Consider this pair of bots: 1) ExtortionBot, who defects for 80 rounds, and then cooperates with you for 20 rounds if and only if you cooperated for all of the first 80 (otherwise it defects for those rounds as well). 2) WeakBot, who always defects for the last 20 rounds, and cooperates with you for the first 80 if and only if it simulates that you will cooperate for the last 20 rounds iff WeakBot cooperates with you for the first 80 (otherwise it defects for the first 80).
The maximum score you can get vs ExtortionBot is 100 points, which is how many points WeakBot gets. The maximum score you can get vs WeakBot is 400 points, which is how many points ExtortionBot gets.
Ergo ExtortionBot/WeakBot forms a Nash Equilibrium. Is that a max-payoff equilibrium, or is it not?
That means that this game is a symmetric bargaining problem. According to Wikipedia, proposed solutions are symmetric, Pareto-optimal (i.e. “max-payoff”) equilibria.
It seems to me that VOFB or something similar to it is a strategy leading to one of these equilibria (do other symmetric Pareto-optimal equilibria exist?)
I think there are many such equilibria, but they all rely on the same basic principle. I’ve clarified this in a top-level comment, along with a simple example of a symmetric Pareto-optimal equilibrium strategy.
The term “max-payoff equilibrium” is ill-defined.
Consider this pair of bots:
1) ExtortionBot, who defects for 80 rounds, and then cooperates with you for 20 rounds if and only if you cooperated for all of the first 80 (otherwise it defects for those rounds as well).
2) WeakBot, who always defects for the last 20 rounds, and cooperates with you for the first 80 if and only if it simulates that you will cooperate for the last 20 rounds iff WeakBot cooperates with you for the first 80 (otherwise it defects for the first 80).
The maximum score you can get vs ExtortionBot is 100 points, which is how many points WeakBot gets.
The maximum score you can get vs WeakBot is 400 points, which is how many points ExtortionBot gets.
Ergo ExtortionBot/WeakBot forms a Nash Equilibrium. Is that a max-payoff equilibrium, or is it not?
That means that this game is a symmetric bargaining problem.
According to Wikipedia, proposed solutions are symmetric, Pareto-optimal (i.e. “max-payoff”) equilibria.
It seems to me that VOFB or something similar to it is a strategy leading to one of these equilibria (do other symmetric Pareto-optimal equilibria exist?)
I think there are many such equilibria, but they all rely on the same basic principle. I’ve clarified this in a top-level comment, along with a simple example of a symmetric Pareto-optimal equilibrium strategy.