And if you do that properly, taking into account other issues like reflective consistency, you won't need the other part of your algorithm at all, since picking fair Pareto-optimal strategies will also allow to correctly deal with defectors.

I'm still perplexed by the fairness part (and Ultimatum game in particular) though. One solution from symmetry seems obvious (not 'cut on equal parts', since what 'equal part' means also depends on the preference orders of each agent), but I don't know in what sense it's universally right, and if it isn't, what should be done.