In this case, assuming immortals had perfect memories and would eventually work out that you didn’t, assuming you were an immortal who can’t remember if you’ve played that particular opponent before (But can vaguely remember an idea of how often you get defected on vs. co-operated with by the entire field) what do you think your optimal strategy would be?
It’s pretty complicated! I think you’d need to write down equations to figure it out properly and it would be very non-trivial. That said, assuming there’s only games and no communication, you probably want to start off cooperating or randomising between cooperation and defection (depending on pay-offs), and then shift to more and more defection over time until you always defect in the end. Meanwhile, the immortals with memories would probably want to start off mostly cooperating but sometimes defecting to figure out who, if anyone, doesn’t have memories. (Disclaimer: while this sounds like a plausible set of equilibrium strategies, there may be more complicated equilibria that I didn’t think of or some other weird cases.)
You’re right.
In this case, assuming immortals had perfect memories and would eventually work out that you didn’t, assuming you were an immortal who can’t remember if you’ve played that particular opponent before (But can vaguely remember an idea of how often you get defected on vs. co-operated with by the entire field) what do you think your optimal strategy would be?
It’s pretty complicated! I think you’d need to write down equations to figure it out properly and it would be very non-trivial. That said, assuming there’s only games and no communication, you probably want to start off cooperating or randomising between cooperation and defection (depending on pay-offs), and then shift to more and more defection over time until you always defect in the end. Meanwhile, the immortals with memories would probably want to start off mostly cooperating but sometimes defecting to figure out who, if anyone, doesn’t have memories. (Disclaimer: while this sounds like a plausible set of equilibrium strategies, there may be more complicated equilibria that I didn’t think of or some other weird cases.)