The only real similarity between Hunger Games and Running Man is that they both center around a "game show" or death. That's where the similarities cease. Running Man isn't even the same type of setup. Hunger Games pits innocents kids against innocent kids and forces them to fight. Running Man more puts one man in a gauntlet against hired mercenaries to survive. In other words, Running Man only has contestant-vs-mercenaries. Hunger Games is contestants-vs-contestants.

It (Hunger Games) could probably be more closely compared to Battle Royale. That one has children facing off against each other to fight for survival and to be the last one standing as each are forced to fight against one another. But even then, Hunger Games only shares the same basic story with Battle Royale. They deal with different themes and tones, etc.

And honestly, none of the three mentioned are original, in that this basic plot is one that goes all the way back to Roman times and the Colosseum. This is just the Colosseum and gladiator fights reinvented.