better off having a “real” commitment than a revocable commitment that Bob can talk her out of
I’m confused what you mean here. In principle Alice can revoke her commitment before the freeze time in this protocol, but Bob can’t force her to do so. And if it’s common knowledge that Alice’s freeze time comes before Bob’s, then: Since Alice knows that there will be a window after her freeze time where Bob knows Alice’s commitment is frozen, and Bob has a chance to revert, then there would be no reason (barring some other commitment mechanism, including Bob being verifiably updateless while Alice isn’t) for Bob not to revoke (to Swerve) if Alice refused to revert from Dare. So Alice would practically always keep her commitment.
The power to revoke commitments here is helpful in the hands of the second-mover, who made the initial incompatible commitment because of, e.g., some lag time between the first-mover’s making and broadcasting the commitment.
The second mover ALREADY had the option not to commit—they could just swerve or crash, according to their decision theory. The revocation period doesn’t actually change payouts or decision mechanisms, and if it doesn’t change the sequence of commitment, I don’t see how it makes any difference at all. If it DOES change the sequence of commitment, then the first-mover would prefer not to lose their advantage, and will just use a non-revocable commitment.
It seems like this is introducing some sort of information or negotiation into the decisions, but I don’t see how. In MANY such games, allowing side-payments or outside-of-game considerations can find better outcomes. This doesn’t do that, as far as I can see.
The second mover ALREADY had the option not to commit—they could just swerve or crash, according to their decision theory.
The premise here is that the second-mover decided to commit soon after the first-mover did, because the proof of the first-mover’s initial commitment didn’t reach the second-mover quickly enough. They could have not committed initially, but they decided to do so because they had a chance of being first.
I’m not sure exactly what you mean by “according to their decision theory” (as in, what this adds here).
if it doesn’t change the sequence of commitment, I don’t see how it makes any difference at all
The difference is that the second-mover can say “oh shit I committed before getting the broadcast of the first-mover’s commitment—I’d prefer to revoke this commitment because it’s pointless, my commitment doesn’t shape the first-mover’s incentives in any way since I know the first-mover will just prefer to keep their commitment fixed.”
As I said, the first-mover doesn’t lose their advantage from this at all, because their commitment is locked (at their freeze time) before the second-mover’s. So they can just leave their commitment in place, and their decision won’t be swayed by the second-mover’s at all because of the rule: “You shouldn’t be able to reveal the final decision to anyone before freeze_time because we don’t want the commitment to get credible before freeze_time.”
The premise here is that the second-mover decided to commit soon after the first-mover did, because the proof of the first-mover’s initial commitment didn’t reach the second-mover quickly enough.
That’s a very critical deviation from the standard problem statement, which should be made very clear. Also, re-reading the timeline, it appears to introduce side-payments (at 0:37 in the timeline), which is also a MAJOR deviation from the standard problem.
These two things (speed of information and ability to negotiate outside of the given payoff matrix) should be separated—both are fairly easy to model, and there will be much simpler solutions to integrate each of them into the decisions, which will be better than the combination of the two limited to a revocation window.
I edited the post to make it clearer that Bob throws out the wheel because he didn’t notice in time that Alice threw.
Yup, side payments are a deviation, that’s why I have this disclaimer in game definition (I edited the post now to emphasize it more):
there also may be some additional actions available, but they are not obvious
Re separating speed of information and negotiations: I think here they are already pretty separate. The first example with 3 protocol rules doesn’t allow negotiations and only tackles the information speed problem. The second example with additional fourth rule enables negotiations. Maybe you could also have a system tackling only negotiations and not the information speed problem, but I’m not sure now how would it look like, or if it would be much simpler.
Another problem (closely tied to negotiations) I wanted to tackle is something like “speed of deliberation” where agents make some bad commitments because they didn’t have enough time to consider their consequences, and later realize they want to revoke/negotiate.
I’m confused what you mean here. In principle Alice can revoke her commitment before the freeze time in this protocol, but Bob can’t force her to do so. And if it’s common knowledge that Alice’s freeze time comes before Bob’s, then: Since Alice knows that there will be a window after her freeze time where Bob knows Alice’s commitment is frozen, and Bob has a chance to revert, then there would be no reason (barring some other commitment mechanism, including Bob being verifiably updateless while Alice isn’t) for Bob not to revoke (to Swerve) if Alice refused to revert from Dare. So Alice would practically always keep her commitment.
The power to revoke commitments here is helpful in the hands of the second-mover, who made the initial incompatible commitment because of, e.g., some lag time between the first-mover’s making and broadcasting the commitment.
The second mover ALREADY had the option not to commit—they could just swerve or crash, according to their decision theory. The revocation period doesn’t actually change payouts or decision mechanisms, and if it doesn’t change the sequence of commitment, I don’t see how it makes any difference at all. If it DOES change the sequence of commitment, then the first-mover would prefer not to lose their advantage, and will just use a non-revocable commitment.
It seems like this is introducing some sort of information or negotiation into the decisions, but I don’t see how. In MANY such games, allowing side-payments or outside-of-game considerations can find better outcomes. This doesn’t do that, as far as I can see.
The premise here is that the second-mover decided to commit soon after the first-mover did, because the proof of the first-mover’s initial commitment didn’t reach the second-mover quickly enough. They could have not committed initially, but they decided to do so because they had a chance of being first.
I’m not sure exactly what you mean by “according to their decision theory” (as in, what this adds here).
The difference is that the second-mover can say “oh shit I committed before getting the broadcast of the first-mover’s commitment—I’d prefer to revoke this commitment because it’s pointless, my commitment doesn’t shape the first-mover’s incentives in any way since I know the first-mover will just prefer to keep their commitment fixed.”
As I said, the first-mover doesn’t lose their advantage from this at all, because their commitment is locked (at their freeze time) before the second-mover’s. So they can just leave their commitment in place, and their decision won’t be swayed by the second-mover’s at all because of the rule: “You shouldn’t be able to reveal the final decision to anyone before freeze_time because we don’t want the commitment to get credible before freeze_time.”
That’s a very critical deviation from the standard problem statement, which should be made very clear. Also, re-reading the timeline, it appears to introduce side-payments (at 0:37 in the timeline), which is also a MAJOR deviation from the standard problem.
These two things (speed of information and ability to negotiate outside of the given payoff matrix) should be separated—both are fairly easy to model, and there will be much simpler solutions to integrate each of them into the decisions, which will be better than the combination of the two limited to a revocation window.
I edited the post to make it clearer that Bob throws out the wheel because he didn’t notice in time that Alice threw.
Yup, side payments are a deviation, that’s why I have this disclaimer in game definition (I edited the post now to emphasize it more):
Re separating speed of information and negotiations: I think here they are already pretty separate. The first example with 3 protocol rules doesn’t allow negotiations and only tackles the information speed problem. The second example with additional fourth rule enables negotiations. Maybe you could also have a system tackling only negotiations and not the information speed problem, but I’m not sure now how would it look like, or if it would be much simpler.
Another problem (closely tied to negotiations) I wanted to tackle is something like “speed of deliberation” where agents make some bad commitments because they didn’t have enough time to consider their consequences, and later realize they want to revoke/negotiate.