Multilinear extensions and quotients of simple games

Studied here is the problem of evaluating the formation of coalitions in cooperative games by considering its internal and external effects. Our analysis is based upon a formal theory of the quotient game and the use of multilinear extensions to compute the Shapley value and the coalitional value. When it applies to simple games, a series of interesting results is obtained. © 1996 John Wiley & Sons, Inc.     

Multi-period airline overbooking with multiple fare classes

Consider a multi-period multi-fare class airline overbooking problem that relates to a single-leg flight. Passengers may cancel their reservations at any time, including being no-shows at flight-time. Canceling passengers receive a refund that depends on their fare class, e.g., supersaver, coach, etc. At flight-time, the airline bumps passengers in excess of flight capacity and pays a penalty for so doing. A continuous state-space dynamic programming model is developed in which the state is the numbers of reservations currently on hand in each fare class. In each period, reservation requests occur in only one fare class and the fraction of reservations canceling in each class is independent of the number of reservations therein. A booking-limit policy is optimal, i.e., in each period the airline accepts reservation requests up to a booking limit if the number of initial reservations in the fare class is less than the booking limit, and declines reservation requests otherwise. The booking limits for each class depend on the numbers of reservations in the other classes. When there are two fare classes the optimal booking limits in each class decrease with the number of reservations in the other class. © 1996 John Wiley & Sons, Inc.     

Optimal number of minimal repairs before replacement of a system subject to shocks

A system is subject to shocks that arrive according to a nonhomogeneous Poisson process. As shocks occur a system has two types of failures. Type 1 failure (minor failure) is removed by a minimal repair, whereas type 2 failure (catastrophic failure) is removed by replacement. The probability of a type 2 failure is permitted to depend on the number of shocks since the last replacement. A system is replaced at the times of type 2 failure or at the nth type 1 failure, whichever comes first. The optimal policy is to select n* to minimize the expected cost per unit time for an infinite time span. A numerical example is given to illustrate the method. © 1996 John Wiley & Sons, Inc.     

Metastases: Exploring the impact of foreign fighters in conflicts abroad

This article examines the historical impact of foreign fighters and how the international community has sought to counter this threat. It argues that foreign fighters have contributed significantly to the metastasis of Salafi-jihadism over the past 30 years. They have globalized local conflicts. They have brought advanced skills to battlefields. Further, the logistics infrastructure built by foreign fighters has allowed Salafi-jihadism to expand rapidly. The challenge for security officials today is how to prevent the foreign fighters in Syria and Iraq from expanding the threat of Salafi-jihadism further. To inform this effort, this article derives lessons learned from past efforts against Arab Afghans in Bosnia (1992–1995) and Abu Musab al-Zarqawi’s foreign volunteers in Iraq (2003–2008).     

Counterinsurgency as armed reform: The political history of the Malayan Emergency

Despite the emphasis in doctrine and academia that counterinsurgency is in its essence political, these operations are all too commonly discussed and approached as primarily military endeavors. Informed by the need to refocus counterinsurgency studies, this article revisits a foundational case of the canon – the Malayan Emergency – to discuss its political (i.e., not military) unfolding. The analysis distinguishes itself by emphasizing the diplomatic processes, negotiations, and deals that gave strategic meaning to the military operations underway. In so doing, the article also generates insight on the use of leverage and elite bargains in creating new political settlements and bringing insurgent conflicts to an end.     

How long until midnight? Intelligence-policy relations and the United States response to the Israeli nuclear program, 1959–1985

Why did the United States fail to stop Israeli acquisition of nuclear weapons? Existing research argues that patrons such as the U.S. should have an easy time halting proliferation by militarily and economically vulnerable clients. Nevertheless, Israel acquired nuclear weapons with relatively little American opposition. Utilizing extensive primary source research, we argue that problematic intelligence-policy relations hindered U.S. efforts to arrest Israeli proliferation as (1) policymakers often gave mixed guidance to the intelligence community, resulting in (2) limited information on Israeli efforts that reinforced policy ambiguity. The results carry implications for understanding the dynamics of nuclear proliferation and intelligence-policy relations.     

A Cryptographic Escrow for Treaty Declarations and Step-by-Step Verification

The verification of arms-control and disarmament agreements requires states to provide declarations, including information on sensitive military sites and assets. There are important cases, however, in which negotiations of these agreements are impeded because states are reluctant to provide any such data, because of concerns about prematurely handing over militarily significant information. To address this challenge, we present a cryptographic escrow that allows a state to make a complete declaration of sites and assets at the outset and commit to its content, but only reveal the sensitive information therein sequentially. Combined with an inspection regime, our escrow allows for step-by-step verification of the correctness and completeness of the initial declaration so that the information release and inspections keep pace with parallel diplomatic and political processes. We apply this approach to the possible denuclearization of North Korea. Such approach can be applied, however, to any agreement requiring the sharing of sensitive information.     

Robust shortest path planning and semicontractive dynamic programming

In this article, we consider shortest path problems in a directed graph where the transitions between nodes are subject to uncertainty. We use a minimax formulation, where the objective is to guarantee that a special destination state is reached with a minimum cost path under the worst possible instance of the uncertainty. Problems of this type arise, among others, in planning and pursuit‐evasion contexts, and in model predictive control. Our analysis makes use of the recently developed theory of abstract semicontractive dynamic programming models. We investigate questions of existence and uniqueness of solution of the optimality equation, existence of optimal paths, and the validity of various algorithms patterned after the classical methods of value and policy iteration, as well as a Dijkstra‐like algorithm for problems with nonnegative arc lengths.© 2016 Wiley Periodicals, Inc. Naval Research Logistics 66:15–37, 2019     

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     

Some new results on the preservation of the NBUE and NWUE aging classes under the formation of coherent systems

We consider the classical problem of whether certain classes of lifetime distributions are preserved under the formation of coherent systems. Under the assumption of independent and identically distributed (i.i.d.) component lifetimes, we consider the NBUE (new better than used in expectation) and NWUE (new worse than used in expectation) classes. First, a necessary condition for a coherent system to preserve the NBUE class is given. Sufficient conditions are then obtained for systems satisfying this necessary condition. The sufficient conditions are satisfied for a collection of systems which includes all parallel systems, but the collection is shown to be strictly larger. We also prove that no coherent system preserves the NWUE class. As byproducts of our study, we obtain the following results for the case of i.i.d. component lifetimes: (a) the DFR (decreasing failure rate) class is preserved by no coherent systems other than series systems, and (b) the IMRL (increasing mean residual life) class is not preserved by any coherent systems. Generalizations to the case of dependent component lifetimes are briefly discussed.