A more efficient nuke would be to threaten to ensure the demise of the defector for this game, and the next. To avoid the spiral of hate going supercritical, you can also tell upfront (and in public) that any retaliation will not be met with further vengeance.
Alice: so, we don’t attack each other for the next 4 rounds.
Bob: okay
Alice: Oh, and if you break your promise, I swear I will do my best to make you lose this game, and the next
Bob: hey, it’s not cool! If you mess up with me on the next game, I will mess up with you on the second next!
Alice: retaliate if you will. I will play normally anyway.
Bob: Wait, you will not seek further revenge?
Alice: Of course not. What would be the point? I don’t want to lose every time, and so don’t you.
So, what are the expectations here? Let’s assume 6 players, with a base expectation of winning of 1⁄6. If Bob breaks the alliance for certain victory, we have Bob 1, Alice 0, Others 0. Then Alice follows through on her threat. Bob, 1, Alice 0, others 1⁄4. Then Bob retaliates. Bob 1, Alice 0, others 1⁄2. And then we play normally. It wouldn’t be wise of Bob to break the alliance for anything less than certain victory, because Alice would likely ensure his demise, leading to an eventual score of Bob 0, Alice 0, others 3⁄4.
Now this could go further, and kill the fun of the game. But I have reasons to believe it may not:
Alice’s promises makes Bob’s retaliation pointless. Not only will it not piss off Alice, but the retaliation will also cost Bob another game. Bob will be aware of this, and may think about it for two seconds.
The other players will be aware of the fight. They won’t be surprised to see Bob and Alice fight each other, and the game won’t be rigged.
Now, making oneself the enemy of the defector for one game and a half may be too much anyway. Just promising to refuse any further alliance for this game and the next may have the desired effect, without some of the nasty consequences.
A more efficient nuke would be to threaten to ensure the demise of the defector for this game, and the next. To avoid the spiral of hate going supercritical, you can also tell upfront (and in public) that any retaliation will not be met with further vengeance.
So, what are the expectations here? Let’s assume 6 players, with a base expectation of winning of 1⁄6. If Bob breaks the alliance for certain victory, we have Bob 1, Alice 0, Others 0. Then Alice follows through on her threat. Bob, 1, Alice 0, others 1⁄4. Then Bob retaliates. Bob 1, Alice 0, others 1⁄2. And then we play normally. It wouldn’t be wise of Bob to break the alliance for anything less than certain victory, because Alice would likely ensure his demise, leading to an eventual score of Bob 0, Alice 0, others 3⁄4.
Now this could go further, and kill the fun of the game. But I have reasons to believe it may not:
Alice’s promises makes Bob’s retaliation pointless. Not only will it not piss off Alice, but the retaliation will also cost Bob another game. Bob will be aware of this, and may think about it for two seconds.
The other players will be aware of the fight. They won’t be surprised to see Bob and Alice fight each other, and the game won’t be rigged.
Now, making oneself the enemy of the defector for one game and a half may be too much anyway. Just promising to refuse any further alliance for this game and the next may have the desired effect, without some of the nasty consequences.