Let's suppose that you look at the code of your counterparty which says "I'll Nuke you unless you Cooperate in which case I Defect", call it "extortionist". You have two hypotheses here:
If you can't actually get any evidence in favor of each hypothesis, you go with your prior and do whatever is the best from the standpoint of UDT/FDT/LDT counterfactual operationalization. I.e., let's suppose payoffs are:
You are playing against extortionist counterparty. Prior probability of extortionist from hypothesis 2 is x. Extortionists from hypothesis 1 can perfectly predict your responce in their decision to self-modify and cover tracks. If they decide to not self-modify, they choose to cooperate conditional on your cooperation. Let's call policy "Nuke extortionist, cooperate with non-extortionist" and "Cooperate with both"
From here, your UDT-expected utility is:
Therefore, you should choose if
i.e.
And 7.27% is a really high frequency of "natural" extortionists, I won't expect it to be this high.
The optimal strategy seems to be Prudent Extorter:
Such agents perform better than your Naive Extorter as they would be able to cooperate with each other and do not nuke a Defection Rock.
When Naive Extorter meets Prudent Extorter they die in a nuclear fire.
I actually have found an example of a strategy that doesn't incentivize someone else to self-modify into Hawkbot: https://www.lesswrong.com/posts/TXbFFYpNWDmEmHevp/how-to-give-in-to-threats-without-incentivizing-them
Basically, when you're faced with a probable extorter, you play Cooperate some of the time (so you don't always get nuked) but either Defect or Nuke back often enough that Hawkbot gets a lower expected value than Cooperate/Cooperate.
Eliezer Yudkowsky wrote, in a place where I can't ask a follow-up question:
Well, what if I told you that I had a perfectly good reason to to become someone that would threaten to nuke Defection Rock, and that it was because I wanted to make it clear that agents that self-modify into a rock get nuked anyway, so there's no advantage to adopting a strategy that does something other than playing Cooperate while I play Defect. I want to keep my other victims convinced that surrendering to me is their best option, and nuking the occasional rock is a price I'm willing to pay to achieve that. In other words, I've transformed the game you're playing from Prisoner's Dilemma to Hawk/Dove, and I'm a rock that always plays Hawk. So what does LDT have to say about that? Are you going to use a strategy that plays "Hawk" (anything other than Cooperate) against a rock that always plays Hawk and gets us both nuked, or are you going to do the sensible thing and play Dove (Cooperate)?