The arguments on the "No" side (which many of them are probably submitted by the same person) are pretty much saying that every single child can't filter reality from fiction. A big speculative pessimistic aspect of video games is how much they influence young children and their behavior, but I believe that this all dependent on who's playing it, we can take GTA 5 for an example, GTA 5 has had ≈33.8 people play its multiplayer mode in one point or another, and this number is massive compared to the people who have played GTA 5's single player and/or multiplayer mode and thought and done something abnormally violent, just due to playing GTA 5 (not taking in account to those that have some sort of mental instability issue). So in short, I would say for children, just as long there is a significant amount of supervision, and it's ensured that they understand that games are fiction, and reality is reality, these kind of video games are okay.
Children are susceptible to violent messages in the world around them, causing negative and long-term mental distress that lasts a lifetime. It is essential that parents take steps to block their young children from seeing violent images or engaging in these kinds of activities in games. Many video games demand some kind of aggression to complete tasks, so parents must be careful to offer context to children so they do not incubate warped perceptions of reality.
Gratuitous violence should not be promoted to children through any medium. While video games can be beneficial to children, it is important that they be permitted to play only age appropriate video games. Being exposed to violence from a young age only accelerates the de-sensitization process that happens as a result of over exposure to violence.
When they are young, children are still in the process of developing morals. Many emulate what they see. If a parent says that it is appropriate for a child to play a violent video game, there is a chance that the child may think that it is okay to use violence in real life.
Violent video games have ratings on them that suggest they only be played by mature audiences, such as older teenagers and adults. While some children are able to play or watch these games without being affected by the violence, many more are unable to understand that the extreme violence, language and themes are not appropriate for every day life.
Violent video games as well as violent movies teach children that it is okay to act with violence in society. Even some criminals such as the Aurora, Colorado shooter who have gone on rampages in recent years have felt like the shootings were a game to them. Children need to be taught the value of human life.
Violent video games make violent acts like murder, robbery, and assault seem ordinary. In some cases, they make these actions seem like appropriate responses to situations. Instead of viewing violence with the proper shock, children get used to violence. This doesn't necessarily mean that they will go out and commit their own violent acts, but it does make them more ambivalent to a violent culture and less likely to try to change it.
People of all ages, especially children, are strongly influenced by the games they play and the programs they watch. Studies have proven that children who are exposed to violence may try to imitate the violent behavior that they see, may become immune to violent behavior and view it as normal, and may become generally more aggressive. Because these are not good qualities for children to possess, violent video games are not appropriate for children.
Violent video games are harmful to children. This issue has been studied by child psychology experts, and parents have been warned repeatedly that violence tends to foster violence. Even participating in virtual violence through a video game encourages a child to act out in real life. For children, the line between real and virtual is very thin and easy to cross.