You bringing in the "three strikes rule", I'm reminded of game theory.

They have the famous (repeat) prisoner's game, where two parties decide to either collaborate or to screw the other party. People ran software simulations of various strategies, and the winner is: Tit for tat. In other words, you start positive (invite), and stay like that until the other person screws you. They you screw them once next time and turn collaborative again immediately after (no hard feelings).

I'm not advocating you play the prisoner's game on people, but it's interesting that people worked formally on something relating to this.