So is the idea that when there’s only one Pareto-optimal outcome above both players’ fallback price, they’ll pick it?
In this case it seems like the failure of this concept is when there’s more than one such outcome and each player likes a different one (which would normally be indicated by no equilibrium of this type—the actual outcome might still depend on details of the players’ source code even after they meet your rationality standards), but by chance there’s a barely above-fallback outcome at the intersection of the outcomes the players really prefer, causing this procedure to return something that might not even be Pareto optimal.
Or maybe I’m misunderstanding, since you said you had a proof?
So is the idea that when there’s only one Pareto-optimal outcome above both players’ fallback price, they’ll pick it?
In this case it seems like the failure of this concept is when there’s more than one such outcome and each player likes a different one (which would normally be indicated by no equilibrium of this type—the actual outcome might still depend on details of the players’ source code even after they meet your rationality standards), but by chance there’s a barely above-fallback outcome at the intersection of the outcomes the players really prefer, causing this procedure to return something that might not even be Pareto optimal.
Or maybe I’m misunderstanding, since you said you had a proof?
E.g.:
(5,1) (6,2) (4,4)
(9,6) (2,2) (2,6)
(5,5) (6,9) (1,5)