EDIT: thanks to Wei Dai for the next step! Now I know that any “purely geometric” construction that looks only at the Pareto set will fail to incentivize players to adopt it. The reason: we can, without changing the Pareto set, give any player an additional non-Pareto-optimal strategy that always assigns them higher utility than my proposed solution, thus making them want to defect. Pretty conclusive! So much for this line of inquiry, I guess.
Well, of course you can’t restrict your attention to the Pareto Set. Every presentation of the bargaining problem characterizes the problem using both the Pareto boundary and a “zero-point”, “threat point”, or “non-agreement point”. The additional strategies that Wei suggests also change the zero-point. That is, they change the problem.
As to whether we can solve fairness, it is already solved—at least in the 2 party perfect information case. And it has been solved since 1953.
Well, of course you can’t restrict your attention to the Pareto Set. Every presentation of the bargaining problem characterizes the problem using both the Pareto boundary and a “zero-point”, “threat point”, or “non-agreement point”. The additional strategies that Wei suggests also change the zero-point. That is, they change the problem.
As to whether we can solve fairness, it is already solved—at least in the 2 party perfect information case. And it has been solved since 1953.