patterns that depend on the product's demand pattern and the change in the customers' price sensitivity over the life cycle of the product. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012     

Technical note: Reexamination of all‐or‐none inspection policies in a supply chain with endogenous product quality

This note studies the optimal inspection policies in a supply chain in which a manufacturer purchases components from a supplier but has no direct control of component quality. The manufacturer uses an inspection policy and a damage cost sharing contract to encourage the supplier to improve the component quality. We find that all‐or‐none inspection policies are optimal for the manufacturer if the supplier's share of the damage cost is larger than a threshold; otherwise, the manufacturer should inspect a fraction of a batch. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

Ruminations of a pachyderm or what I learned in the counter‐insurgency business

The Lord's Resistance Army (LRA) has created a pervasive climate of fear in northern Uganda. This study addresses the purpose of this conduct. Diverging from the traditional ‘greed-grievance’ approach to the study of new wars, the LRA's behaviour is analyzed from a strategic perspective. Specifically, the article focuses on the LRA's use of mutilation, abduction, surprise, and unpredictable attacks. The conclusion is that the LRA is strategically using fear as a force multiplier, to further its organizational survival, and as a way to fight a political ‘dirty war’.     

Optimal allocation of minimal repairs in parallel and series systems

In reliability engineering, the concept of minimal repair describes that the repair brings the failed unit (eg, system or component) to the situation which is same as it was just before the failure. With the help of the well‐known Gamma‐Poisson relationship, this paper investigates optimal allocation strategies of minimal repairs for parallel and series systems through implementing stochastic comparisons of various allocation policies in terms of the hazard rate, the reversed hazard rate, and the likelihood ratio orderings. Numerical examples are presented to illustrate these findings as well. These results not only strengthen and generalize some known ones in the seminal work of Shaked and Shanthikumar, but also solve the open problems proposed by Chahkandi et al.'s study and Arriaza et al.'s study.     

An extreme-point approach for obtaining weighted ratings in qualitative multicriteria decision making

Many attempts have been made in the past to obtain estimates for the weights and ratings values of a multicriteria linear utility function. In particular, the problem arises when both criteria importance and alternatives' ratings are expressed in a qualitative ordinal manner. This article proposes an extreme-point approach for obtaining the overall ratings in the presence of ordinal preferences both for the criteria importance and the alternatives' rankings. In particular it is shown that Borda's method of scores is obtained as a special case. © 1996 John Wiley & Sons, Inc.     

Availability of an operating system during a given time interval: A dynamic programming approach

We consider the problem of running a one-unit failure system such that the probability that the system is operating over an entire prespecified time interval (or at least at some time instant during the interval) is maximized. A fixed number of unused units having identically distributed random operating times are at the controller's disposal. Simple assumptions are made on the stochastic failure mechanism. In particular, the time required to activate a unit for the system is supposed to be constant. Analyzing the associated dynamic programming equations yields closed-form solutions. © 1996 John Wiley & Sons, Inc.     

Locational tying of complementary retail items

We study a selling practice that we refer to as locational tying (LT), which seems to be gaining wide popularity among retailers. Under this strategy, a retailer “locationally ties” two complementary items that we denote by “primary” and “secondary.” The retailer sells the primary item in an appropriate “department” of his or her store. To stimulate demand, the secondary item is offered in the primary item's department, where it is displayed in very close proximity to the primary item. We consider two variations of LT: In the multilocation tying strategy (LT‐M), the secondary item is offered in its appropriate department in addition to the primary item's department, whereas in the single‐location tying strategy (LT‐S), it is offered only in the primary item's location. We compare these LT strategies to the traditional independent components (IC) strategy, in which the two items are sold independently (each in its own department), but the pricing/inventory decisions can be centralized (IC‐C) or decentralized (IC‐D). Assuming ample inventory, we compare and provide a ranking of the optimal prices of the four strategies. The main insight from this comparison is that relative to IC‐D, LT decreases the price of the primary item and adjusts the price of the secondary item up or down depending on its popularity in the primary item's department. We also perform a comparative statics analysis on the effect of demand and cost parameters on the optimal prices of various strategies, and identify the conditions that favor one strategy over others in terms of profitability. Then we study inventory decisions in LT under exogenous pricing by developing a model that accounts for the effect of the primary item's stock‐outs on the secondary item's demand. We find that, relative to IC‐D, LT increases the inventory level of the primary item. We also link the profitability of different strategies to the trade‐off between the increase in demand volume of the secondary item as a result of LT and the potential increase in inventory costs due to decentralizing the inventory of the secondary item. © 2009 Wiley Periodicals, Inc. Naval Research Logistics 2009     

Optimal cutoff strategies in capacity expansion problems

Capacity expansion refers to the process of adding facilities or manpower to meet increasing demand. Typical capacity expansion decisions are characterized by uncertain demand forecasts and uncertainty in the eventual cost of expansion projects. This article models capacity expansion within the framework of piecewise deterministic Markov processes and investigates the problem of controlling investment in a succession of same type projects in order to meet increasing demand with minimum cost. In particular, we investigate the optimality of a class of investment strategies called cutoff strategies. These strategies have the property that there exists some undercapacity level M such that the strategy invests at the maximum available rate at all levels above M and does not invest at any level below M. Cutoff strategies are appealing because they are straightforward to implement. We determine conditions on the undercapacity penalty function that ensure the existence of optimal cutoff strategies when the cost of completing a project is exponentially distributed. A by-product of the proof is an algorithm for determining the optimal strategy and its cost. © 1995 John Wiley & Sons, Inc.     

