We don’t know for sure, even though the question is important for education and parenting. Many studies show that kids who regularly play violent games show more savage behaviour, but this is only a correlation and not a cause. It could be that aggressive children prefer violent games, not that the games caused their aggression.
In some studies, the victor of a video game has been given the opportunity to punish their opponent by blasting them with noise, for example. It has been found that winners of violent games are more likely to punish their opponent than winners of non-violent games. Violent games with a positive goal, such as saving others from virtual zombies, seem to have less negative impact.
Other research shows that losing the game or finding the controls frustrating is what leads to violence, not the content of the actual game itself. We might note that US sales of violent video games have steadily increased since the mid 1990s, while violent crime has declined – especially among juveniles.