Lathany

You're welcome! There's a short story by Robert Sheckley, which title I can't remember (although the_original1 says he can find it quickly) that's very similar to the book The Running Man. It's a guy who goes on a game show to win a plot of land outside the extremely overcrowded city, and he has to escape the city in so many days. To compare it to a movie, I'd say it's more like Escape from New York than The Running Man!