Stephen King's the running man would make a perfect game....
in the book an unemployed father goes to the games network to compete for money and gets on the game show the running man. You get $100 for every hour you remain free and are given $4800 and a 48 hour head start. You can go anywhere in the continental US, but any law enforcement can apprehend you, as well as the show's 'hunters', who try to track you down.
There are two catches:
1. Any viewer who watches the show and spots you can report it to the network and win cash, so almost everyone is against you.
2. You must send in two tape recordings of yourself to the studio daily for the evening broadcast. The game studio 'claims' that they don't trace your postmark, but we all know that's a lie

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It could play out Assassin's Creed style, though the emphasis would be on hiding, changing your identity, moving from location to location, not drawing attention to yourself. Though many gamers could try the guns blazing route and see how far that gets them. If it were an online game you could have gamers take on the role of the hunters.