However, the Capitol is responsible for creating and managing the Hunger Games. There is a Gamemaker, a person who is in charge of the actual game, deciding on the rules, obstacles, and the general direction of the Games.
While the Gamemaker is in charge of the execution of the Games, the true power behind them lies with the President of Panem (in the books, President Snow, and in the movies, President Coriolanus Snow), who ultimately calls the shots and sets the overall tone of the event.
So, while there isn't one specific "lead game maker," the responsibility for the Hunger Games lies with the Capitol as a whole, with the Gamemaker as the direct overseer and the President of Panem pulling the strings behind the scenes.