Zvi mentioned hyperbolic discounting. What if an agent's preferences are actually described by hyperbolic discounting? Then different versions of the agent in time have different preferences, so they are essentially different agents. Consider just two such agent-moments. Each agent-moment would prefer both not eating garlic bread to both eating, but prefers even more itself eating while the other doesn't eat.

Since they have different preferences and the earlier agent-moment can't physically force the later agent-moment to make a certain choice, the analogy with PD seems pretty good and TDT does seem relevant here.