If Adam is a “5%-Bot” not controlled by something further (always makes the offer of 5% without any thought), Becky would want to accept even if deciding updatelessly, so updatelessness is not sufficient. If it’s a functional decision by a single algorithm controlling both players, what is this algorithm’s utility function? If the utility function likes 80⁄20 in Becky’s favor, this is what gets decided. The algorithm itself doesn’t need updatelessness and may also be causal (in which case Becky always accepts and Adam chooses an offer that, when accepted, maximizes joint utility).
Most importantly for the basic problem statement, the issue of choosing the joint utility function doesn’tgo away even if you allow players to separately reason about each other.
a) the chances are the other player will have roughly similiar commitments to you.
b) 50⁄50 is a shelling point that works well for an acausal Trade.
So when choosing my precommitments I know that anything too high is likely to be rejected, anything to low is a waste, and 50⁄50 is likely to be about what most people will choose—as evidenced from the fact that I’m happy to choose it.
If Adam is a “5%-Bot” not controlled by something further (always makes the offer of 5% without any thought), Becky would want to accept even if deciding updatelessly, so updatelessness is not sufficient. If it’s a functional decision by a single algorithm controlling both players, what is this algorithm’s utility function? If the utility function likes 80⁄20 in Becky’s favor, this is what gets decided. The algorithm itself doesn’t need updatelessness and may also be causal (in which case Becky always accepts and Adam chooses an offer that, when accepted, maximizes joint utility).
Most importantly for the basic problem statement, the issue of choosing the joint utility function doesn’t go away even if you allow players to separately reason about each other.
I would say:
a) the chances are the other player will have roughly similiar commitments to you. b) 50⁄50 is a shelling point that works well for an acausal Trade. So when choosing my precommitments I know that anything too high is likely to be rejected, anything to low is a waste, and 50⁄50 is likely to be about what most people will choose—as evidenced from the fact that I’m happy to choose it.