It’s not part of the definition of PD that players can condition on each others’ strategies. In fact PD was specifically constructed to prevent this (i.e., specifying that each prisoner has to act without observing how the other acted).
I think it’s usually part of the definition of a PD that you know who you are in a prisoner’s dilemma with.
I do think we are hitting the limits of analogy here and it’s not super clear how to extend the usual definition of a prisoner’s dilemma to more exotic scenarios like the one we are discussing, but in the limit I feel like the prisoner’s dilemma becomes totally meaningless if you remove all knowledge of who you are coordinating with from the equation. The fundamental challenge in a prisoner’s dilemma is predicting what your partner in the dilemma is trying to do, and if you have no information on that, there is no hope for any kind of coordination (and I doubt anyone would argue there is a predictably winning strategy for a prisoner’s dilemma against a completely randomly chosen mind/algorithm).
I think it’s usually part of the definition of a PD that you know who you are in a prisoner’s dilemma with.
I do think we are hitting the limits of analogy here and it’s not super clear how to extend the usual definition of a prisoner’s dilemma to more exotic scenarios like the one we are discussing, but in the limit I feel like the prisoner’s dilemma becomes totally meaningless if you remove all knowledge of who you are coordinating with from the equation. The fundamental challenge in a prisoner’s dilemma is predicting what your partner in the dilemma is trying to do, and if you have no information on that, there is no hope for any kind of coordination (and I doubt anyone would argue there is a predictably winning strategy for a prisoner’s dilemma against a completely randomly chosen mind/algorithm).