If you have an imperfect memory and you think they don’t, wouldn’t you want to pre-commit to attempting co-operation with any immortal entities you face, given they are very likely to remember you, even if you don’t remember them? This is of course assuming that most or all other immortal entities you’re likely to face in the Dilemma do in fact have perfect memories.
If you can’t remember, and they can work that out, then they can defect on you every time and get more points, at no penalty other than making you less and less optimistic about cooperation with rarely-encountered entities.
That could eventually cut into their profits, but it becomes a tragedy of the commons, with you being the commons.
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.)
Or if you have an imperfect memory and you think they don’t...
If you have an imperfect memory and you think they don’t, wouldn’t you want to pre-commit to attempting co-operation with any immortal entities you face, given they are very likely to remember you, even if you don’t remember them? This is of course assuming that most or all other immortal entities you’re likely to face in the Dilemma do in fact have perfect memories.
If you can’t remember, and they can work that out, then they can defect on you every time and get more points, at no penalty other than making you less and less optimistic about cooperation with rarely-encountered entities.
That could eventually cut into their profits, but it becomes a tragedy of the commons, with you being the commons.
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.)