@Molfo But the "last player rotates sectors" option is extremely flawed too, because it only works when the last player acts in an optimal manner. If the last player somehow favors the player who picked the best faction anyway, player 2 and 3 are left in the dust through no fault of their own.
I think a good solution to the auction problem is already in this thread - the post by AntoineBR. It is an improved version of my initial idea.