Two parties don’t go into all out war because it would create a power vacuum that would be filled by a third party and weaken them to the third party
sounds like a truel. Though, in that game but also in a simple duel, if you get into an all-out war then you may be destroyed even without the participation of a third party, so the rational move may be to avoid war in the first place.
It seems like a sort of symbiotic relationship, something like mutualism. That is, the two parties benefit each other by mutually increasing both species’ chances of survival. In this case, by keeping the third party down.
Or something like that. It’s not a perfect description, but with a little massaging I think it’s close.
ETA: And I should note, in case it’s not readily apparent, that that’s a biological relationship. Still, it seems very close to a sort of service-service mutualism. Mutualism (biology) - Wikipedia
As you describe it, it’s seems to be the opposite of one party attempting to divide and conquer. There doesn’t seem to be any antonym phrases or terms for divide and conquer. That is actually really depressing to think about it, that could mean it has happened more often than not and a term or definition wasn’t created… Just my $0.02
Unify and Defy!
ETA: That’s my own term, not a pre-existing one as desired by the OP. And I’d still throw my weight behind mutualism, even if it’s a biological term.
Arguably was the case with the Sino-Japanese war in the 30’s & 40’s: Nationalists, Communists, & Japanese. I know the 2 Chinese factions viewed it that way at least.
I’m pretty confident that WOPR has a name for this scenario, but I don’t recall what it is. They went by so quickly.
I googled WOPR scenarios and came up with a list someone generated on reddit. While one or two have fun names that could perhaps be appropriated to describe this scenario, none jumps out as specifically applicable.
WOPR is imperfect?!?
The enemy of my enemy is my friend? A and B decide on nonaggression because of C. A and B are both enemies of C, but that may be the only thing they agree on. Because their common enemy C is a greater threat, they remain at peace with each other. The same may simultaneously be true of A and C w/r/t B, and B and C w/r/t A. Three-way mutually assured destruction, as it were.
Lol. That works. I actually like Unify and Defy… I wonder how often it actually occurs, though.