Optimal nonmyopic gambling strategy for the generalized Kelly criterion

We consider the optimal wagers to be made by a gambler who starts with a given initial wealth. The gambler faces a sequence of two-outcome games, i.e., “win” vs. “lose,” and wishes to maximize the expected value of his terminal utility. It has been shown by Kelly, Bellman, and others that if the terminal utility is of the form log x, where x is the terminal wealth, then the optimal policy is myopic, i.e., the optimal wager is always to bet a constant fraction of the wealth provided that the probability of winning exceeds the probability of losing. In this paper we provide a critique of the simple logarithmic assumption for the utility of terminal wealth and solve the problem with a more general utility function. We show that in the general case, the optimal policy is not myopic, and we provide analytic expressions for optimal wager decisions in terms of the problem parameters. We also provide conditions under which the optimal policy reduces to the simple myopic case. © 1997 John Wiley & Sons, Inc. Naval Research Logistics 44: 639–654, 1997     

Measuring newness

This article deals with “newness,” an important characteristic of research-and-development (R&D) projects. Newness consumes resources and provides effectiveness or profit, and is mainly considered to be of a qualitative nature yielding only to an expert's intuition. This article is focused on a numerical measure of newness and the closely connected concept of technological advance. The measure is described in a technical parameter space against a set of analogous objects, presented by its center, eigenvalues and eigenvectors. Specific features and behavior of the selected measure of newness are analyzed. A numerical example is also included. © 1996 John Wiley & Sons, Inc.     

An algorithm for optimal shipments with given frequencies

This article deals with the problem of minimizing the transportation and inventory cost associated with the shipment of several products from a source to a destination, when a finite set of shipping frequencies is available. A mixed-integer programming model—shown to be NP-hard—is formulated for that problem. The computational complexity of some similar models applied to different problems is also investigated. In particular, whereas the capacitated plant location problem with operational cost in product form is NP-hard, the simple plant location problem with the same characteristics can be solved in polynomial time. A branch-and-bound algorithm is finally worked out, and some computational results are presented. © 1996 John Wiley & Sons, Inc.     

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.     

An Opportunity Structure for Terrorism: Moderate Leadership Departures in Nationalist Movements

Why does terrorist violence escalate from some ethnic groups but not others? According to theoretical insights, many groups endure conditions that should spur on terrorist campaigns, but in reality only some carry them out. In contrast to studies emphasising motivations, this article constructs a framework centred on opportunity structures that contributes to our understanding of the rise of terrorism waged along ethnic lines. It argues that beyond grievances or other motivations, terrorist campaigns develop from communities when moderate political leaders depart from their positions in nationalist movements, causing terrorists to fill the subsequent power vacuum, while little terrorism occurs when leaders do not relinquish the nationalist agenda. This argument is evaluated with evidence from the Tamil and Muslim cases in the context of the Sri Lankan Civil War. Tamil United Liberation Front leaders left the Tamil nationalist movement in the early 1980s, enabling the Liberation Tigers of Tamil Eelam’s rise to dominate the nationalist agenda for three decades, while the Sri Lanka Muslim Congress did not relinquish the Muslim cause, which in part precluded the normalisation of violence in the community.     

Defense Firms Adapting to Major Changes in the French R&D Funding System

The structural changes inside the French innovation system have impacted the role of defense firms since the late 1980s. Major changes have affected the defense budget and public R&D funding system in particular. The aim of this article is to understand French defense firms’ repositioning within the National Innovation System (NIS) based on an analysis of their R&D behavior over a long period of time (1987–2010). We show that French defense firms remain major players in the NIS and faced up to these major changes by adapting the funding of their R&D and their research priorities and rolling out new innovation capabilities. Additionally, they developed new innovation models to take advantage of new collaborative partnerships developed for civil and military markets.     

Maintaining systems with heterogeneous spare parts

We consider the problem of optimally maintaining a stochastically degrading, single‐unit system using heterogeneous spares of varying quality. The system's failures are unannounced; therefore, it is inspected periodically to determine its status (functioning or failed). The system continues in operation until it is either preventively or correctively maintained. The available maintenance options include perfect repair, which restores the system to an as‐good‐as‐new condition, and replacement with a randomly selected unit from the supply of heterogeneous spares. The objective is to minimize the total expected discounted maintenance costs over an infinite time horizon. We formulate the problem using a mixed observability Markov decision process (MOMDP) model in which the system's age is observable but its quality must be inferred. We show, under suitable conditions, the monotonicity of the optimal value function in the belief about the system quality and establish conditions under which finite preventive maintenance thresholds exist. A detailed computational study reveals that the optimal policy encourages exploration when the system's quality is uncertain; the policy is more exploitive when the quality is highly certain. The study also demonstrates that substantial cost savings are achieved by utilizing our MOMDP‐based method as compared to more naïve methods of accounting for heterogeneous spares.     

Solving partially observable agent‐intruder games with an application to border security problems

In this paper, we introduce partially observable agent‐intruder games (POAIGs). These games model dynamic search games on graphs between security forces (an agent) and an intruder given possible (border) entry points and high value assets that require protection. The agent faces situations with dynamically changing, partially observable information about the state of the intruder and vice versa. The agent may place sensors at selected locations, while the intruder may recruit partners to observe the agent's movement. We formulate the problem as a two‐person zero‐sum game, and develop efficient algorithms to compute each player's optimal strategy. The solution to the game will help the agent choose sensor locations and design patrol routes that can handle imperfect information. First, we prove the existence of ?‐optimal strategies for POAIGs with an infinite time horizon. Second, we introduce a Bayesian approximation algorithm to identify these ?‐optimal strategies using belief functions that incorporate the imperfect information that becomes available during the game. For the solutions of large POAIGs with a finite time horizon, we use a solution method common to extensive form games, namely, the sequence form representation. To illustrate the POAIGs, we present several examples and numerical results.     

New sources of military change – armed forces as normal organizations

The literature on how European states have adapted to the post-cold war security environment ffocuses invariably on different understandings of military transformation, a process which is seen as inherently different from other forms of organizational change. However, as this paper argues, new management practices, going back to the introduction of so-called New Public Management (NPM) reforms throughout Europe in the 1980s, have eventually penetrated also the last bastion of the old state – the defense sector. Taking a critical approach to the idea of military transformation and existing theories of military change, the paper demonstrates how other international developments have pushed towards what may be seen as a “normalization” of Europe’s defense sectors. This has important implications for how we approach and understand change in contemporary defense organizations.