Here's a question that's been distracting me for the last few hours, and I want to get it out of my head so I can think about something else.

You're walking down an alley after making a bank withdrawal of a small sum of money. Just about when you realize this may have been a mistake, two Muggers appear from either side of the alley, blocking trivial escapes.

Mugger A: "Hi there. Give me all of that money or I will inflict 3^^^3 disutility on your utility function."

Mugger B: "Hi there. Give me all of that money or I will inflict maximum disutility on your utility function."

You: "You're working together?"

Mugger A: "No, you're just really unlucky."

Mugger B: "Yeah, I don't know this guy."

You: "But I can't give both of you all of this money!"

Mugger A: "Tell you what. You're having a horrible day, so if you give me half your money, I'll give you a 50% chance of avoiding my 3^^^3 disutility. And if you give me a quarter of your money, I'll give you a 25% chance of avoiding my 3^^^3 disutility. Maybe the other Mugger will let you have the same kind of break. Sound good to you, other Mugger?"

Mugger B: "Works for me. Start paying."

You: Do what, exactly?

I can see at least 4 vaugely plausible answers:

Pay Mugger A: 3^^^3 disutility is likely going to be more than whatever you think your maximum is and you want to be as likely as possible of avoiding that. You'll just have to try resist/escape from Mugger B (unless he's just faking).

Pay Mugger B: Maximum disutility is by it's definition of greater than or equal to any other disutility, worse than 3^^^3, and has probably happened to at least a few people with utility functions (although probably NOT to a 3^^^3 extent), so it's a serious threat and you want to be as likely as possible of avoiding that. You'll just have to try resist/escape from Mugger A (unless he's just faking).

Pay both Muggers a split of the money: For example: If you pay half to each, and they're both telling the truth, you have a 25% chance of not getting either disutility and not having to resist/escape at all (unless one or both is faking, which may improve your odds.)

Don't Pay: This seems like it becomes generally less likely than in a normal Pascal's mugging since there are no clear escape routes, and you're outnumbered, so there is at least some real threat unless they're both faking.

The problem is, I can't seem to justify any of my vaugely plausible answers to this conundrum well enough to stop thinking about it. Which makes me wonder if the question is ill formed in some way.

Thoughts?