Without changing "the official rules" of the game, what sorts of house rules can be imposed on player interaction to speed up game-play for games that generally encourage players to discuss options (in cooperative games) or cut deals with each other (in competitive games).
For instance, I imagine adding a rule to some board games which makes secret deals more difficult that says "once per turn, you may pass a note to someone else at the table. Otherwise you can't discuss anything in secret." To make it more interesting, one might even add a die roll:
1 <- Throw away the note 2-5 <- Successful pass 6 <- Reveal the note for everyone else at the table to see
But I imagine such a rule might backfire and slow down the game even more; especially if people start trying to come up with systems to encrypt their notes.
Although my friends would probably tell you that this is a lie and that I'm usually the worst offender, I'm not thrilled with sacrificing game-pace for the sake of over-analyzing.
EXPLANATION: This question is meant to be general, but the Game of Thrones board-game was the particular example I had in mind. I played this game with a group which had added the (IMHO awful) house rule that anyone may look at anyone else's house cards still in hand. Supposedly this rule was added to keep people from writing down which cards everyone else had played already and to minimize the advantage more experienced players have. What it did was ensure that everyone spent time analyzing all possible outcomes of each battle before the battle is even fought. Unsurprisingly, the same group had to also add a house rule that the game only lasts 5 turns rather than 10.