There is no conclusive evidence on the effects of violent video games on children, so the decision of whether to allow them to play is the parents' decision. Violent games, along with other forms of entertainment, have long been scapegoated for their role in influencing people to commit violent acts.
First-person shooter games such as the "Call of Duty" franchise are under the heaviest fire. These games allow players to step into the role of a soldier and gun down hordes of enemies. More realistic graphics on modern systems can make the violence look real, but it is not.
In January 2013 in the wake of the Sandy Hook shooting, President Obama asked Congress to budget $10 million to fund such studies. To date, studies into the effects of violent games on children have not produced any conclusive data; that is, some show a link, others do not, and there is no consensus about the cause-and-effect.
When it comes to deciding whether or not to let children play violent games, it depends on how old and mentally developed the child is, previous aggressive tendencies and the ability of parents to watch and supervise gameplay to provide guidance. It's wise to pay attention to the ratings on the covers of games: if a game is rated M, it is deemed unsuitable for children under 17.