The pioneering work of Richardson [41] set the stage for subsequent attempts to analyze quantitatively many questions of strategic military and economic competition between -- and among -- nations. Some of his insights came from his work on a classic chaotic system, our weather. He has already anticipated many developments which only were realized decades later, when fast computers became available. Many phenomena that are exhibited by chaotic systems appear to have striking parallels in the interaction of human societies [6]. The interpretation that chaos always has a high risk of conflict is not always correct. For example in [11] we discuss how low level bounded chaos can indicate a stabilizing, democratic discussion and interaction. Conditions that lead to an orderly but unbounded arms races can have a much higher risk of war. Some of these arguments have also been discussed in an model on the impact of SDI on the strategic arms race [43]: This research indicated that very fast rates of deployment of SDI systems can lead to unstable and unpredictable solutions which can be interpreted as indications of chaotic processes. The numerical value of the predicted number of ICBMs for each side after a 30 year arms race could take any value between zero and 10,000 missiles. More recently, the end of the cold war and its impact on the international security system have been studied. The end of the simple situation of a two-nation superpower competition leads to a multi-polar world in which alliances can form and change [48]. Some elements of this problem have been studied in [8],[25] and will be discussed in the next section. Today the situation is much more complex, the potential futures of multiple, interacting, adaptive and intelligent agents will require new approaches for example for the international organizations (see e.g. the discussion in [31]).