The “best” values in KS are those that result when you optimize one player’s payoff under the constraint that the second player’s payoff is higher than the disagreement payoff.
I’m not sure this is the case? Wiki does say “It is assumed that the problem is nontrivial, i.e, the agreements in [the feasible set] are better for both parties than the disagreement”, but this is ambiguous as to whether they mean some or all.
Googling further, I see graphs like this where non-Pareto-improvement solutions visibly do count.
I agree that your version seems more reasonable, but I think you lose monotonicity over the set of all policies, because a weak improvement to player 1′s payoffs could turn a (-1, 1000) point into a (0.1, 1000) point, make it able to affect the solution, and make the solution for player 1 worse. Though you’ll still have monotonicity over the restricted set of policies.
In the original paper they have “Assumption 4” which clearly states they disregard solutions that don’t dominate the disagreement point. But, you have a good point that when those solutions are taken into account, you don’t really have monotonicity.
I’m not sure this is the case? Wiki does say “It is assumed that the problem is nontrivial, i.e, the agreements in [the feasible set] are better for both parties than the disagreement”, but this is ambiguous as to whether they mean some or all. Googling further, I see graphs like this where non-Pareto-improvement solutions visibly do count.
I agree that your version seems more reasonable, but I think you lose monotonicity over the set of all policies, because a weak improvement to player 1′s payoffs could turn a (-1, 1000) point into a (0.1, 1000) point, make it able to affect the solution, and make the solution for player 1 worse. Though you’ll still have monotonicity over the restricted set of policies.
In the original paper they have “Assumption 4” which clearly states they disregard solutions that don’t dominate the disagreement point. But, you have a good point that when those solutions are taken into account, you don’t really have monotonicity.