Sos I had this idea - a comedic element of a game in which that awareness is explicit.
Imagine, if you will, a Special Missions style game where the contemporary PCs go off to do heroic things (however they do heroic things: maybe they're Mission Impossible conmen, maybe they're gunslingers with hearts of gold, whatever) under some vague authority from somewhere which means most of their missions are handed down to them, with the handler of the week coming along to advise. Nice episodic bit with a rotating NPC providing a key information and secondary skills as a GM mouthpiece who has a limited ability to keep them inside the campaign's predetermined strategies.
In about 1/4 to 1/3 of the missions that delivery comes from a 'cast and shot to be immediately distrusted' member of a parallel agency - maybe it's the CIA if they're under the aegis of the FBI, again, whatever - who the players know from word one is playing them for suckers. So the straightforward mission is now complicated by a) figuring out what the morally/strategically correct solution to the mission they're being used as patsies for is and b) finding a way to isolate/ remove/ mock their temporary handler in a suitably comedic fashion. They can't just kill him of course - he is ostensibly a good guy and they'd get into a lot of trouble for putting two into the back of his head. So they need to do something else, like...
... tricking him into boarding a plane heading for Tahiti, removing him from the action for days and leaving him to explain it on his expense report.
... seducing him and leaving him handcuffed and somewhere out of the action, with the hotel staff being told that he's on a drug purge and they should just keep leaving him kiwi juice till he dries out.
... drugging him and having him wake up in the middle of a civil war reenactment battlefield (or somewhere else equally ridiculous).
... forging orders that make MPs hustle him off onto a plane heading for a Penguin Research station just north of McMurdo
... drop breadcrumbs that lead him into the middle of a high special effects movie shoot (or NERO style LARP).
Each time this guy shows up the players know that a) they have to spend resources getting him out of the way and b) they should let the lesser angels of their nature run wild.
Just a thought