Greg Egan was the first I heard talking about how exponential growth is unsustainable. He talked about it from a hard sci-fi standpoint, noting that you are limited to cubic expansion once your frontier reaches the speed of light.
I am interested in exponential growth in a softer science fiction, where Faster Than Light travel is commonplace and the limit to expansion occurs when you bump into a competing culture. Assuming conflict is inevitable, what kind of culture ultimately wins?
Fast expansionists might lose out because they spread themselves too thin and meet other cultures earlier in their development. But if they are aggressive -- especially if they are xenocidal -- they might win by stealing other cultures' technology.
Slow expansionists might lose out because they do not control as much resources as the big empire, even if they are older and more advanced.
It seems the future belongs to the bullies, but who knows. Maybe there is a confluence of phenomena we do not know about that punishes bullies. If such a confluence exists, how might it look?
Edit: Some clarification
In my universe I assume nothing moves at relativistic velocity compared to anything else, or maybe there is a preferred frame, so space-like movement doesn't get messy. Except when it does, Star Trek style, because it makes for an interesting story. I mentioned hard sci-fi as a contrast to what I am trying to do in my work.
I also assume there are no free niches for whatever reason. Maybe old cultures tend to fill all of the available niches, or they all magically require the same niche.
I use the word "culture" because a civilization can fracture into competing factions or comprise several species. "Culture" seems like a good catch-all term.
By "win" I mean "dominate". Under what circumstances do the aggressive expansionist cultures not dominate the universe?