With growing tensions in today's world, new powers rising and contesting old powers, two nations risk ending up in a so called security dilemma: One nation's increase in security threatens its opposing nation. The consequence could be the escalation of military buildups into arms races. With ongoing technological advancements, militaries around the world are expanding on autonomous capabilities that need less and less human control. In this research, I investigate under which conditions arms races for these systems between two fictitious nations may occur and how the nations can influence these. For this, I construct a system dynamics model based on literature and expert consultations and conduct experiments to generate a wide range of possible scenarios. The model results suggest that different types of arms races for autonomous military capabilities occur under specific conditions: the inferior nation lacks behind the superior nation and fills this initial gap not with a greater number of autonomous systems, but with higher quality autonomous systems, leading to an arms race in quality. Bilateral disarmament in the form of regulations on the level of autonomy seem not to be the answer for the superior nation: some of the arms racing is reduced, but the superior nation now loses both racing and non-racing scenarios. Restrict an opponent in their technological development is more effective for the superior nation. Still, the inferior nation is able to win in the specific case, where the superior nation requires "too much" human control. Generally, arms races can further be reduced when both nations avoid to be too "reactive" to each other's arming actions. This suggests, that a third party could step in and aim at relaxing the tensions between the two nations. Further, this third party could also aim at encouraging the inferior nation to raise its ethical standards. To conclude, the model can give insight into which decisions a nation or a third party can take with different goals in mind. These include, for the nations involved in a competition as a result from tensions, to either win the race towards autonomy or to prevent its opponent from winning it. A third party, interested in a peaceful world without having nations piling up autonomous military capabilities, might aim at preventing arms races whatsoever.