I don’t see why TDT players would fail to cooperate under conditions of common knowledge. Are you talking about a case where they each know the other is TDT but think the other doesn’t know they know, or something like that?
I don’t know the whole answer, but for example consider what happens with Pareto-efficiency in PD when you allow mixed strategies (and mixed strategy is essentially the presence of nontrivial dependence of the played move on the agent’s state of knowledge, beyond what is restricted by the experiment, so there is no actual choice about allowing mixed strategies, mixed strategies are what’s there by default even if the problem states that players select some certain play). Now, the Pareto-efficient plays are those where one player cooperates with certainty, while the other cooperates or defects with some probability. These strategies correspond to bargaining between the players. I don’t know how to solve the bargaining problem (aka fairness problem aka first-mover problem in TDT), but I see no good reason to expect that the solution in this case is going to be exactly pure cooperation. Which is what I meant by the insufficiency in correspondence between true PD and pure cooperation: true PD seems to give too little info, leaving uncertainty about the outcome, at least in this sense. This example doesn’t allow both players to defect, but it’s not pure cooperation either.
I don’t see why TDT players would fail to cooperate under conditions of common knowledge. Are you talking about a case where they each know the other is TDT but think the other doesn’t know they know, or something like that?
I don’t know the whole answer, but for example consider what happens with Pareto-efficiency in PD when you allow mixed strategies (and mixed strategy is essentially the presence of nontrivial dependence of the played move on the agent’s state of knowledge, beyond what is restricted by the experiment, so there is no actual choice about allowing mixed strategies, mixed strategies are what’s there by default even if the problem states that players select some certain play). Now, the Pareto-efficient plays are those where one player cooperates with certainty, while the other cooperates or defects with some probability. These strategies correspond to bargaining between the players. I don’t know how to solve the bargaining problem (aka fairness problem aka first-mover problem in TDT), but I see no good reason to expect that the solution in this case is going to be exactly pure cooperation. Which is what I meant by the insufficiency in correspondence between true PD and pure cooperation: true PD seems to give too little info, leaving uncertainty about the outcome, at least in this sense. This example doesn’t allow both players to defect, but it’s not pure cooperation either.