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Decius comments on The Number Choosing Game: Against the existence of perfect theoretical rationality - Less Wrong
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There is an optimal strategy for negotiation. It requires estimating the negotiation zone of the other party and the utility of various outcomes (including failure of negotiation).
Then it's just a strategy that maximizes the sum of the probability of each outcome times the utility thereto.
The hard parts aren't the P(X1)U(X1) sums, it's getting the P(X1) and U(X1) in the first place.