It is interesting that experimental results of traveller’s dilemma seems to give results which deviate strongly from the Nash Equilibrium, and in fact quite close to the Pareto Optimal Solution.
This is pretty strange for a game that has only one round and no collusion (you’d expect it to end as Prisoner’s Dilemma, no?)
It is rather different from what we would see from the dollar auction, which has no Nash Equilibrium but always deviate far away from the Pareto optimal solution.
I suspect that the this game being one round-only actually improves the Pareto efficiency of its outcomes:
Maybe if both participants are allowed to change their bid after seeing each other’s bid they WILL go into a downward spiral one cent by one cent until they reach zero or one player gives up at some point with a truce, just like how dollar auctions always stop at some point.
When there is only one round, however, there is no way for a player to make their bid exactly 1 or 2 cents less than the other player, and bidding any less than that is suboptimal compared to bidding more than the other player, so perhaps there is an incentive against lowering one’s bidding indefinitely to 0 before the game even starts, just like no one would bid $1000 in the dollar auction’s first round.
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.
It is interesting that experimental results of traveller’s dilemma seems to give results which deviate strongly from the Nash Equilibrium, and in fact quite close to the Pareto Optimal Solution.
This is pretty strange for a game that has only one round and no collusion (you’d expect it to end as Prisoner’s Dilemma, no?)
It is rather different from what we would see from the dollar auction, which has no Nash Equilibrium but always deviate far away from the Pareto optimal solution.
I suspect that the this game being one round-only actually improves the Pareto efficiency of its outcomes:
Maybe if both participants are allowed to change their bid after seeing each other’s bid they WILL go into a downward spiral one cent by one cent until they reach zero or one player gives up at some point with a truce, just like how dollar auctions always stop at some point.
When there is only one round, however, there is no way for a player to make their bid exactly 1 or 2 cents less than the other player, and bidding any less than that is suboptimal compared to bidding more than the other player, so perhaps there is an incentive against lowering one’s bidding indefinitely to 0 before the game even starts, just like no one would bid $1000 in the dollar auction’s first round.
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.