Logo IMG


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

comments powered by Disqus

Connect With Us:

Facebook Icon Sm Twitter Icon Google+ Icon Pinterest Icon RSS Feed

Sigma Xi/Amazon Smile (SciNight)

Latest Multimedia

VIDEO: Citizen Scientists Aid Researchers in Studying Camel Crickets

MJEpps CricketsThey may bounce really high and look strange, but don't worry, they are harmless...they even scavenge for crumbs off of your floor! A continental-scale citizen science campaign was launched in order to study the spread and frequency of native and nonnative camel crickets in human homes across North America.

Mary Jane Epps, PhD, an author of the paper, went into more detail about the study and significance of citizen scientists in an interview with Katie-Leigh Corder, web managing editor.

To view all multimedia content, click "Latest Multimedia"!

Subscribe to Free eNewsletters!

  • Sigma Xi SmartBrief:

    A free daily summary of the latest news in scientific research. Each story is summarized concisely and linked directly to the original source for further reading.

  • American Scientist Update

  • An early peek at each new issue, with descriptions of feature articles, columns, Science Observers and more. Every other issue contains links to everything in the latest issue's table of contents.

  • Scientists' Nightstand

  • News of book reviews published in American Scientist and around the web, as well as other noteworthy happenings in the world of science books.

    To sign up for automatic emails of the American Scientist Update and Scientists' Nightstand issues, create an online profile, then sign up in the My AmSci area.


Of Possible Interest

Book Review: Don't Try This at Home

Book Review: Stocking Nature’s Arsenal

Book Review: Have You Seen This Species?

Subscribe to American Scientist