And here's a reformulation of Counterfactual Mugging in the same vein. Find two subjects who don't care about each other's welfare at all. Flip a coin to choose one of them who will be asked to give up $100. If ze agrees, the other one receives $10000.

This is very similar to a rephrasing of the Prisoner's Dilemma known as the Chocolate Dilemma. Jimmy has the option of taking one piece of chocolate for himself, or taking three pieces and giving them to Jenny. Jenny faces the same choice: take one piece for herself or three pieces for Jimmy. This formulation makes it very clear that two myopically-rational people will do worse than two irrational people, and that mutual precommitment at the start is a good idea.

This stuff is still unclear to me, but there may be a post in here once we work it out. Would you like to cooperate on a joint one, or something?