Regarding (2), the main problem is that this creates an incentive for agents to choose orderings that favor themselves when there is overlap between the acceptable regions, and this creates a high chance that they won’t be able to agree on an ordering at all. Jessica Taylor’s solution solves the problem of not being able to find an ordering, but at the cost of all the surplus utility that was in the region of overlap. For example, if Janos and I are deciding how to divide a dollar, I offer that Janos keeps it, and Janos offers that I keep it, that solution would have us set it on fire instead.
Instead, perhaps we could redefine the algorithm so that “cooperation at point N” means entering another round of negotiation, where only points that each agent finds at least as good as N are considered, and negotiation continues until it reaches a fixed point.
How to actually convert this into an algorithm? I haven’t figured out all the technical details, but I think the key is having agents prove things of the form “we’ll coordinate on a point I find at least as good as point N”.
I thought about that at some point, in the case where they’re biased in their own directions, but of course there it just reintroduces the incentive for playing hardball. In the case where they’re each overly generous, they already have the incentive to bias slightly more in their own direction.
However, there’s not an obvious way to translate the second round of negotiation into the modal framework...
Regarding (2), the main problem is that this creates an incentive for agents to choose orderings that favor themselves when there is overlap between the acceptable regions, and this creates a high chance that they won’t be able to agree on an ordering at all. Jessica Taylor’s solution solves the problem of not being able to find an ordering, but at the cost of all the surplus utility that was in the region of overlap. For example, if Janos and I are deciding how to divide a dollar, I offer that Janos keeps it, and Janos offers that I keep it, that solution would have us set it on fire instead.
Instead, perhaps we could redefine the algorithm so that “cooperation at point N” means entering another round of negotiation, where only points that each agent finds at least as good as N are considered, and negotiation continues until it reaches a fixed point.
How to actually convert this into an algorithm? I haven’t figured out all the technical details, but I think the key is having agents prove things of the form “we’ll coordinate on a point I find at least as good as point N”.
I thought about that at some point, in the case where they’re biased in their own directions, but of course there it just reintroduces the incentive for playing hardball. In the case where they’re each overly generous, they already have the incentive to bias slightly more in their own direction.
However, there’s not an obvious way to translate the second round of negotiation into the modal framework...