I haven’t played the game, and I’m not a game theoris, but think your argument is symmetric and that seems worng? If Alice had drawn LFF, the same argument would tell her to pass FF. I think you need an additional axiom that liberals prefer liberal policies be passed, liberal chancellors will always pick liberal policies when possible, and that the game is zero sum. But maybe that was too obvious to bother stating.
I haven’t played the game, and I’m not a game theoris, but think your argument is symmetric and that seems worng? If Alice had drawn LFF, the same argument would tell her to pass FF. I think you need an additional axiom that liberals prefer liberal policies be passed, liberal chancellors will always pick liberal policies when possible, and that the game is zero sum. But maybe that was too obvious to bother stating.