On computing the expected discounted return in a markov chain

The discounted return associated with a finite state Markov chain X₁, X₂… is given by g(X₁)+ αg(X₂) + α²g(X₃) + …, where g(x) represents the immediate return from state x. Knowing the transition matrix of the chain, it is desired to compute the expected discounted return (present worth) given the initial state. This type of problem arises in inventory theory, dynamic programming, and elsewhere. Usually the solution is approximated by solving the system of linear equations characterizing the expected return. These equations can be solved by a variety of well-known methods. This paper describes yet another method, which is a slight modification of the classical iterative scheme. The method gives sequences of upper and lower bounds which converge mono-tonely to the solution. Hence, the method is relatively free of error control problems. Computational experiments were conducted which suggest that for problems with a large number of states, the method is quite efficient. The amount of computation required to obtain the solution increases much slower with an increase in the number of states, N, than with the conventional methods. In fact, computational time is more nearly proportional to N², than to N³.     

Computing equilibria via nonconvex programming

The problem of determining a vector that places a system in a state of equilibrium is studied with the aid of mathematical programming. The approach derives from the logical equivalence between the general equilibrium problem and the complementarity problem, the latter being explicitly concerned with finding a point in the set S = {x: < x, g(x)> = 0, g(x) ≦ 0, x ≧ 0}. An associated nonconvex program, min{? < x, g(x) > : g(x) ≦ 0, x ≧ 0}, is proposed whose solution set coincides with S. When the excess demand function g(x) meets certain separability conditions, equilibrium solutions are obtained by using an established branch and bound algorithm. Because the best upper bound is known at the outset, an independent check for convergence can be made at each iteration of the algorithm, thereby greatly increasing its efficiency. A number of examples drawn from economic and network theory are presented in order to demonstrate the computational aspects of the approach. The results appear promising for a wide range of problem sizes and types, with solutions occurring in a relatively small number of iterations.     

Impact of an all volunteer force upon the navy in the 1972-1973 timeframe

This paper develops estimates of true volunteer levels for 1972 and 1973, based on experience gained through 1970 draft lottery data. The paper also formulates estimates of the qualitative characteristics of a 1972-1973 Navy volunteer force, and establishes a relationship between rate of volunteerism and military pay. Utilizing estimates generated in the paper, Navy military personnel budget requirements for FY '72 and '73 are presented.     

Innovation for seapower: U.S. Navy strategy in an age of acceleration

ABSTRACT

A call for innovation as a means to outpace the acceleration of technological change and to bolster capabilities quickly is a central theme of contemporary U.S. Naval Strategy. The need for innovation is accepted, but the integration of readily available technologies into the Fleet is slow. Innovation unfolds according to “Navy-Time,” a cycle lasting between a long-decade and thirty-years. To accelerate the innovation process in the U.S. Navy, the article offers a Concept of Operations for Innovation that outlines how a deliberate process of analysis, weaponisation and integration can move new ideas and weapons into the Fleet in a strategically relevant time-frame.     

US grand strategy and the origins of the developmental state

ABSTRACT

Scholars have credited a model of state-led capitalism called the ‘developmental state’ with producing the economic miracles of Japan, South Korea, and Taiwan. This article examines how the developmental state was shaped by the Cold War. US grand strategy focused on accelerating economic development among allies that were under the greatest threat from Communist China and North Korea. American aid agencies became involved in the process of state-building in Japan, South Korea, and Taiwan and supported economic planning. I verify this claim by contrasting US policies on Taiwan with US policies in the Philippines, which faced a weaker Communist threat.