Opening it up is NOT a good solution. I mean, the Hungry Games is supposed to be this grand thing! Having it open would demolish that, while at the same time seeing the same people game after game gets dull. We need to have some kind of "time out", like in Stars. Say, if you get 30th-21st, you must wait two more games to join. Then 20th-11th is three games, 10-th-5th is four games, 4th-2nd is five games, and 1st is six games.
Also, I think more sponsor spots would be nice. Like, five the first day costing what they do now. Day two costs are the same, but 5T$ more on each. Day three is 5T$ more from day two and so on. Though, these numbers can change. This would make it more interactive for mentors and for sponsors, because honestly people stop watching after the first day.