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# Mathematical Models of Arms Control and Disarmament

Gerald H. Kramer

Vol. 57, No. 4 (WINTER 1969)

MATHEMATICAL MODELS OF ARMS CONTROL & DISARMAMENT: Application of Mathematical Structures to Politics. T. L. Saaty; 190 pages; \$10.95; John Wiley & Sons, 1968 (Operations Research Society of America Publications, Number 14).

The purpose of this book is “to explore some basic problems of arms control through mathematical models and to show that such models might be used to study idealizations of problems arising in the arms control area.” Accordingly, the greater part of the book is devoted to a series of examples.

The first chapter is a general discussion of arms control and disarmament, which sets the framework for the rest of the book. Chapter 2, “Models of Arms Races,” presents a series of models of various aspects of the arms race, including several generalizations of Richardson’s arms-race model, a dynamic model of a missile war based on optimal control theory, and models of deterrence stability and of arms reduction. The third chapter is basically an expository introduction to the theory of games, mainly two-person theory, with examples drawn from proliferation and the Vietnam war. Chapter 4, on negotiations, describes a game model of disarmament negotiation in which each side seeks to preserve the relative balance of power, and surveys some results on games with imperfect information. Chapter 5, on “violation inspection phenomena,” formulates the statistical problem of detecting test-ban violations from classical, Bayesian, and decision-theoretic points of view, and applies game theory to the problems of choosing inspection systems and violation-inspection strategies. The final chapter reviews some empirical work on conflicts and aggression, and concludes with the author’s “nonscientific speculations” on war, peace, and the future. The particular models and applications described are for the most part only illustrative, and are not intended to be sufficiently detailed to be of immediate policy relevance. The mathematical material in the text is interspersed with a variety of interesting asides and insights by the author.

As this description indicates, the book is not a comprehensive or systematic introduction to arms control, or to any particular approach to it. It is, however, a useful and readable introduction to some of the kinds of mathematical work being done in the area.—Gerald H. Kramer, Cowles Foundation, Yale University

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