Answer and Explanation:
How are the Games used to maintain control over the districts?
The Hunger Games are a display of power. The Capitol established the Games after the districts attempted a rebellion. Now, people from each district are forced to compete and fight to death. By doing this, the Capitol makes it clear that it has the power to kill, if it wishes. So much so that people would rather risk having their own kids' names drawn to the deadly Games than fighting for freedom. It is as if they think it is better to lose one or two with a certain frequency than battling and losing thousands of lives at once, not seeing that such a sacrificial ritual will never lead to change.
Conversely, how are the Games used to keep the Capitol happy and content?
The Games keep the people in the Capitol entertained. While people in the districts barely survive each day, in the Capitol they have too much of everything. Not having to starve, hunt, work, fight to live, they become easily bored. This cruel, barbaric display of violence is, therefore, a lot of fun for them.