If one of the PD players has a third option of “get two bucks guaranteed and screw everyone else”—if the game structure doesn’t allow other players to punish him—then no algorithm at all can punish him. Or did you mean something else?
The “good and fair” solution needs to offer him a Pareto improvement over the outcome that he can reach by himself.
Wei Dai, thanks. I gave some thought to your comments and they seem to constitute a proof that any “purely geometric” construction (that depends only on the Pareto set) fails your criterion. Amending the post.
The “good and fair” solution needs to offer him a Pareto improvement over the outcome that he can reach by himself.
Wei Dai, thanks. I gave some thought to your comments and they seem to constitute a proof that any “purely geometric” construction (that depends only on the Pareto set) fails your criterion. Amending the post.
Sorry, I was being stupid. You’re right.