I think a key difference is that in PD, (Defect, Cooperate) is a Pareto outcome (you can’t make it better for the cooperator without making it worse for the defector). While (0, 0) is far from the Pareto boundary. So people can clearly see that naming numbers around 0 is a massive loss, so they focus on avoiding that loss rather than optimising their game vs the other player.
Thanks, I forgot the proof before replying your comment.
You are correct that in PD (D,C) is Pareto, and so the Nash Equilibrium (D,D) is much closer to a Pareto outcome than the Nash Equilibrium (0,0) of TD is to its Pareto outcomes (somewhere along each person getting a million pounds, give or take a cent)
It still strange to see a game with only one round and no collusion to land pretty close to the optimal, while its repeated version (dollar auction) seems to deviate badly from the Pareto outcome.
It still strange to see a game with only one round and no collusion to land pretty close to the optimal, while its repeated version (dollar auction) seems to deviate badly from the Pareto outcome.
It is a bit strange. It seems this is because in the dollar auction, you can always make your position slightly better unilaterally, in a way that will make it worse once the other player reacts. Iterate enough, and all value is destroyed. But in a one-round game, you can’t slide down that path, so you pick by looking at the overall picture.
I think a key difference is that in PD, (Defect, Cooperate) is a Pareto outcome (you can’t make it better for the cooperator without making it worse for the defector). While (0, 0) is far from the Pareto boundary. So people can clearly see that naming numbers around 0 is a massive loss, so they focus on avoiding that loss rather than optimising their game vs the other player.
I haven’t found any information yet, but I suspect there is a mixed Nash somewhere in TD.
There is no mixed Nash equilibrium in the TD example above (see the proof above).
Thanks, I forgot the proof before replying your comment.
You are correct that in PD (D,C) is Pareto, and so the Nash Equilibrium (D,D) is much closer to a Pareto outcome than the Nash Equilibrium (0,0) of TD is to its Pareto outcomes (somewhere along each person getting a million pounds, give or take a cent)
It still strange to see a game with only one round and no collusion to land pretty close to the optimal, while its repeated version (dollar auction) seems to deviate badly from the Pareto outcome.
It is a bit strange. It seems this is because in the dollar auction, you can always make your position slightly better unilaterally, in a way that will make it worse once the other player reacts. Iterate enough, and all value is destroyed. But in a one-round game, you can’t slide down that path, so you pick by looking at the overall picture.