Differential-game examination of optimal time-sequential fire-support strategies

Optimal time-sequential fire-support strategies are studied through a two-person zero-sum deterministic differential game with closed-loop (or feedback) strategies. Lanchester-type equations of warfare are used in this work. In addition to the max-min principle, the theory of singular extremals is required to solve this prescribed-duration combat problem. The combat is between two heterogeneous forces, each composed of infantry and a supporting weapon system (artillery). In contrast to previous work reported in the literature, the attrition structure of the problem at hand leads to force-level-dependent optimal fire-support strategies with the attacker's optimal fire-support strategy requiring him to sometimes split his artillery fire between enemy infantry and artillery (counterbattery fire). A solution phenomnon not previously encountered in Lanchester-type differential games is that the adjoint variables may be discontinuous across a manifold of discontinuity for both players' strategies. This makes the synthesis of optimal strategies particularly difficult. Numerical examples are given.     

Performance of heuristics for the uncapacitated lot-size problem

Although the uncapacitated lot-size problem can be solved optimally very efficiently, heuristics are often used instead in practice. Recent research on the performance of these heuristics has focused on worst-case analysis and empirical testing. This article extends earlier worst-case results, for several of the commonly used heuristics, to more specific problem classes to obtain a better understanding of when a heuristic can be expected to perform well and when it is likely to perform poorly. In particular, we obtain bounds for the finite-horizon problem (earlier results all assume an infinite horizon) and for problems in which demand is (i) constant, and (ii) bounded from above or below. We also show how the heuristics can be classified into three categories, with heuristics in each category using similar rules to construct feasible production schedules. Using this categorization, our analysis reveals that a small change in the definition of a heuristic can often have a significant impact on its performance. © 1992 John Wiley & Sons, Inc.     

Mandated defence offsets: can they ever deliver?

Defence offsets are elements of defence procurement deals additional to the primary content. Offsets are usually expected to yield technological or industrial benefits to the purchasing country (e.g. countertrade, technology transfers, or additional jobs) and military buyers often require suppliers to make offsets available “cost-free.” The authors argued previously that such strategies achieve little of value to buyers that lack market power and are unnecessary otherwise, since purchasers with the market power to extract more value for money from foreign suppliers can do so anyway. This article also focuses on the supply side of offset deals. The USA is the world's largest defence offsets supplier but the US government opposes offsets demands as economically inefficient and trade distorting. Even if offsets are inefficient and trade distorting, they may still benefit a materiel-exporting country such as the USA as they may induce exports and create associated benefits for the offsets provider.     

National interests and the power of ‘language’: West German diplomacy and the conference on security and cooperation in Europe, 1972–1975

Based on newly released documents from the German foreign ministry archives, this article investigates Bonn's goals, strategies and negotiation tactics at the Conference on Security and Development in Europe (CSCE). By focusing in particular on the multilateral preparatory talks in 1972/73 when the general Conference framework was negotiated and national and alliance positions were determined, it will be shown that (1) the Federal Republic of Germany was the key Western player at the CSCE, and (2) its policies were largely driven by national, Deutschlandpolitik interests – although on the surface the emphasis was always on a multilateral approach and a united Western (EPC/NATO) position. Furthermore, this article will reveal the significance of the ‘politics of language’ in West German diplomacy; and offer some wider reflections on the importance of language and its symbolism in international relations.     

Xunzi on the Role of the Military in a Well-Ordered State

Chapter 15 of the Xunzi stands as the most comprehensive account of the early Confucian analysis of warfare. Unlike a range of other early, non-Confucian discussions on warfare, particular strategies and tactics are taken to be of secondary importance. Thus, Xunzi refuses to discuss practical military strategy without framing it within a much broader ethical, social, and political context. On his account, a well-ordered, flourishing state necessarily rests upon a particular set of rituals and social norms in which people can cultivate themselves morally. Such a state has nothing to fear from any enemy, no matter how tactically sophisticated or militarily skilled. To many, such a view seems overly optimistic. However, given that Xunzi is anything but Pollyannaish in other parts of the text and is quite pessimistic about human nature in general, it behooves us to dig a bit more deeply into his ideas about military affairs and examine whether they can be understood in a more plausible light. This article provides a reading of Xunzi’s views on military affairs that is internally consistent and corresponds with Xunzi’s broader ethical and political views, while also showing why someone of Xunzi’s obvious intellectual acumen might hold such a view.     

Countering terrorism in Northern Ireland: the role of intelligence

This article aims to review some of the key lessons learnt by the Royal Ulster Constabulary's (RUC) Special Branch in the 37 years of the troubles in Northern Ireland. Above all counter-terrorism is an intelligence led operation and Special Branch are the key agency for this in all UK police forces, who have now benefited enormously from the expertise that the RUC's Special Branch built up over the years and have passed on to their colleagues throughout the UK. Intelligence is more often than not a human role and relies on human agencies, which was the case in Northern Ireland. The bulk of intelligence gathering was carried out at quite low levels although the sifting and analysing of it became a more specialist skill. Electronic intelligence and computerised systems were often quite low down in the order of priorities and uses, which tends to confound popular impressions. Agents, informers and good old fashioned ‘coppers’ who knew their patch were much more important both in terms of gathering information and in terms of undermining the terrorists morale from within and it was these factors that fundamentally defeated the IRA in Northern Ireland.