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.
Minor note. Your choice of utilities makes a 50/50 mixture of Cooperate:Defect and Defect:Cooperate better than the Cooperate:Cooperate outcome. So Cooperate:Cooperate isnt on the pareto frontier.
Does any process in which they ended up the way they did without considering your decision procedure count as #2? Like, suppose almost all the other agents it expects to encounter are CDT agents that do give in to extortion, and it thinks the risk of nuclear war with the occasional rock or UDT agent is worth it.
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)?