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The purpose of this paper is to present another historical case that supports the theory that power equality – and not power inequality – reduces international tension and makes the world more peaceful.

The paper refers to two mathematical models that back this theory and focuses on the case of the American and Soviet military expenditures during the last 25 years of the superpowers' rivalry. Both datasets are adjusted for inflation and expressed in constant US dollars. The 25‐year interval is divided into two main subintervals into the basis of data characteristics, and four regression lines are determined.

The regression lines of the US and USSR military expenditures corresponding to the first‐time interval intersect in 1971, when the main decisions regarding the SALT Treaty were made. The same lines for the second interval intersect in 1989, when the Cold War ended. The USA decided to escalate the Vietnam War during the period in which their military expenditures were significantly higher than the Soviet ones. Similarly, the Soviet Union invaded Afghanistan when its military expenditures were considerably bigger than the American ones. Subsequently, it is possible to affirm that the 1976‐1991 US‐USSR arms race is another important empirical case that supports the theory asserting that power equalization reduces international tension.

By using three simple statistical techniques – adjustment for inflation, determination of the relevant regression lines, and calculation of intersection points – the paper shows that two sets of highly significant empirical data reinforce the theory that power equalization reduces international tension.

The results of the November 2004 US elections suggest that the initial missile defense capabilities fielded in 2004 will be developed and expanded during the next 4 years. This process will require a significant amount of money, and therefore, the problem of optimal allocation of funds becomes relevant.

In this paper, the author presents a theoretical dynamic model for appropriation of funds for developing and deploying defensive systems and maintaining/modernizing offensive systems such as the country's security to be optimized. The offensive systems are regarded as state variables, and the defensive systems as control variables. The criterion of performance consists in the minimization of the number of incoming missiles which cannot be destroyed by the defensive systems. The optimal solutions are calculated by using the Pontryaguine principle.

One observes that depending on the impact of the development of missile defense systems on the modernization of offensive systems, different policies of fund appropriation should be considered. One also remarks that under given circumstances only one (in theory), or a couple of very close policies (in practice) may be regarded as optimal.

The relationship between the development of missile defense systems and the modernization of offensive systems (or the creation of new offensive systems) is studied by using dynamic systems theory. The optimal appropriation of financial funds is done by applying the principle of Pontryaguine.

The purpose of this paper is to explain the tendency of escalation of a regular bilateral arms race, or the arms race spiral.

Inspired by the Richardson‐type models, a system of two differential equations is used for describing a bilateral arms race. But the variation of one adversary's armaments and/or military expenditures is not associated with the amount of the other's armaments and/or military expenditures as it is usually done in this type of model. It is linked instead with their variation, as it practically happens in governments' decision‐making processes.

The association of the two variations suggests that when one adversary tends to match the increase of the other's armaments and/or military expenditures, these tend to increase to infinity for a given fixed point in time.

The mathematical result indicates that the tendency of completely matching the increase of adversary's armaments or military expenditures acts as an accelerator that causes the continuous escalation of the arms race. Therefore, as long as a substantial change in the relationship between the two adversaries – implying a complete change of the model's coefficients – does not happen, the arms race escalates, and the so‐called spiral is observed.

In this article the mathematical formula of entropy is used to evaluate the degree of anarchy specific to multipolar, bipolar, and balance of power international political systems. Several entropic properties characteristic to these systems are deduced, and it is proved that alliances decrease international systems' entropy. Each international system it is observed is characterized by a specific amount of structural strain, and that under the assumptions of structural neo‐realism the entropy and structural strain move in opposite ways. On the basis of these findings a few properties regarding the stability of international systems are divided and the effects of alliances on international structural strain are examined. In the last part of the paper theoretical conclusions are tested against three empirical cases – the Cold War bipolar system, the XIXth Century European system, and the current one. The article ends with several methodological suggestions regarding a possible generalization of the entropic model.