I think I might be misunderstanding what you wrote.

I thought you were saying that Eliezer was assuming that the people were not egoists, and if they were, it would all fall apart. I was replying that if they weren't egoists, none of this would be necessary, and it's intended to show that even egoists can work together if that's what it takes to win.

It's also possible that just some of them are egoists. If it's enough of them, you'd still have to do that stuff Eliezer mentioned.