John V. Gillespie

A Formal Analysis of Some Issues in Balance of Power Theories

Two general issues raised in discussions of balance of power theories are considered in this paper: the relationship between, on the one hand, the power ratio goals of nations and the size of the international system and, on the other hand, the systems “war propensity.” These relationships are explored through the application of differential game theory. A mathematical model is proposed in which nations are assumed to operate according to certain dynamics, and to have specified goals and certain information about the international system. The “war propensity” of the system is then defined in terms of dangerous power configurations, and the impact of power ratio goals and system size is considered. Several variations on the basic model are analyzed: (1) systems with or without coalitions, (2) different conceptualizations of the dangerous power distribution, and (3) systems containing different types of nations, to wit, major powers and minor powers.

Parameter estimation by numerical minimization methods

The purpose of this paper is to discuss a technique which can be used to solve estimation problems for which the more commonly accepted analytical methods such as linear regression analysis are inappropriate. The estimation method proposed consists of using computer alogrithms for numerical minimization of functions. The basic method of functional minimization is discussed and examples are provided. Various measures of fit for non‐unique solutions, and statistical tests on the parameter estimates are addressed. The paper concludes that functional minimization is not a panacea for all parameter estimation problems, but for many models can provide parameter estimates and statistical tests which otherwise would not be available.

Transforming a Nation-Dominant International System

This paper investigates the problem of system transformation. Focusing on one attribute of system structure, the distribution of power, it is shown that certain power distributions are incompatible with certain optimizing behaviors. Specifically, it is shown that if a system contains a dominant nation, a nation whose power exceeds the sum of the power of all remaining nations, and if nations optimize using stochastic inputs, then the dominant nation will lose its superiority. It is further shown, through a generalization of the argument, that the application of stochastic inputs also insures against subsystem dominance, thus providing a guarantee against “spheres of influence” by some nations over subsets of nations. The general argument is substantiated by showing that similar results can be obtained by way of two different forms of analysis.

Accumulation in Arms Race Models: A Geometric Lag Perspective

where x(t) and y(t) are the armaments of two opposing nations (most commonly measured by military expenditures), Ax and Ay are the rates of change in the armaments, and k, 1 , a, b, g, and h are constants. Richardson argued in his basic model that the rate of change in a nation’s armaments could be explained by three factors: (1) threat, the terms ky(t) and !x(t) where k and P are “threat coefficients”; (2) economic burden and fatigue, the terms ax(t) and by(t) where a and b are “economic burden coefficients”; and (3) grievance, the terms g and h. Research on Richardson’s equations has taken several forms. First, some scholars have attempted to examine the empirical fit of the equations or some modification of the equations.* Second, some scholars have

Embedded Game Analysis of a Problem in International Relations

The behavior of two groups of nations, superpowers and regional powers, engaged in an arms race represented as a differential game are studied. The various nations are assumed to arm themselves according to a balance of power, the policemen, or the second attack rationale. The regional nations are assumed to control the disposition of strategic resources desired by the superpowers. To obtain these, the superpowers provide assistance to the regional nations. The optimal trajectory corresponding to the above three rationales is computed, and the stability of the trajectory is studied. After a change in the international situation, the regional nations may alter the distribution of the material to the various nations. The effect of this on the stability of the resulting optimal trajectory is investigated.

Macro-Quantitative Analysis CONFLICT, DEVELOPMENT, AND DEMOCRATIZATION Volume I, SAGE Readers in Cross-National Research

An exciting area of social exploration, cross-national research raises numerous problems in the logic of social inquiry-the methods of data collection and analysisand imposes a basic challenge to conventional study of foreign political and social systems. Macro-Quantitative Analysis is of interest to social scientists of all disci576 pages plines, containing articles by political scientists, 1971