... Since I am, of course a FAI (Sarcasm!) I can tell you the answer to this. They obviously split the future time-streams of the universe by each committing instant civilization-wide suicide or not based on a quantum lottery. Anthropic engineering in this way ensures they do not have to fight each other at all, which would entail actual risk of people getting hurt,

No, seriously, you want us to take guesses at how weakly godlike entities are going to interact ? Pftrttfffff,mwhahahahahaahaaa.