i want to clarify a little bit of a misconception.
when you set up a prisoner's dilemma, you have a choice between competing and cooperating. you fail when you both choose competition over cooperation, and you win when you both choose cooperation over competition.
cooperating, in context, doesn't usually mean just dropping out - there's going to be more to it than that.
with buttigieg and biden, some kind of deal where they split the map up, molotov-ribbentrop style, would have been a better way to cooperate.
as it is, taking buttigieg out doesn't help biden much with the rank and file that make up his base, who are largely low information and uneducated voters, and the types of educated voters that buttigieg did attract are just likely to look elsewhere, as they have biden pretty low on their list. there's no actual co-operation, here.
so, and i know this is somewhat counter-intuitive, but this is actually less like the option of mutual co-operation and more like the option where they both defect, even if it looks otherwise at first glance.
the counter-intuitive twist is that, in the context of this specific two-person subgame, dropping out is actually defecting. co-operation would mean a deal where they split the map up, some kind of strong endorsement or maybe even announcing a shared ticket. as it is, i don't think there's much that buttigieg can do to deliver his voters to biden on such short notice, so dropping out is functionally just releasing them to the other candidates - and that's defection. unless there is cooperation, it doesn't undo the relation of competition, which is what defines the defection, and the players have still failed.
does that make sense?