Final Lecture. Cheating, Detection, Punishment, and Forgiveness in Repeated Games. The Stage Game. Prisoners’ dilemma structure applies in many situations Lovers or roommates Colluding oligopolists Arms control agreements Common-pool resources Cooperating vampire bats …many more.
and if the probability d of playing again is not too small.
So your discounted payoff from playing always defect is
In general, cooperation can be sustained only if the probability of getting caught is large enough and the temptation T is small enough.
Suppose each bat shares when he has a good day and the other is needy, so as long as the other has always shared when the reverse is true—If ever the other had a good day and didn’t share when you had a bad day, you will never share with him.
If not always regular and proper.