One is that set of possible fallback points will, in general, not be a single point
Thinking out loud: Might you be able to iterate the bargaining process between the agents to decide which fallback point to choose? This of course will yield infinite regress if no one of the iterations yields a single fallback point. But might it be that the set of fallback points will in some sense become smaller with each iteration? (For instance have smaller worst-case consequences for each players’ utilities) (Or at least this might happen in most real-world situations, even if there are fringe theoretical counter-examples) If that were the case, at a certain finite iteration one of the players would be willing to let the other decide the fallback point (or let it be randomly decided), since the cost of further computations might be higher than the benefit of adjusting more finely the fallback point.
On a more general note, maybe considerations about a real agent’s bounded computation can pragmatically resolve some of these issues. Don’t get me wrong: I get that you’re searching for theoretical groundings, and this would a priori not be the stage in which to drop simplifications. But maybe dropping this one will dissolve some of the apparent grounding under-specifications (because real decisions don’t need to be as fine-grained as theoretical abstraction can make it seem).
Thinking out loud: Might you be able to iterate the bargaining process between the agents to decide which fallback point to choose? This of course will yield infinite regress if no one of the iterations yields a single fallback point. But might it be that the set of fallback points will in some sense become smaller with each iteration? (For instance have smaller worst-case consequences for each players’ utilities) (Or at least this might happen in most real-world situations, even if there are fringe theoretical counter-examples) If that were the case, at a certain finite iteration one of the players would be willing to let the other decide the fallback point (or let it be randomly decided), since the cost of further computations might be higher than the benefit of adjusting more finely the fallback point.
On a more general note, maybe considerations about a real agent’s bounded computation can pragmatically resolve some of these issues. Don’t get me wrong: I get that you’re searching for theoretical groundings, and this would a priori not be the stage in which to drop simplifications. But maybe dropping this one will dissolve some of the apparent grounding under-specifications (because real decisions don’t need to be as fine-grained as theoretical abstraction can make it seem).