In the finite (e.g. 100 round) Iterated Prisoner's Dilemma, sources like Wikipedia claim that All-Defect is a dominant strategy, which is then proven by backwards induction.
I understand this argument, and understand why All-Defect can be considered rational. But for it to be dominant, it must be the case that there is no better strategy given any strategy played by the opponent. And this seems false to me.
What if your opponent plays Tit-for-tat? It is rightly claimed that All-Defect will win against Tit-for-tat. But that seems quite irrelevant for the question of dominance, as Tit-for-tat gains much more utility against Tit-for-tat than All-Defect does against Tit-for-tat.
So given that my opponent plays Tit-for-tat, I would much rather play Tit-for-tat than All-Defect. Does this not mean that All-Defect isn't dominant? Where am I going wrong?