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.
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.