@Icefractal: you nominally described five different forms of negation without mentioning which of them, if any, is supposed to cover two of the most common ones:

Player: "I choose X."
Game master: "By basic rules of game, X is not possible. Choose something else."

And:

Player 1: "I choose X."
Player 2: "I choose Y, which trumps X."

In the latter case, Player 2 may be a game master, but is drawing from the same pool of options their players are.