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.     

Strategic Defense and Attack for Series and Parallel Reliability Systems: Reply to Rejoinder

Kovenock and Roberson's (2012a, b) replication of Hausken’s (2008a) equations and parameter restrictions do not enhance our insight into the defense and attack of reliability systems. This reply intends to fill the remaining understanding gaps.     

A cost–benefit analysis of terrorist attacks

A cost–benefit analysis of terrorist attacks is developed and placed within a systematic theoretical structure. For the target or object of the attack, we consider the lost value of human lives, lost economic value, and lost influence value, counted as benefits for the terrorist. The corresponding losses for the terrorist are counted as costs. The terrorist attacks if benefits outweigh costs. Bounded rationality is enabled where the three kinds of benefits and costs can be weighted differently. We account for two ex ante probabilities of successful planning and attack, and enable the terrorist to assign different weights to its multiple stakeholders. We introduce multiple time periods, time discounting, attitudes towards risk, and subcategories for the benefits and costs. The cost–benefit analysis is illustrated with the 11 September 2001 attack, and 53 incidents in the Global Terrorism Database yielding both positive and negative expected utilities. The paper is intended as a tool for scientists and policy-makers, as a way of thinking about costs and benefits of terrorist attacks.     

Approximations and empirics for stochastic war equations

The article develops a theorem which shows that the Lanchester linear war equations are not in general equal to the Kolmogorov linear war equations. The latter are time‐consuming to solve, and speed is important when a large number of simulations must be run to examine a large parameter space. Run times are provided, where time is a scarce factor in warfare. Four time efficient approximations are presented in the form of ordinary differential equations for the expected sizes and variances of each group, and the covariance, accounting for reinforcement and withdrawal of forces. The approximations are compared with “exact” Monte Carlo simulations and empirics from the WWII Ardennes campaign. The band spanned out by plus versus minus the incremented standard deviations captures some of the scatter in the empirics, but not all. With stochastically varying combat effectiveness coefficients, a substantial part of the scatter in the empirics is contained. The model is used to forecast possible futures. The implications of increasing the combat effectiveness coefficient governing the size of the Allied force, and injecting reinforcement to the German force during the Campaign, are evaluated, with variance assessments. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2005.