How did Robertson influenced it?
I see Robertson's interest in John Jane existing and remaining inside the loop, and talking him into remaining on it.
But how exactly he influenced it?
As I see, we have here a looping paradox. John Jane is his own both father and mother, and also he steals himself from maternity hospital and takes to orphanage.
It was always John Jane's actions and he was always free to make choices. Robertson just provided the time machine and talked him into doing it, but never forced him to do anything or stopped him from taking some action.
Also, I know this question is dumb, but how did it started? John Jane is in loop, but doesn't have a begining. How can somebody that starts not existing be his own father/mother?
Yes, I know this movie is a joke, exacerbating this idea. It's possible for a guy to have a dauther with some random girl, then date his dauther and have a son. He'll be both his father and grandfather, and she will be both his mother and sister.
Then take this idea, take the bastard son and send him back in time, and make him be the first guy that has the dauther. He'll be the father and grandfather of himself.
The movie takes this idea and makes the same person be his father, mother, lover, and also the person that takes the actions of making that all possible.
The question is, where's Robertson is all this??