The movie I was thinking of is "The Running Man," based on a Stephen King story (I believe written under a pen name).

Here are some excerpts from IMDb: http://www.imdb.com/title/tt0093894

The year is 2017. The world economy has collapsed. The United States has sealed off its borders and has become a military controlled police state which controls TV, movies, art, books, communication and censorship. In the police state America has become, criminals have a choice. They can serve their sentences in prison or they can take part in "The Running Man," a government-owned violent game-show where contestants running for freedom are pursued by "Stalkers" (bounty hunters). "The Running Man" is the top rating show on network TV....

.... With full control over the media, the government attempts to quell the nation's yearning for freedom by broadcasting a number of game shows on which convicted criminals fight for their lives.

~S~