Friend Citizen, are you happy? Are you questioning a well run Alpha Complex staffed by a computer who is honest, fair, and doesn't choose fault randomly? Are you questioning an Alpha Complex not infested with secret societies manipulating Friend Computer to their own, treasonous, aims?
You should be shot! Wait, wait, are you telling Friend Computer that your fellow troubleshooter is a mutant mind-controlling traitor who told you to say that? Ok. Cleanup in Aisle 4, please.
First, you said something rather telling in your question, Friend Citizen who is not on their next clone:
At this point, the other players only felt reason to betray me, and were discussing the idea out loud, with me in the room.
One of the most critical guidelines promulgated to ultraviolet clearance citizens is:
There shall be no out of character conversations. Anything said at the able is said, or done, by the characters.
Clearly, treasonous talk is treasonous, and should be reported to friend computer to better our wonderful Alpha Complex.
It so good to hear that your fellow troubleshooters are so trusting as to share their treasonous plans with you. Please report them to IntSec immediately, friend citizen. Remember, in our utopia, planned in the impregnable bunker that we call Alpha Complex, nothing can possibly go wrong. Anything which does go wrong is clearly the fault of a communist, mutant, or traitor. These are grave crimes, citizen, and Friend Computer must punish those responsible. Friend Computer, in its infinite wisdom, has delegated some (small) measures of authority to the various departments and working groups. If it didn't why... the communists would win! You're not suggesti...
Cleanup in Aisle 1, please.
We regret to inform you that your previous clone was clearly infected with some sort of communist virus. Thank you for your participation. Have three loyalty points.
A good game of Paranoia hinges on the computer being... itself. If players aren't given opportunities for betrayal and finger pointing, if things don't go wrong for no reason... they might cooperate. FNORD! This is unacceptable. The nature of the computer depends on the style of game, Zap, Classic, or Straight... but the cardinal rule is that the computer always wins, the computer is always right, and the computer is way way too insane and busy to actually be running Alpha Complex. You cannot pull this off without friend computer, but the way to encourage betrayal is to be subtle. Don't tip your hand if you don't have to. You are loyal, any skullduggery must be done in secret. Try to control the recording device. There must always be a scapegoat in debrief, and if you can demonstrate that the corpses of your comrades... the corpses of your fellow troubleshooters were at fault, then you will be commended. The way to get your troubleshooters to betray you is to be the most effective bastard. But it does require an effectively run game with enough fear, uncertainty, and doubt to make betrayal... profitable, товарищ. Use their unthinking loyalty to advantage, and advance through the ranks on their adequately blamed corpses until you can finally subvert alpha complex... for the workers!