Yes, while it might be tempting to say that the main conflict of The Hunger Games trilogy is character vs. character—Katniss vs. President Snow—but even after Snow's fall from power, Katniss has to continue to fight against societal tyranny. Would-be President Coin would be just as corrupt as former President Snow was. This is why Katniss shoots Coin when she is supposed to shoot Snow.
There is an element of character vs. self in these stories, too. Katniss struggles with who and what to prioritize in her life. Her mother and sister are her top priority, but after that, she struggles with herself—especially during the first games in which she participates: should she pretend to feel more for Peeta than she really does? Or should she allow herself to really feel something for Peeta despite Gale's expectations and the feelings she has for him? Which one should she pick? Gale has been her best friend for many years—he rescues her family when their district is bombed. Peeta, however, understands the way Katniss's mind has been affected by the games; it seems that they both have PTSD and can relate to one another's struggles with their past traumas. Katniss has a hard time pretending, even when it saves her and Peeta's lives, but she has a hard time making real choices as well.
The main conflict inThe Hunger Gamesis Man vs. Society. Katniss, who is picked to fight in the Hunger Games, wants to survive not because it is expected of her in society, but because she values her own life and wants to live and protect her family and friends. The Capitol wants Katniss to put on a good show, to kill the other children, and to use her as a tool to increase their power over their citizens.
By fighting against the Capitol and revealing them to be a petty force concerned only with superficial comfort, as well as lying to change the rules and force fatal conflicts inside the Hunger Games, Katniss fights against accepted socital opinion. Her actions spur a civil war, showing how the power of the individual can overcome even a massive government structure.
I agree with comment #1
The conflict in the hunger games is the capitol wants power and stability but the districts want freedom and independence. Also Snow wants revenge for Katniss dissobeying him.
There is both internal and external conflict within the Hunger Games with the main conflict on Man vs. Society because Katniss wants to go against the Capitol as she hates it but is conflicted because with President Snow watching over, her family could be in grave danger. Other conflicts can include her confusion of who she loves between Peeta and Gale as well as survival of the fittest.