The stochastic duel with time-dependent hit probabilities

The fundamental stochastic duel considers two opponents who fire at each other at either random continuous or fixed-time intervals with a constant hit probability on each round fired. Each starts with an unloaded weapon, unlimited ammunition, and unlimited time. The first to hit wins. In this article we extend the theory to the case where hit probabilities are functions of the time since the duel began. First, the marksman firing at a passive target is considered and the characteristic function of the time to a hit is developed. Then, the probability of a given side winning the duel is derived. General solutions for a wide class of hit probability functions are derived. Specific examples of both the marksman and the duel problem are given.     

Learning and costs in airframe production: A multiple-output production function approach

This article examines the influence of both production rate and learning on airframe program costs. A dynamic multiple-output production model is developed and is used to observe the cost impact of changes in production rate and learning. Several simulations are performed to demonstrate the sensitivity of the optimal time path of cost to changes in the model parameters. The model is applied by estimating parameters from the F102 airframe program.     

Interpreting the Nuclear Non-Proliferation Treaty

Interpreting the Nuclear Non-Proliferation Treaty, by Daniel H. Joyner. Oxford University Press, 2011. 192 pages, $100.     

Alternatives for defense in the Post‐Soviet World: A guide for economists to the U.S. debate

The defense establishments of all major powers are changing to reflect changes in the foundations of national security strategy and resource allocation. The authors believe economists should play an active role in formulating these changes and offer an orientation to the U.S. debate, presenting three major alternatives: the “Base Force” (Bush Administration), Mr. Aspin's Force “C,” and the “Low” Alternative (Prof. Kaufmann and Dr. Steinbruner). These alternatives are compared using first‐order measures of capabilities, budgets and risk. Budgetary estimates are based on newly‐developed analytical tools.     

Reward,punishment or inducement? US economic and military aid, 1946–1996

If the US has wielded power as global hegemon, then there should be evidence of a linkage between American resources and the ability to influence behavior. However, there is widespread disagreement on how this power is manifested (see Krause, ). Methodological and epistemological issues have hampered empirical studies of US hegemonic behavior. For example, does the US reward past behavior or does it offer inducements for future behavior? We document and discuss these issues in terms of the aid–foreign policy compliance nexus. The empirical portion of our paper tests whether US military and non‐military aid are correlated with foreign policy similarity. The main merits of our study are that: (1) we test a new measure of foreign policy similarity developed by Signorino and Ritter () and compiled by Gartzke et al. (); (2) we relax the causality issue and test using vector autoregression (VAR) for 76 developing countries; and (3) our time horizon is a minimum of 30 years for each country. Our central finding is that aid is most often used as a reward. More specifically, foreign policy similarity leads to greater economic aid for most African countries, foreign policy similarity leads to greater military aid for a majority of Latin American states, and there are no overarching patterns for Asia and the Middle East. We discuss the implications of our findings in the context of the bargaining and structural approaches to statecraft.     

Specialization in defence forces

The choice between balanced and specialized defence forces depends on the technology of defence output (e.g. whether a force scope multiplier is present), the existence of scope and scale economies, the platform customization costs and, of course, the level of defence budgets. Minimum force element levels (thresholds), and scale economies facilitate specialization as opposed to scope economies (e.g. platform‐sharing), scale diseconomies and the force scope multiplier (e.g. defence weakest‐link technology). When a balanced force is not optimal, the option value of a non‐optimally maintained force element must also include the opportunity cost arising from suboptimal force elements. Shrinking defence budgets may produce two surprising phenomena. If some force elements are shut down as a result of thresholds, the surviving ones may increase in platform numbers as well as enjoying closer‐to‐most‐desirable platforms. Furthermore, if heritage force elements are shut down within the budget contraction environment, overall defence capability might rise.