In the Alice/Bob diagrams, I am confused why the strategies are parameterized by the frequency of cooperation. Don’t these frequencies depend on what the other player does, so that the same strategy can have different frequencies of cooperation depending on who the other player is?
First off, I’m not trying to illustrate the many-player game here. So imagine there’s just Alice and Bob. I agree that the many-player version is relevant, but I was just dealing with the complexities that arise from iteration.
Second, yeah, absolutely: strategies in iterated games can be any function of the history. But that’s a really complicated strategy space to try and draw. Essentially I’m showing you just a very high-level summary, focusing on frequency of cooperation as a salient feature.
The idea is that frequency is something each player can observe about the other. Alice can implement a Grim Trigger strategy to enforce any given frequency of cooperation from Bob. It needs to have some wiggle room, to allow chance fluctuations in frequency without pulling the Grim Trigger; but Alice can include wiggle room while enforcing tight enough a guarantee that Bob is forced to cooperate with the desired frequency in the limit, and Alice runs only a small risk of spuriously Grim Triggering.
In the Alice/Bob diagrams, I am confused why the strategies are parameterized by the frequency of cooperation. Don’t these frequencies depend on what the other player does, so that the same strategy can have different frequencies of cooperation depending on who the other player is?
First off, I’m not trying to illustrate the many-player game here. So imagine there’s just Alice and Bob. I agree that the many-player version is relevant, but I was just dealing with the complexities that arise from iteration.
Second, yeah, absolutely: strategies in iterated games can be any function of the history. But that’s a really complicated strategy space to try and draw. Essentially I’m showing you just a very high-level summary, focusing on frequency of cooperation as a salient feature.
The idea is that frequency is something each player can observe about the other. Alice can implement a Grim Trigger strategy to enforce any given frequency of cooperation from Bob. It needs to have some wiggle room, to allow chance fluctuations in frequency without pulling the Grim Trigger; but Alice can include wiggle room while enforcing tight enough a guarantee that Bob is forced to cooperate with the desired frequency in the limit, and Alice runs only a small risk of spuriously Grim Triggering.