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khafra comments on Taking the awkwardness out of a Prenup - A Game Theoretic solution - Less Wrong
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Schelling's introduction mentions that his work sits in a space between pure theoretical game theory and purely pragmatic or psychological bargaining. A pre-commitment is part of a bargaining process, so if you can pre-commit before the one you're bargaining with (not necessarily chronologically) you win. If you both pre-commit simultaneously, you both lose.
How about making a pre-commitment that only applies if the other person hasn't made one?
Because you need to know if they've made a commitment, and using old information can get you burned if as stated, you pre-commit simultaneously.
OK, then a pre-commitment that only applies if you have no solid information that the other person has one in effect. (I don't think those adjustments should have been difficult to make.) Makers of pre-commitments are incentivized to broadcast their commitments with credible info to back them up, right?