If you want numbers you need to define the problem more precisely.
The ground is well-trodden for humans the lives of which do not usually consist solely of playing PD with each other.
For PD tournaments there is no agreement on the optimal strategy in general (or, rather, it depends on what do your opponents do). If you want to see how changing the expected length of the game affects a particular strategy, you need to specify that particular strategy first.
You’re describing the Unexpected Hanging paradox.
Also , the idea that the concept of afterlife leads to more responsible behavior in this life is a very well-trodden ground.
Re well-trodden ground: Well, yes, but as far as I can find, mainly in a vague, emperical, qualitative way. I’m looking for the /numbers/.
If you want numbers you need to define the problem more precisely.
The ground is well-trodden for humans the lives of which do not usually consist solely of playing PD with each other.
For PD tournaments there is no agreement on the optimal strategy in general (or, rather, it depends on what do your opponents do). If you want to see how changing the expected length of the game affects a particular strategy, you need to specify that particular strategy first.