I think this "Pirate Oath" thing cuts to the point exactly. In the allowance examples, this is basically what I mean by 'stubbornness.' The strange thing to me is that it seems like it's often in a pirate or a kid's best interest to make an unbreakable oath.
But, gah! Yeah, it gets really complicated!
And there seem to be an obvious problem with giving multiple kids in the allowances cases (or pirates in the original problem) the ability to make unbreakable oaths - if Ben makes an oath that he'll reject the split unless he gets $9, then it's in Alfie's best interest to give him $9 (that's basically what Fanny did to Elmo). However, it's also in Alfie's interest to try to make the same oath before Ben does. So, the order in which they're able to make oaths appears to matter :-/
I want to preserve the symmetry, so let's say that they both have to write any unbreakable oaths simultaneously. Now it's in both of their advantage to make sure that their oaths aren't contradictory. So, there should be a strategy again, right? Let's assume they're not allowed to communicate at all before writing their oaths. What happens?
no subject
But, gah! Yeah, it gets really complicated!
And there seem to be an obvious problem with giving multiple kids in the allowances cases (or pirates in the original problem) the ability to make unbreakable oaths - if Ben makes an oath that he'll reject the split unless he gets $9, then it's in Alfie's best interest to give him $9 (that's basically what Fanny did to Elmo). However, it's also in Alfie's interest to try to make the same oath before Ben does. So, the order in which they're able to make oaths appears to matter :-/
I want to preserve the symmetry, so let's say that they both have to write any unbreakable oaths simultaneously. Now it's in both of their advantage to make sure that their oaths aren't contradictory. So, there should be a strategy again, right? Let's assume they're not allowed to communicate at all before writing their oaths. What happens?