The plot is similar to every genre. Someone is forced into participating in an activity that makes its own revenge.
The logic or aim of the SAW series seems to be that the antagonist (or protagonist depending on how you look at it) gets others to do vengeance for him. In most cases, he gives his pawns choices, knowing full well that their emotions force them to make the wrong choices.
The SAW series uses machines that causes violence on humans, but the logic, or the philosophy behind the plot can be used to create other situations that don't use nearly the amount of violence in the film, and can be applied to a wider audience. There are two examples that lightly touch on the idea however; the opportunity to use the pro/antagonist in a similar vein as SAW is wasted.
White Collar is a series about a white-collar criminal who is forced into doing right by the FBI. Burn Notice is a series about a secret intelligence agent working his way back into the good graces of his former employer, forced into a vocation of A-Team and MacGyver activities.
The key ingredient is the Pay-It-Forward. The succeeding victims continue to pay-it-forward. In other words, the survivors acquire a radical philosophy of teaching, and find someone who was wronged, but secretly manipulate them into paying the method forward.
A very bizarre concept indeed.
