Two-player games -- especially in tournament play -- can lend themselves to quick-kill strategies or "degenerate" decks that would be easy to counter in a multi-player game. The following rules are official for two-player tournament games, and suggested for all play:

Play to no less than 12 groups.

Neither player may attack the other until each has taken a full turn; Player 2 can't jump instantly on Player 1.

Eliminate the "automatic takeover" phase. Except for the puppet that you start the game with, no group may be taken over without a die roll. To take over a Resource, spend your Illuminati token -- no more than one per turn.