If Machiavelli was around to see The Hunger Games, I think he would agree with some of the actions President Snow took in the movie. Machiavelli argued that if the choice came down to being feared or loved, it is better to be feared. His reasoning was "fear preserves you by a dread of punishment, which never fails". He basically is saying that the fear of punishment keeps people from doing anything to upset the person they fear.
President Snow shows it's better to be feared by creating the Hunger Games. These games take a man and women (Tributes) from each of the twelve districts and have them fight it out to the death. These games are highly publicized as famous people serve as sponsors to help each of the tributes survive. They are also recorded for the public to see as the action is happening, like a T.V show! He explains at the Reaping video that there was a rebellion a long time ago and that was the reason for the creation of the Games. Now people are afraid of rebelling because they might get chosen for the Games.
Another aspect of The Hunger Games is the fact that the victors of each games get treated so well. According to The Hunger Games Wiki, victors get paid for life from the Capitol, receive special status in their own District, and living arraignments in the Victors Village. These prizes give each tribute a sense of hope, and President Snow says hope is very important in the purpose of the Games. "Why don't we just line up 24 people and execute them all at once, it'd be easier...hope is the only thing stronger than fear, but too much hope is dangerous". The conversation pictured is about how each tribute gives their District hope and that is another reason they don't rebel. In this case though, Katniss might be giving them too much hope.
Finally, Machiavelli stated hatred should be avoided because "he can endure very well being feared whilst not hated". In other words, people can still put up with you if you're feared. However, in this case being hated will only fuel a rebellion. An example is the riot in District 11 after Rue died. Those people hated the Capitol for forcing a little girl with practically no chance of winning to compete in the Games. So as a result, they started a riot that the Capitol ended shortly after.