Isn't it a threat to reject unfair offers in the Ultimatum Game?

LessWrong presents a genuine paradox in game theory. In the Ultimatum Game, two players split ten dollars: one proposes the split, the other accepts or rejects. Reject it, and both get zero. Standard game theory advises rejecting unfair offers to build a reputation that prevents unfair proposals in the future. But here's the puzzle: building that reputation means making a credible commitment to a punishment that harms both players if your fairness demands aren't met. That's a threat. And if game theory says threats are bad because they teach people threatening works, why is this particular threat considered good?

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