What's it called again? "The ___ trap"? Where countries spiral into unwanted war.

Ok guys, I'm a bit OCD with having to google and verify/clarify/read more about things that pop into my head, but for the life of me I can't find a search phrase which gives me the answer to what I'm looking for, which is bugging me now.

I'm trying to think of the name given a phenomenon, where two countries spiral into war without either side actually wanting to. The principal (which I was actually trying to refresh on, so bear with me here) is something like this:
First country A may be wary of country B, because the former has loads of gold and the latter has economic problems. So even though country B hasn't actually made any threats or anything, just in case, country A makes a series of outposts along the border. Country B see's this and takes notice, deciding they too better secure their border, so they too build posts and re-position garrisons. Then back to country A again, they see that a lot of their increased force is negated by country B, and so they step it up a notch and position missiles near the border zone to make sure they would have the upper hand if unexpected war broke out. Country B see's this and becomes alarmed. They wonder why A has made such a move, so they start holding drills in the area and re-position heavy weapons, specifically intended to combat A... back to country A again, now they are worried. They see heavy weapons on the border and military drills obviously created with them in mind, and so now A starts to fear this is early preparations for a war against them.... etc etc etc, until they completely view each other as the enemy or actually go to war- despite the fact that they don't really hate each other or have offensive objectives, rather they just spiraled into a trap of chain reactions.

So darn it, what's the name given to that kind of thing? I think it's called "The ____ trap" maybe?? Who ever can tell me wins a cookie.
@_Chimurenga_ @Hoverpot
No, that's not exactly what I meant..

AH! One more burst of googling and I have found it! (yay, i'm saved from death by OCD urges)

The Hobbesian trap
(or Schelling's dilemma) is a theory that explains why preemptive strikes occur between two groups, out of bilateral fear of an imminent attack. Without outside influences this situation will lead to a fear spiral (catch-22, vicious cycle, Nash equilibrium) in which fear will lead to an arms race which in turn will lead to increasing fear. The Hobbesian trap can be explained in terms of game theory. Although cooperation would be the better outcome for both sides, mutual distrust leads to the adoption of strategies that have negative outcomes for individual players and all players combined.[1] The theory has been used to explain outbreaks of conflicts and violence, spanning from individuals to states.

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