A Google scholar search of the words "video game" AND "violence" shows at least two literature reviews, which gather and asses the state of knowledge on video games' potential effects on behavior. You'll want to locate and read the cited articles on your own, though, to determine how the relationship is assessed, how carefully the data were gathered, what controls were used, how carefully the authors tested for spurious evidence, etc.
If you have access to a university library with a good publication database and periodical section, try a keyword search for "video games," "behavior," "violence," "adolescents" (since a common theme among media scaremongering seems to be deleterious effects of videogames among the oh-so-impressionable youth), and others, and see where that takes you. Periodicals staff can also be quite useful, if asked. Shoot for psychology or developmental health publications, if you can (though certainly not exclusively), and remember to check the references section of any reports you find, if the authors cite any previous research; no sense in ignoring good research, and a thorough reading of early studies will help you build a robust literature review of your own. Remember, even if an article posits a relationship between gaming and violence, you'll want to asses the strength of that relationship, since scientists are not above half-assed research.
Good luck. Now I wish I were doing this, myself.
