I think it doesn’t matter how long they have to decide, if we are resolved to ignore intuitive hunches for Schelling points and causal updating (which are important in practice, but not in principle). You can see any problem as one-step by deciding a whole (possibly infinite) strategy instead of just the next action. The questions governing the way this strategy should be chosen are similar (for the purposes of my comment) to what happens with simple ultimatum game.
The original problem is symmetrical: there is a potential trade which will benefit both A and B, and they need to strike a price. The Ultimatum game is asymmetrical: one player goes first. This seems to me a conclusive proof that this problem cannot be modelled as an Ultimatum game.
You can see any problem as one-step by deciding a whole (possibly infinite) strategy instead of just the next action.
I don’t think this works in the large unless P=NP (or something of the sort). In the small, e.g. analysing chess, it reduces the problem to no steps at all: both players exhaustively analyse the game and know the outcome without playing a single move. (I’m using “small” and “large” in the sense of the dispute between small-world and large-world Bayesians.) If that worked for the bargaining problem, A and B would independently come up with the same price and no bargaining process would be necessary. No-one has posted a method of doing so.
I think it doesn’t matter how long they have to decide, if we are resolved to ignore intuitive hunches for Schelling points and causal updating (which are important in practice, but not in principle). You can see any problem as one-step by deciding a whole (possibly infinite) strategy instead of just the next action. The questions governing the way this strategy should be chosen are similar (for the purposes of my comment) to what happens with simple ultimatum game.
The original problem is symmetrical: there is a potential trade which will benefit both A and B, and they need to strike a price. The Ultimatum game is asymmetrical: one player goes first. This seems to me a conclusive proof that this problem cannot be modelled as an Ultimatum game.
I don’t think this works in the large unless P=NP (or something of the sort). In the small, e.g. analysing chess, it reduces the problem to no steps at all: both players exhaustively analyse the game and know the outcome without playing a single move. (I’m using “small” and “large” in the sense of the dispute between small-world and large-world Bayesians.) If that worked for the bargaining problem, A and B would independently come up with the same price and no bargaining process would be necessary. No-one has posted a method of doing so.