Eliezer, would your ideas from this post apply here?

There could be many acceptable negotiating equilibria between what you think is the 'fair' point on the Pareto boundary, and the Nash equilibrium. So long as each step down in what you think is 'fairness' reduces the total payoff to the other agent, even if it reduces your own payoff even more.

If I'm not too confused, the Nash equilibrium is [P1: A], and the Pareto boundary extends from [P1: B, P2: Y] to [P1: C, P2: Y]. So the gains from trade give P1 1-3 extra points, and P2 0-2 extra points. As others have pointed out, a case could be made for [P1: C, P2: Y], as it maximizes the total gains from trade, but maybe, taking your idea of different concepts of fairness from the linked post, P2 should hold P1 hostage by playing some kind of mixed X,Y strategy unless P1 offers a "more fair" split.

Is that behavior by B the kind of thing that the reasoning in the linked post endorses?