You find yourself in a PD against a perfect copy of yourself. At the end of the game, I will remove the money your clone wins, destroy all records of what you did, re-merge you with your clone, erase both our memories of the process, and let you keep the money that you won (you will think it is just a gift to recompense you for sleeping in my lab for a few hours). You had not previously considered this situation possible, and had made no precommitments about what to do in such a scenario. What do you think you should do?

Given that you're going to erase my memory of this conversation and burn a lot of other records afterward, it's entirely possible that you're lying about whether it's me or the other me whose payout 'actually counts.' Makes no difference to you either way, right? We all look the same, and telling us different stories about the upcoming game would break the assumption of symmetry. Effectively, I'm playing a game of PD followed by a special step in which you flip a fair coin and, on heads, swap my reward with that of the other player.

So, I'd optimize for the combined reward to both myself and my clone, which is to say, for the usual PD payoff matrix, cooperate. If the reward for defecting when the other player cooperates is going to be worth drastically more to my postgame gestalt, to the point that I'd accept a 25% or less chance of that payout in trade for virtual certainty of the payout for mutual cooperation, I would instead behave randomly.