I don't think violent games and violent behavior are related. I read somewhere that even though violent media is more prevalent than ever right now, the number of violent crimes has actually decreased.
According to the Times, between 1994 and 2010 the number of violent crimes among youth offenders fell by more than half, to 224 crimes per population of 100,000. At the same time, sales of video games have more than doubled since 1996.
http://www.polygon.com/2013/2/13/39...es-coincide-with-drop-in-violent-youth-crimes
Take that for what's it worth. This isn't really something you can 'prove' though, as there are way too many variables at play. I don't believe the article I linked really proves anything, but I do agree that violent video games do not cause violence. Who knows, maybe it helps violence. Maybe there are kids out there who are psychologically damaged and want to do violent things, but end up just playing GTA for hours. I know that's bad for the child who has those problems, but I think we can all agree that we would MUCH rather have him play GTA, rather than act out his violent problems in real life.
If you think about it, though, there are millions of gamers who play games like GTA everyday. Only a handful of kids actually go out and act on the violence. If violent games were the cause of these violent crimes, we'd have a lot more violence these days.
For me, personally, I'm neutral when it comes to violent video games. As a kid, there weren't too many violent games, and I think I felt cool when I finally got to play some. I didn't enjoy being violent, it was just a taboo thing so, naturally, it felt cool to do. That wore off pretty quickly though. Now I don't really care either way. As long as a game is fun, I'll play it.