Again, I would imagine that a battle between two AGIs would be determined by the amount of resources controlled within the proximate area of the battle.

Since they can trade globally, what's locally available must be irrelevant.

(I was talking about what it takes to stop a non-AGI civilization, hence a bit of misunderstanding.)

And if you get an alien AGI, you don't need to rush towards it, you only need to have had an opportunity to do so. Everyone is better off if instead of inefficiently running towards fighting the new AGI, you go about your business as usual, and later at your convenience the new AGI surrenders, delivering you all the control you could gain by focusing on fighting it and a bit more. Everyone wins.