That's what made the “black comedy” role-playing game Paranoia so much fun:

> The player characters frequently receive mission instructions from the Computer that are
> incomprehensible, self-contradictory, or obviously fatal if adhered to, and side-missions
> which conflict the main mission. They are issued equipment that is uniformly dangerous,
> faulty or "experimental" (i.e. almost certainly dangerous and faulty). Additionally, each
> player character is generally an unregistered mutant and a secret society member, and has
> a hidden agenda separate from the group's goals, often involving stealing from or killing
> teammates. Thus, missions often turn into a comedy of errors, as everyone on the team seeks
> to double-cross everyone else while keeping their own secrets. The game's manual encourages
> suspicion between players, offering several tips on how to make the gameplay as paranoid as
> possible…