Standard theory around here is that you should reject offers where you'd get less than $5.
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standard theory around here is also that nobody should make or give in to threats
You're massively and incorrectly overgeneralizing the standard theory. In ideal rational-actor perfect predictor scenarios, one should be known as the type of person who doesn't take bad deals, and they only way to do that against perfect predictors is to BE the type of person who doesn't take bad deals.
The two things which don't apply in your post:
1) you have no reason to believe the other person knows you or that your intent has any impact on their offer. They're not a perfect predictor, so turning down their $2 just costs you $2, without changing the probability that they offer more in other universes or future interactions.
2) It only applies to certain types of threat (where it's not a direct causal clear action). Nobody's advocating you withhold your wallet from an armed mugger.
I think this gets at one of the central problems with the concept of game-theoretic threats. I don't know if anyone ever figured out an especially solid formal solution — it sort of comes down to finding some reasonable conception of a privileged null (or default) action, as I understand it.
50/50 is sort of an obvious Schelling point norm? If neither of you want to give into blackmail and have to agree to get any money at all, it seems like a relatively symmetric situation. But interesting question…
Why should you do what they demand, when, as is the defining characteristic of a threat, it's only good for them if you give in?
Suppose that you made the Ultimatum of giving $1 out of $10 and your rival precommited to rejecting any unfair Ultimatums, while you know that the rival WILL uphold the precommitment. Then attempting not to give in would leave you worse off than actually giving in.
The main issue is that the rival's attempt to give in would incentivise you to threaten the rival. On the other hand, if Player 1 was in such debt that only receiving at least $8 could save them, then I would expect Player 1 to be justified in setting the Ultimatum of $8, especially if we account for the standard theory being more complex than merely rejecting unfair offers on sight.
me and my friends'll be picking up all the free $5 bills you and your enemies spite each other with.
TLDR: title.
In the Ultimatum Game, there are $10 to be divided between two players. First, Player 1 proposes a split, such as "I get $8 and you get $2" or "we both get $5". Then, Player 2 either accepts this proposal or rejects it. If they reject it, both players get nothing.
Standard theory around here is that you should reject offers where you'd get less than $5. It's a little counterintuitive at first, because if you're offered $2, you might think "why not just take it? The alternative is to get nothing." But the standard reason to reject it is that, if you make a consistent (or predictable-in-advance) policy of rejecting unfair offers, then people won't make you unfair offers, because they know they'll get nothing if they do.
This feels an awful lot like a threat to me, now that I think about it... and standard theory around here is also that nobody should make or give in to threats. The reason being: if you give in to threats, all you're doing is showing people that threatening you is a good idea, and that might entice them into making threats when they wouldn't otherwise have done that.
Think of a manipulative partner saying "if you don't do these dishes right now, I'll break up with you" — I think people say this when they know they're talking to a spineless loser who'll get up and go miserably do the dishes, and not when they know they're talking to a well-spined person who will say "what? fuck you". Because if they're talking to someone who won't give in, then they have to go ahead and break up with you over one load of dishes, and that's not actually in their interests. So, goes standard theory, be the person who won't be influenced by that nonsense, and the nonsense won't come.
But wait a second. Suppose you're playing the ultimatum game with someone, and you're Player 1. Obviously, your own favorite outcome is to get all $10 for yourself, but that leaves the other person with $0 which makes them indifferent between accepting and rejecting. So maybe instead, you plan to offer them $1 while keeping $9 for yourself. That way, it's in their own interests to accept the offer.
You're not trying to hurt them; you're trying to have more money.
But they look across the table at you, and say "if you offer me less than $5, I'll make sure we both get nothing".
Why is that not a threat? Why should you give in and change your plan away from what would otherwise be your default, in the absence of their self-harming commitment that they only made because they think it'll work on you? Why should you do what they demand, when, as is the defining characteristic of a threat, it's only good for them if you give in?