The first two books to me have a strange ending, I would change the first book with Katniss going home and enjoying her winnings, with a hint about her relationship with Peeta. The second book I would have ended it with the arena being destroyed.
Then started the last book with her rescue. For me the last book does not work as it follows this formula, which it has already over the first two books:
Readers are introduced to the hero’s world. A “call to adventure” or a disturbance interrupts the hero’s world. The hero may ignore the call or the disturbance. The hero “crosses the threshold” into a dark world. A mentor may appear to teach the hero. Various encounters occur with forces of darkness. The hero has a dark moment within themselves that they must overcome in order to continue. A talisman aids in battle (e.g., the shield of Athena for Perseus; the sword, Excalibur, for King Arthur). The final battle is fought. The hero returns to their own world
I would completely change the last book and have Katniss end up the leader, showing that Coin was corrupt and there was a plot to remove Coin.
P.s. I would also have it that the people in the games do not really die, that using advance technology keeps them alive but in captivity, to be rescued at the end.