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.
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.