I’ll accept no less than 50%, and fight if we disagree
Do you mean the commitments follow an “all or nothing” pattern, where if both sides commit to 51% they’re doomed?
I imagine that commitments might be less extreme, where overlap is costly but not fatal:[1]
If each side commits to taking 51%, the rule of their commitment is to punish the other side by destroying anything more than 49% the other side takes, and then further destroying 0.5% for every 1% less than 51% they receive.
Each side takes 50%, but destroy 1% of the other side’s pie so each side is only left with 49%. They both realize they received 2% less than the target 51%. This means each side destroys 1% of what the other side has, so each side now only has 48%. This is 3% less than 51%, so they further destroy 0.5% of what the other side has so they’re both left with %. This continues to %, %, %, and so on. Of course, they can skip the formalities and just jump to 47% which is the final state.
It is important to punish the other side for punishing you, at least a little.
If you only destroy what they other side takes past 49%, but you do not destroy further based on how little you got, then the other side can get away with committing to take 70% of the pie, betting on the small chance you are a sucker and only ask for 30%. If they are correct, they get away with 70% of the pie. If they are wrong, then you will destroy their pie until they are left with only 49%, and they will destroy your pie until you are left with less than 30%, but they still get the maximum amount they could have gotten if they committed any lesser amount. This means it doesn’t hurt for them to commit to take 70%. It only hurts you, and has a small chance of benefiting them.
PS: I’m not saying your post is wrong, since it’s clearly titled “A high-level model of AI bargaining” rather than “A very detailed model of AI bargaining!” I just feel this detail is worth mentioning.
Do you mean the commitments follow an “all or nothing” pattern, where if both sides commit to 51% they’re doomed?
I imagine that commitments might be less extreme, where overlap is costly but not fatal:[1]
If each side commits to taking 51%, the rule of their commitment is to punish the other side by destroying anything more than 49% the other side takes, and then further destroying 0.5% for every 1% less than 51% they receive.
Each side takes 50%, but destroy 1% of the other side’s pie so each side is only left with 49%. They both realize they received 2% less than the target 51%. This means each side destroys 1% of what the other side has, so each side now only has 48%. This is 3% less than 51%, so they further destroy 0.5% of what the other side has so they’re both left with
It is important to punish the other side for punishing you, at least a little.
If you only destroy what they other side takes past 49%, but you do not destroy further based on how little you got, then the other side can get away with committing to take 70% of the pie, betting on the small chance you are a sucker and only ask for 30%. If they are correct, they get away with 70% of the pie. If they are wrong, then you will destroy their pie until they are left with only 49%, and they will destroy your pie until you are left with less than 30%, but they still get the maximum amount they could have gotten if they committed any lesser amount. This means it doesn’t hurt for them to commit to take 70%. It only hurts you, and has a small chance of benefiting them.
PS: I’m not saying your post is wrong, since it’s clearly titled “A high-level model of AI bargaining” rather than “A very detailed model of AI bargaining!” I just feel this detail is worth mentioning.
PS: this idea was copied from an old post of mine, but it’s not a good post because I no longer believe in the other things I wrote in that post.