It’s theoretically indeterminate. To figure this out you would need to develop a specific bargaining structure such as A makes a take it or leave it offer to B.
Since the question is (partially) of descriptive nature, theoretically you can just rerun the universe up until 5 seconds after they struck the deal and check the outcome. If you mean that existing theories don’t give any useful answers, I agree, although again for the descriptive question we can have some useful stats.
The problem is that if A is perfectly rational, in a sense, he can’t make a credible take it or leave it offer. If he offers $10,000, B knows he would be willing to pay $11,000, so he rejects. On the other hand, A knows B would take less than $10,000, so why offer that much in the first place? That’s why I suspect it’s just intractable.
Do any of the elaborate decision theories popular around these parts solve this problem?
No, our decision theories don’t have any new insights for solving bargaining games. But such games are widely studied elsewhere, so maybe you can find a model that solves your problem if you feed it some more detail. Sorry for the disappointing response :-(
No, our decision theories don’t have any new insights for solving bargaining games.
I think they do give the insight that there can be no simple solution. Each player does have to think about the other’s thinking to get further advantage. Even if one of the players is (safely boxed) superintelligent and the other isn’t, as ASP problem demonstrates.
Don’t they at least a little bit? Isn’t pre-commitment a natural feature of TDT? That doesn’t necessarily solve such problems, but it does seem like its relevant. I suppose that’s not a new insight; guess I answered my own question.
Allowing players to precommit isn’t enough to pin down a single outcome in a bargaining game. Different combinations of precommitments can lead to different deals, or even failure to make a deal at all if they are incompatible.
In this context what the pseudo precommitment does is allow B to metaphorically break out of an ultimatum game even if A was somehow able to limit the situation to an ultimatum. Note: this would apply even if only B was using TDT and A was using a CDT.
The problem is that if A is perfectly rational, in a sense, he can’t make a credible take it or leave it offer
Of course he can—he signs an enforceable contract to pay C $500,001 in the case that he is ever seen to be offering B more than $8191 for the land, and has done with it.
...but when he signs this contract, he may find out that B signed a contract refusing to accept anything less than $450,000 for the land, or else pay some large some to D. If there’s any lag in communication between the two of them, this is an extremely risky strategy.
The problem is that if A is perfectly rational, in a sense, he can’t make a credible take it or leave it offer.
I think James meant adding a new limitation to the situation such that there is only one chance to make the deal and one person goes first. ie. Turn it into an ultimatum game.
Do any of the elaborate decision theories popular around these parts solve this problem?
No. At least not if there isn’t also a solution specified in Causal Decision Theory. The same problem exists in both. In fact using Timeless Decision Theory makes the problem apply even in the ultimatum game variant. Because even if I was perfectly rational if A offered me $11,000 I would tell him or her to go @#$@#$ @#$@#$.
It’s theoretically indeterminate. To figure this out you would need to develop a specific bargaining structure such as A makes a take it or leave it offer to B.
That would not help unless you also stipulate that a specific (broken) decision theory is to be used.
It’s theoretically indeterminate. To figure this out you would need to develop a specific bargaining structure such as A makes a take it or leave it offer to B.
Since the question is (partially) of descriptive nature, theoretically you can just rerun the universe up until 5 seconds after they struck the deal and check the outcome. If you mean that existing theories don’t give any useful answers, I agree, although again for the descriptive question we can have some useful stats.
The problem is that if A is perfectly rational, in a sense, he can’t make a credible take it or leave it offer. If he offers $10,000, B knows he would be willing to pay $11,000, so he rejects. On the other hand, A knows B would take less than $10,000, so why offer that much in the first place? That’s why I suspect it’s just intractable.
Do any of the elaborate decision theories popular around these parts solve this problem?
No, our decision theories don’t have any new insights for solving bargaining games. But such games are widely studied elsewhere, so maybe you can find a model that solves your problem if you feed it some more detail. Sorry for the disappointing response :-(
I think they do give the insight that there can be no simple solution. Each player does have to think about the other’s thinking to get further advantage. Even if one of the players is (safely boxed) superintelligent and the other isn’t, as ASP problem demonstrates.
Don’t they at least a little bit? Isn’t pre-commitment a natural feature of TDT? That doesn’t necessarily solve such problems, but it does seem like its relevant. I suppose that’s not a new insight; guess I answered my own question.
Allowing players to precommit isn’t enough to pin down a single outcome in a bargaining game. Different combinations of precommitments can lead to different deals, or even failure to make a deal at all if they are incompatible.
In this context what the pseudo precommitment does is allow B to metaphorically break out of an ultimatum game even if A was somehow able to limit the situation to an ultimatum. Note: this would apply even if only B was using TDT and A was using a CDT.
Of course he can—he signs an enforceable contract to pay C $500,001 in the case that he is ever seen to be offering B more than $8191 for the land, and has done with it.
...but when he signs this contract, he may find out that B signed a contract refusing to accept anything less than $450,000 for the land, or else pay some large some to D. If there’s any lag in communication between the two of them, this is an extremely risky strategy.
I think James meant adding a new limitation to the situation such that there is only one chance to make the deal and one person goes first. ie. Turn it into an ultimatum game.
No. At least not if there isn’t also a solution specified in Causal Decision Theory. The same problem exists in both. In fact using Timeless Decision Theory makes the problem apply even in the ultimatum game variant. Because even if I was perfectly rational if A offered me $11,000 I would tell him or her to go @#$@#$ @#$@#$.
That would not help unless you also stipulate that a specific (broken) decision theory is to be used.