OK, here's another violent game I remember playing around the same age (13-16 yrs). I think it was based on the innocent little kids' game called "A Tisket, A Tasket". We played this in boy scouts, with the supervision and approval of the adults Scoutmaster, I might add.
In this game, everyone stood in a circle facing inward, with hands behind their backs. The scoutmaster selected someone from the ring, and placed a belt in his hands. This person, the Belter I suppose he'd be called, prowled slowly around the outside of the ring, until he would suddenly place the belt in your hands. He would then run around the circle counter-clockwise while you chased him, beating the hell out of him with the belt. You kept this up until he reached the space you had vacated, at which point you became the belter.
I tried to onlygive the belt to kids who had asthma or were very small, etc, however I can remember Steve Klinglesmith who was about 5 ft 10 and weighed 180 or so, stepping back to wrestle the belt from my grasp, and then me having to run like I had the Devil behind me around the circle.