To me this feels quite a lot more natural than the previous version. It’s not clear whether the vulnerability to threats is a positive or negative feature.
Part of your stated original motivation for exploring this was that traditional bargaining solutions didn’t deal with power. We could adapt your solution here to define a defection point: the scenario where the first agent has the negative utility function of the second agent, and vice-versa. Then we could investigate the Nash bargaining solution with respect to this defection point. Without more thought (and perhaps playing with some examples), it’s not obvious to me if that’s better or worse than your proposal here.
To me this feels quite a lot more natural than the previous version. It’s not clear whether the vulnerability to threats is a positive or negative feature.
Part of your stated original motivation for exploring this was that traditional bargaining solutions didn’t deal with power. We could adapt your solution here to define a defection point: the scenario where the first agent has the negative utility function of the second agent, and vice-versa. Then we could investigate the Nash bargaining solution with respect to this defection point. Without more thought (and perhaps playing with some examples), it’s not obvious to me if that’s better or worse than your proposal here.